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Three likelihood-based methods for mean and covariance structure analysis with nonnormal missing data

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Abstract

Sure, and longitudinal studies in the social and behavioral sciences generally contain missing data. Mean and covariance structure models play an important role in analyzing such data. Two promising methods for dealing with missing data are a direct I,maximum-likelihood and a two-stage approach based on the unstructured mean and covariance estimates obtained by the EM-algorithm. Typical assumptions under these two methods are ignorable nonresponse and normality of data. However, data sets in social and behavioral sciences are seldom normal. and experience with these procedures indicates that normal theory based methods for nonnormal data very often lead to incorrect model evaluations. By dropping the normal distribution assumption, we develop more accurate procedures for model inference. Based on the theory of generalized estimating equations, a way to obtain consistent standard errors of the two-stage estimates is given. The asymptotic efficiencies of different estimators are compared under various assumptions. Ne also propose a minimum chi-square approach and show that the estimator obtained by this approach is asymptotically at least as efficient as the two likelihood-based estimators for either normal or nonnormal darn. The major contribution of this paper is that for each estimator, we give a test statistic whose asymptotic distribution is chi-square as long as the underlying sampling distribution enjoys finite fourth-order moments. Ne also give a characterization for each of the two likelihood ratio rest statistics,when the underlying distribution is nonnormal. Modifications to the likelihood ratio statistics are also Riven. Our working assumption is that the missing data mechanism is missing comptetely at random. examples and Monte Carlo studies indicate that, for commonly encountered nonnormal distributions, the procedures developed in this paper are quite reliable even for samples with missing data that ar-e missing at random.

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... Other techniques include available-case procedures, weighting procedures and imputation-based procedures [7]. The latter is discussed further here, since imputation methods can be applied to the MCAR and MAR cases [8]. ...
... Furthermore, such techniques may result in standard errors and bias on results. Model-based approaches include regression-based techniques, Expectation Maximization [9] and Multiple Imputation [8]. Neural network based approaches have been successfully implemented a number of times [1], [9], [10]. ...
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This paper presents an impact assessment for the imputation of missing data. The data set used is HIV Seroprevalence data from an antenatal clinic study survey performed in 2001. Data imputation is performed through five methods: Random Forests, Autoassociative Neural Networks with Genetic Algorithms, Autoassociative Neuro-Fuzzy configurations, and two Random Forest and Neural Network based hybrids. Results indicate that Random Forests are superior in imputing missing data in terms both of accuracy and of computation time, with accuracy increases of up to 32% on average for certain variables when compared with autoassociative networks. While the hybrid systems have significant promise, they are hindered by their Neural Network components. The imputed data is used to test for impact in three ways: through statistical analysis, HIV status classification and through probability prediction with Logistic Regression. Results indicate that these methods are fairly immune to imputed data, and that the impact is not highly significant, with linear correlations of 96% between HIV probability prediction and a set of two imputed variables using the logistic regression analysis.
... Standard ML estimates assume the distribution of variables are multivariate normal. Data that departs substantially from multivariate normality requires the use of robust ML estimators, the most common of which are MLM (Satorra-Bentler scaled χ 2 ) and MLR (Yuan-Bentler T2* test statistic) (Satorra and Bentler, 1994;Yuan and Bentler, 2000). MLR has the added ability to estimate models that violate the assumption of multivariate normality and include missing data (Brown, 2015). ...
... We found insufficient evidence to reject the assumption of MCAR or MAR (p = 0.59). Given our data can be assumed MCAR or MAR, we used the full information ML method to handle missing data, and we estimated the measurement model using the robust MLR estimator (Yuan and Bentler, 2000). ...
... We decomposed the observed structure into three components: grand means, between-person components, and within-person components. Since the data were nonnormally distributed, we used the "MLR" estimator in the lavaan function to obtain robust standard errors (Yuan & Bentler, 2000), as well as a full information maximum likelihood (FIML) for handling missing data (Lee & Shi, 2021). Model goodness-of-fit was achieved if the Comparative Fit Index (CFI) and ...
... the Tucker-Lewis Index (TLI) were greater than 0.90 and the root mean squared error of approximation (RMSEA) was lower than 0.06 (Yuan & Bentler, 2000). ...
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Background Alcohol, the most consumed drug in the United States, is associated with various psychological disorders and abnormal personality traits. Despite extensive research on adolescent alcohol consumption, the impact of early alcohol sipping patterns on changes in personality and mental health over time remains unclear. There is also limited information on the latent trajectory of early alcohol sipping, beginning as young as 9–10 years old. The dorsal anterior cingulate cortex (dACC) is crucial for cognitive control and response inhibition. However, the role of the dACC remains unclear in the relationship between early alcohol sipping and mental health outcomes and personality traits over time. Methods Utilizing the large data from the Adolescent Brain Cognitive Development study (N = 11,686, 52% males, 52% white, mean [SD] age 119 [7.5] months, 9807 unique families, 22 sites), we aim to comprehensively examine the longitudinal impact of early alcohol sipping patterns on psychopathological measures and personality traits in adolescents, filling crucial gaps in the literature. Results We identified three latent alcohol sipping groups, each demonstrating distinct personality traits and depression score trajectories. Bilateral dACC activation during the stop‐signal task moderated the effect of early alcohol sipping on personality and depression over time. Additionally, bidirectional effects were observed between alcohol sipping and personality traits. Conclusions This study provides insights into the impact of early alcohol consumption on adolescent development. The key finding of our analysis is that poor response inhibition at baseline, along with increased alcohol sipping behaviors may accelerate the changes in personality traits and depression scores over time as individuals transition from childhood into adolescence.
... All measurement and structural models were fitted using the lavaan package (Rosseel, 2012) in R (R Core Team, 2022). As seen in Figure 2.2, the responses to the indicators of travel satisfaction were not normally distributed (negatively skew with positive means); thus, a robust variant of the maximum likelihood estimator developed by Yuan and Bentler (2000) called maximum likelihood estimation with robust standard errors and a Satorra-Bentler scaled test statistics (MLM) was used for estimating measurement and structural models. ...
... Figure 3.2, the responses to outcome variables (destination satisfaction and revisit intention) and indicators of the latent factor (travel satisfaction) were not normally distributed (negatively skew with positive means); thus, a robust variant of the maximum likelihood estimator developed byYuan and Bentler (2000) called maximum likelihood estimation with robust standard errors and a Satorra-Bentler scaled test statistics (MLM) was used for estimating measurement and structural models.3.5 Results and discussions 3.5.1 Confirmatory factor analysis results: measurement structure of travel satisfaction The measurement structure of travel satisfaction was defined from nine scale items assessing travel experience using CFA. Travel satisfaction, being a domain of overall life satisfaction and wellbeing, is believed to be composed of three dimensions: the first two dimensionspositive deactivation (PD) and positive activation (PA)are related to the affective experience of travel whereas the third dimension refers to cognitive evaluation (CE) of travel. ...
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The study of long-distance travel has received minimal attention in the travel behavior literature, despite its significant contribution to overall vehicle miles traveled and vehicular emissions. Therefore, this dissertation investigates current travel behavior and anticipated changes that could be brought about by autonomous vehicles (AVs) in the case of long-distance recreational travel. This dissertation has four research objectives: (i) developing a reliable scale to measure long-distance recreational travel satisfaction and identifying the commonality and differences between long-distance and short-distance travel satisfaction, (ii) interconnecting travel behavior and tourism literature by establishing a link between travel satisfaction and tourism satisfaction, (iii) anticipating the acceptance and use of AVs for long-distance recreational travel and understanding the factors affecting such behavior, and (iv) quantifying the impact of vehicle automation, onboard environment, and in-vehicle time use on the choice of AVs and the value of travel time (VOTT) associated. The primary data collection is done through a survey of 696 visitors to the national parks in the US, and several analyses are conducted to address the four research objectives. The first contribution of this dissertation is the modification of the satisfaction with travel scale in the context of long-distance recreational travel, offering the conceptual strength and the generalizability of the scale. In addition, several differences in long-distance travel behaviors are also revealed compared to commute behaviors, mainly related to the impacts of age, income, and travel duration on travel satisfaction. Second, by establishing the relationships between travel satisfaction and tourism attributes, this dissertation strongly suggests revising the theories adopted in understanding tourists’ behaviors by incorporating the travel satisfaction component. This result also offers a managerial implication that the tourism destination management effort also needs to monitor on the tourist experiences on the way between home and destination to improve tourist attractions. Third, the structural model results indicate that the frequency and length of long-distance recreational trips will likely be higher in the AV era. This brings the attention of tourism destination managers not only to manage the tourists’ demand at destinations but also to manage the traffic on the roads leading to the tourism destinations. The potential increase in travel demand is linked to the increased potential of in-vehicle activities in AVs. Lastly, the VOTT of human-driven vehicles, autonomous vehicles, and autonomous vehicles with work and leisure interiors are estimated to be 34.70, 31.00, and $30.30 per hour, respectively. Based on the analysis results, it is concluded that vehicle automation will likely benefit individuals by enabling more productive use of travel time, but it could exacerbate the problem of increasing car sizes leading to higher energy consumption and space requirements, necessitating consideration of these negative aspects for the sustainability of the transportation system. Finally, this dissertation identifies the consideration of energy consumption and emissions, the effects of vehicle electrification along with automation, and changes that could be brought by teleworking in long-distance travel behavior and patterns as future research avenues.
... We controlled the group-level effects (nesting of players within teams) through the correction of standard errors of the parameters using the Mplus COMPLEX instruction (Muthén & Muthén, 2019). The robust maximum likelihood (MLR) estimator was used, as it offers higher greater robustness for non-normal observations and can handle missing random data (Yuan & Bentler, 2000). Moreover, the model was tested using the "Bootstrap or bootstrapping method" with 95% bias correction (MacKinnon et al., 2004) to perform a more comprehensive analysis of the hypothesized model. ...
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The present study aimed to analyze the relationship of transformational coach leadership with team identification and group cohesion, and its subsequent positive outcomes. Also, to examine the role of team identification and group cohesion in explaining the impact of the coach’s transformational leadership on perceived team performance and intention to return. Adopting a longitudinal design, a total of 260 male soccer players aged between 13 and 18 years (M = 15.84, SD = 1.30) participated in the study, completing measures at the middle and end of the season (two months apart). The Structural Equation Modeling (SEM) showed that: (1) transformational leadership was positively related to team identification and task cohesion; (2) team identification was positively associated to social and task cohesion, and intention to return; (3) only task cohesion showed a significant and positive relationship with intention to return and perceived team performance; (4) team identification positively mediated the relationship between transformational coach leadership and social and task cohesion, and intention to return; and (5) only task cohesion acted as a positive mediator between the transformational coach leadership and intention to return, and perceived team performance. Therefore, results suggest that transformational coach leadership is an important variable to consider with youth players in order to achieve individual and team positive consequences in the team sports context.
... By computing standard errors using a sandwich estimator, the MLR framework enhances the stability of results against violations of standard statistical assumptions [99]. Given our need to test interactions with a continuous moderator (gender affirmation) and binary variables, and to model the correlation structure within our binary data accurately, MLR is the preferred method of analysis within Mplus [102]. ...
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Transgender and gender-expansive young people, ages 13–24 years, experience disproportionate HIV risk yet are among those with the lowest US PrEP uptake rates (< 10%). Factors influencing PrEP outcomes for this population are poorly understood. This study examines the effects of gender minority stressors, gender affirmation, and heavy substance use on their PrEP outcomes using data from the CDC’s 2018 START study (N = 972). A conceptual model integrating the gender minority stress and gender affirmation models was developed, mapping relevant START items onto it. Structural equation modeling (Mplus-8.9) was used to examine factors related to their PrEP intentions. Most participants were 18–24 (68%), trans-female (46%), white (45%), and reported heavy substance use (40%). Medical discrimination increased internalized transphobia (b = 0.097, SE = 0.034, p = 0.005) and perceived stigma (b = 0.087, SE = 0.034, p = 0.010). Family rejection increased perceived stigma (b = 0.181, SE = 0.032, p < 0.001) and heavy substance use (b = 0.260, SE = 0.053, p < 0.001). Perceived stigma also increased heavy substance use (b = 0.106, SE = 0.037, p = 0.004). Perceived stigma (b=-0.085, SE = 0.027, p = 0.002) and heavy substance use (b=-0.161, SE = 0.031, p < 0.001) decreased PrEP intentions, while gender affirmation increased them (b = 0.045, SE = 0.019, p = 0.020). A 1-point increase in gender affirmation reduced heavy substance use risk by -0.179 (SE = 0.030, p < 0.001) in the presence of family rejection and by -0.074 (SE = 0.041, p = 0.074) when perceived stigma was present. This study underscores heavy substance use as a potential barrier to PrEP uptake for transgender/gender-expansive youth. Future research could explore how gender affirmation acts as a protective factor against the negative impact of family rejection and perceived stigma on heavy substance behaviors among these populations.
... Naturally, choosing the most appropriate distribution to represent the data is vital for drawing accurate predictions. See the various discussions in Broadwater andChellappa (2010), Pham Ngoc et al. (2023), Yuan and Bentler (2000), Wieser et al. (2020) and Adiatma et al. (2021). The proposed ESML distribution is specifically designed to handle right-skewed and leptokurtic data with a decreasing trend. ...
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This article introduces a novel probability distribution to model economic variables with high kurtosis and heavy tails showing a decreasing trend. From a mathematical viewpoint, it corresponds to the distribution of the ratio of two independent random variables, one with the modified Lindley distribution and another with the beta distribution. In some sense, it can be described as an extended three-parameter version of the Lindley distribution that has the ability to model data with high kurtosis. After presenting this distribution in more in-depth details, a comprehensive analysis is given, including its associated functions, moments, skewness, and kurtosis characteristics. Furthermore, a parametric estimation work is carried out. A simulation approach is used to validate the performance of the obtained estimates. The applicability of the proposed distribution is demonstrated by fitting real-world data into various socioeconomic scenarios.
... Accordingly, the Yuan-Bentler (YB) estimator (K.-H. Yuan & Bentler, 2000) was used to evaluate first and second hypotheses. This estimator was used as it was found to be robust when using categorical variables as continuous and it also corrects test statistics and standard errors for nonnormality of the manifest variables (Beauducel & Herzberg, 2006;Finney & DiStefano, 2006;Trautwein et al., 2012). ...
... Second, for addressing RQ1, LPA was performed using MPLUS 8.0 to identify potential profiles of participants based on their self-reported levels of MRS. Maximum likelihood estimation with robust standard errors was employed to estimate the parameters of these latent profiles, ensuring unbiased estimates under the assumption that missing data occurred completely at random (Yuan and Bentler 2000). ...
Article
Using a person-centered approach, the present study aimed to investigate the potential profiles of motivational regulation strategies for writing (MRSW) and examine the predictive effect of L2 writing anxiety on the membership of MRSW profiles. Data were collected from a sample of 604 secondary school students with two questionnaires. The Second Language Writing Strategies for Motivational Regulation Questionnaire (L2WSMRQ) was employed to identify the possible MRSW profiles, and the Second Language Writing Anxiety Inventory (SLWAI) was administered to reveal the association between these profiles and L2 writing anxiety among this population. Three distinct profiles (i.e., low, medium, and high MRSW profile) were identified via latent profile analysis. Multinomial logistic regression revealed that cognitive anxiety and avoidance behavior served as effective predictors of the membership of MRSW profiles. These findings may shed light on the heterogeneous configuration patterns of strategy use in EFL writing and provide practical implications for practitioners and researchers aiming to offer personalized instructions tailored to different profiles and anxiety levels.
... Finally, RMSEA values of 0.05 or less reflect excellent model fit, while values less than 0.10 reflect acceptable model fit (Hu & Bentler, 1999). Standardized beta coefficients (β) were evaluated to determine the magnitude, directionality, and significance of pathways (Yuan & Bentler, 2000). ...
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Throughout the years, immigration has been a significant movement in the USA and leads to the examination of acculturative stress. By employing the acculturation stress and vulnerability models, the present study aimed to examine the association among acculturation stress, self-esteem, depression, family cohesion, and familism in first-generation immigrant children. Longitudinal data from the Children of Immigrants Longitudinal Study (CILS) were used. The analytical sample (n = 5262) was predominantly female (51.1%) and between the ages of 12 and 18 (M = 14.23) years old. SPSS 27 and AMOS 27 were utilized to conduct a path analysis to examine the relationships among acculturation stress, self-esteem, depression, family cohesion, and familism. Our results showed good fit (χ2/df ratio = 11.49; CFI = 0.91; RMSEA = 0.05, CI [.04, .05]) for the full path model. Acculturation stress had a significant, negative association with depression (β = − 0.12, p < .001); a significant, negative association with self-esteem (β = − 0.12, p < .001); and a significant, positive association with family cohesion (β = 0.60, p < .01) and the familism index (β = 0.05, p < .05). Acculturation stress was found to be predictive of self-esteem, depression, and family cohesion for first-generation immigrant children between the ages of 12 and 18 years old. This study provides general implications for how mental health providers can understand the struggles and provide culturally competent therapeutic services for children and their families.
... The structural model is then estimated using these weights (saved in an expanded data set), so class shift is not possible. For the estimation of this model, maximum likelihood parameter estimates (MLR) with standard errors robust to non-normality and nonindependence of observations are used (in this case, corrects for nestedness of data and non-normal auxiliary variables) (Yuan and Bentler, 2000). The MLR standard errors are computed using a sandwich estimator which corrects for all kind of misspecifications. ...
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It has been theorised and evidenced that social contacts and resources are unevenly distributed amongst individuals; therefore individuals gain different returns in terms of labour market outcomes. Aim: To explore the patterns of accessed social capital in Chilean society and to determine how these patterns are associated with the socioeconomic position of individuals and predicted by ascribed and achieved conditions. Methodology: A quantitative secondary data analysis was carried out, using data from the cross-sectional Social Stratification Survey administered in Chile in 2009. The sample used for the study consisted of 2583 employed adults ranging from 25 to 64 years old. An LCA was used to examine the patterns of network resources, and to construct a social capital latent variable, whereas a Mixture Regression Analysis using the BHC method was conducted to analyse how the social capital measurement component predicts occupational status, and how network resources are also predicted by ascribed and achieved conditions. Results: Findings indicated that, above the spectrum of volume of contacts on which the social capital structure lays, it is possible to subtype network resources in five distinct groups, whose acquisition is influenced by parental status and educational level. These classes were also found to be significantly associated with socioeconomic position; a higher volume of network resources predicted a higher attained status, but especially when these were high status contacts. Discussion: The study supports and expands on previous results on social capital, and contributes to the scarce Latin-American literature on the role of social resources in socio-economic inequalities. It reinforces the importance of including the notion of social capital and networking in interventions for overcoming poverty. In addition, this study encourages other researchers to explore patterns of social capital using the Position Generator.
... Structural equation modelling enabled us to specify a five-factor measurement model by loading each item on its respective latent factor (stimulation, comfort, affection, behavioural confirmation and status). The CFA models were fitted by robust maximum likelihood estimation (MLE), which provides a test statistic that is asymptotically equivalent to the Yuan-Bentler (2000) T2 test statistic with standard errors that are robust against violations of multivariate normality (Lei, 2009). In addition to Satorra-Bentler χ 2 tests, which appropriately accompany MLE, the root mean square error of approximation (RMSEA) (Steiger & Lind, 1980), comparative fit index (CFI) (Hu & Bentler, 1999) and standardised root mean square residual (SRMR) (Hu & Bentler, 1999) were used to evaluate the absolute fit of the T1 and T2 models. ...
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Adolescent well-being is increasingly scrutinized due to its decline. This study was conducted to validate a theory-driven instrument for the measurement of well-being needs with a sample of Dutch adolescents. The short (15-item) Social Production Function Instrument for the Level of well-being (SPF-ILs) measures whether a person’s needs for stimulation, comfort, behavioural confirmation, affection and status are met. In this study, its psychometric properties for adolescents were examined. Data collected in spring 2018 (T1) and spring 2019 (T2) from 1,304 Dutch adolescents (53.0% girls) aged 11–17 (mean, 13.7 ± 1.1) years were used. The instrument’s factor structure, internal consistency, construct validity, and gender and age factorial invariance were evaluated. The results showed that the SPF-ILs is valid and reliable for the assessment of adolescents’ well-being needs realisation. Confirmatory factor analyses supported the five-factor (stimulation, comfort, behavioural confirmation, affection and status) model, showing good internal consistency (α = 0.86 at T1, 0.88 at T2), convergent/divergent validity, as well as gender and age factorial invariance. Comparison across groups revealed the expected differences in the realisation of physical (comfort and stimulation) and social (behavioural confirmation, status and affection) well-being needs between girls and boys and over time. SPF-ILs use increases our understanding of how adolescents achieve well-being via the fulfilment of well-being needs. The maintenance of adolescents’ well-being is a global challenge, and this study revealed clear differences in adolescents’ realisation of well-being needs, increasing our understanding of what interventions are needed to support such realisation.
... For model estimation, the implemented robust maximum likelihood estimator (MLR) was used. This estimator has the advantage of using standard errors and goodness-of-fit statistics to correct for possible non-normality [29]. Technology acceptance, technology competence belief, and technology control belief were specified as latent variables to account for measurement error at the indicator level. ...
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The COVID-19 pandemic challenged universities to maintain teaching, leading to online classes becoming the standard teaching mode and accelerating digitalization. Learning from the influence of these developments on students’ technology commitment may hold valuable information for various stakeholders. The present study investigated the development of three facets of technology commitment in higher education during the first two semesters under the COVID-19 pandemic: technology acceptance, technology competence belief, and technology control belief. The sample consisted of N = 132 graduate students at one German university who filled out questionnaires at two measurement points in two waves. The change in all three facets of technology commitment over time was examined with latent change models. There was a significant increase in technology competence belief. This change was stronger for students in the second COVID-19 semester than those in the first COVID-19 semester. Participants’ age, sex, and the number of webinars attended during the semester of data collection had no significant effect on the change in the three facets of technology commitment. Overall, the present study provides new insights into the development of technology commitment during the COVID-19 pandemic, proposes an explanatory approach for the change in technology commitment, and emphasizes the relevance of direct experience with technology in the development of technology competence belief at different skill levels. The results indicate that students can increase their level of technology competence belief, by engaging directly with new technology.
... The social science field has broadly used MLPM for empirical research (Jaccard & Brinberg 2021). Further, this study used the Robust maximum likelihood method to accurately estimate standard errors and to address missing data (Muthen & Muthen, 2015;Yuan & Bentler, 2000). Table 2 presents the multigroup multiple regression results examining the association between risk factors and perceptions of justifiability of three types of interpersonal violence (i.e., IPV against wife, child physical abuse, and violence against others) across five regions in Asia. ...
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In Asia, rates of interpersonal violence are increasing, with significant regional disparities. However, long-term, continental-scale research considering regional differences across the Asia regions is limited. Guided by the ecological model, we examined five ecological risk factors (low life satisfaction/happiness, economic hardship, neighborhood disadvantage, patriarchal values, and religiosity) associated with perceptions of justification of interpersonal violence (i.e., intimate partner violence [IPV] against wife, child physical abuse, and violence against others) in five regions in Asia (i.e., East, West, Central, South, and Southeast). Using the World Values Survey ( n = 32,307), a multigroup multiple regression model was used with robust maximum likelihood estimation using Mplus ver. 8. In the entire Asia sample model, perceptions of justifiability of IPV against wife were positively associated with low life satisfaction/happiness; economic hardship; neighborhood disadvantage; and patriarchal values, while they were negatively associated with religiosity. Perceptions of justifiability of child abuse were positively associated with low life satisfaction/happiness; neighborhood disadvantage; and patriarchal values, while they were negatively associated with economic hardship and religiosity. Perceptions of justifiability of violence against others were positively associated with economic hardship and neighborhood disadvantage, while they were negatively associated with religiosity. Each region presented unique risk factor associations. Considering the high rates of interpersonal violence in Asia, understanding the risk factors associated with perceptions of justifying specific types of interpersonal violence can provide an initial insight into preventing violence in Asia. Further, as many Asians dwelling outside Asian regions are still influenced by their culture, religion, language, and norms of the region of origin, the study findings may shed light on future studies to consider in the interpersonal violence literature.
... MLR was suitable only for data without missing values or incomplete either Missing Completely at Random (MCAR) or Missing at Random (MAR) type. MLR is robust to models in which the data violate the assumption of multivariate normality (39). As the non-normality characteristics were reported from multivariate normality checking and all missing data had been deleted, it was then decided that MLR could be used as the estimator instead of MLM, which can deal with missing data. ...
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Background Abdominal bloating (AB) is a common, bothersome symptom that negatively affects most adults. Although social support may help people suffering from AB, limited validated questionnaire is available. This study aimed to validate the newly developed Abdominal Bloating Social Support (SS-Bloat) scale for the Malaysian context. Method We conducted a cross-sectional study in which we used purposive sampling and a self-administered questionnaire. Based on the literature review, experts’ input and in-depth interviews, new items were generated for SS-Bloat scale. Content validity was assessed by experts and pre-tested with 30 individuals with AB. Construct validity was determined based on exploratory factor analysis (EFA) and confirmatory factor analysis (CFA). Reliability was determined based on Cronbach’s alpha and composite reliability (CR). Results During the development stage, eight items were generated for SS-Bloat scale and remained the same after content validity and pre-testing. A total of 152 participants with a mean age of 31.27 years old (68.3% female, 32.7% male) completed the questionnaire. Based on the EFA, three problematic items were removed. The total variance explained was 35.6% with acceptable reliability (α = 0.66). The model was then tested using CFA. The initial model did not fit the data well. After several model re-specifications, the final measurement model of SS-Bloat scale fit the data well with acceptable fit indices (comparative fit index [CFI] = 0.994 and Tucker-Lewis index [TLI] = 0.984). The CR was satisfactory with value of 0.84. Conclusion SS-Bloat scale was deemed valid and reliable for assessing the level of social support among AB patients. The questionnaire can be useful for both research studies and clinical purposes, as it is easy to use.
... In all analyses, we used R software with the "dplyr" package for basic data analyses, the "lavaan" package for factor analyses, and the "lme4" package for MLM analyses. In the factor analyses, we used the Robust Maximum Likelihood (MLR) estimator to account for deviations from normality 36 and relied on the following thresholds of fit: CFI > 0.90, RMSEA < 0.08, SRMR < 0.08 37,38 . In the cross-national Multigroup Confirmatory Factor Analyses, we relied on the thresholds: ΔCFI < − 0.02, ΔRMSEA < 0.03 39 . ...
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A theoretical perspective on grandiose narcissism suggests four forms of it (sanctity, admiration, heroism, rivalry) and states that these forms conduce to different ways of thinking and acting. Guided by this perspective, we examined in a multinational and multicultural study (61 countries; N = 15,039) how narcissism forms are linked to cognitions and behaviors prompted by the COVID-19 pandemic. As expected, differences in cognitions and behaviors across narcissism forms emerged. For example, higher narcissistic rivalry predicted lower likelihood of enactment of COVID-19 prevention behaviors, but higher narcissistic sanctity predicted higher likelihood of enactment of COVID-19 prevention behaviors. Further, whereas the heroism, admiration, and rivalry narcissism forms acted in a typically antisocial manner, with high narcissism predicting greater endorsement of unfounded health beliefs, the sanctity form acted in a prosocial manner, with higher narcissism being linked to lower endorsement of unfounded COVID-19 health beliefs. Thus, the findings (a) support the idea of four narcissism forms acting differently, and (b) show that these differences reflect a double-edged sword, sometimes linking to an anti-social orientation, and sometimes linking to a pro-social orientation.
... 54 The maximum likelihood estimator with robust standard error (SE) was utilized to take into account the possible influence of non-normal data distribution on the parameter estimation. 55 Besides, 95% bias-corrected confidence interval (CI) with 10,000 resampling were obtained for all of the parameter estimates. Pseudo R 2 were reported for perceived stress and depressive level. ...
Article
Objective: Although previous studies have validated the effect of childhood trauma on depressive level, few studies have utilized the diathesis-stress theory to investigate the specific roles of perceived stress and rumination in the pathway between childhood trauma and depression in Chinese college students. This study aims to demonstrate the mediation effect of perceived stress and the moderation effect of rumination in the pathway between childhood trauma and depressive level in Chinese college students. Methods: A total of 995 Chinese college students in Guangzhou were included in this study by recruitment advertisement from October to December 2021. And they were asked to finish four self-report questionnaires, including Childhood Trauma Questionnaire-Short Form, Perceived Stress Scale, the 22-item Ruminative Response Scale, and Beck Depression Scale-II. Then the data were analyzed with Mplus 8.3. Results: Results revealed significant correlations among childhood trauma, perceived stress, rumination and depressive level. Further analyses revealed that perceived stress played a mediation role between childhood trauma and depressive level (estimate=0.09, standard error [SE]=0.02, t=5.93, 95% confidence interval [CI]=0.06-0.12), and rumination played a moderation role between childhood trauma and perceived stress (estimate=-0.17, SE=0.06, t=-2.86, 95% CI=-0.28- -0.05]) as well as between childhood trauma and depressive level (estimate=0.10, SE=0.04, t=2.74, 95% CI=0.03-0.16). Conclusion: These results revealed the mediation effect of perceived stress and the moderation effect of rumination in the pathway between childhood trauma and depressive level in Chinese college students, which helped us to understand how the childhood trauma influenced the depressive level and gave us multi-dimensional indications for reducing the effect of childhood trauma on depressive level.
... We inspected the data via simple descriptive statistics and then conducted factor analyses via the "lavaan" package (Roseell, 2012) and multilevel modeling via the "lme4" package (Bates et al., 2015). In the factor analyses, we used the Robust Maximum Likelihood estimator to account for deviations from normality (Yuan & Bentler, 2000) and relied on the following thresholds of fit indices: CFI > .90, RMSEA < .08, ...
... [38]. MLR was used to handle non-normal data [39]. Non-independence by study sites was accounted by the CLUSTER option. ...
... FIML produces consistent and fully efficient parameter estimates in SEM under MAR and multivariate normality (Arbuckle, 1996, Enders & Bandalos, 2001. Simulation studies have shown FIML to produce parameter estimates with good statistical properties, showing low bias and good coverage (e.g., Enders, 2001;Yuan & Bentler, 2000). FIML is available only for con-ML estimation, which means missing data handling for cat-LS requires a different strategy. ...
... To test the factorial validity of the ITQ, confirmatory factor analysis (CFA) was used. The correlated six-factor model and the two-factor higher-order model were tested, and these models were estimated using robust maximum likelihood estimation (Yuan and Bentler, 2000). Good model fit is indicated by a non-significant chisquare (χ 2 ) value, comparative fit index (CFI) and Tucker-Lewis fit index (TLI) values >0.90 and closer to 1, and root mean square error of approximation (RMSEA) and standardised root mean square residual (SRMR) values <0.08 and closer to 0. The Bayesian information criterion (BIC) is used to compare alternative models, and the model with the lower value is considered statistically superior. ...
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Background ICD-11 complex post-traumatic stress disorder is a more severe condition than post-traumatic stress disorder, and recent studies indicate it is more prevalent among military samples. In this study, we tested the psychometric properties of the International Trauma Questionnaire, assessed the relative prevalence rates of post-traumatic stress disorder and complex post-traumatic stress disorder in the sample population and explored relationships between complex post-traumatic stress disorder and post-traumatic stress disorder and a range of risk factors. Methods Survey participants ( N = 189) were mental health support-seeking former-serving veterans of the Australian Defence Force (ADF) recruited from primary care. Confirmatory factor analysis was used to test the factorial validity of the International Trauma Questionnaire. Results The latent structure of the International Trauma Questionnaire was best represented by a two-factor second-order model consistent with the ICD-11 model of complex post-traumatic stress disorder. The International Trauma Questionnaire scale scores demonstrated excellent internal reliability. Overall, 9.1% (95% confidence interval = [4.8%, 13.5%]) met diagnostic requirements for post-traumatic stress disorder and an additional 51.4% (95% confidence interval = [44.0%, 58.9%]) met requirements for complex post-traumatic stress disorder. Those meeting diagnostic requirements for complex post-traumatic stress disorder were more likely to have served in the military for 15 years or longer, had a history of more traumatic life events and had the highest levels of depression, anxiety and stress symptoms. Conclusion The International Trauma Questionnaire can effectively distinguish between post-traumatic stress disorder and complex post-traumatic stress disorder within primary care samples of Australian Defence Force veterans. A significantly greater proportion of Australian Defence Force veterans met criteria for complex post-traumatic stress disorder than post-traumatic stress disorder. Australian military mental health services should adopt the International Trauma Questionnaire to routinely screen for complex post-traumatic stress disorder and develop complex post-traumatic stress disorder specific interventions to promote recovery in Australian Defence Force veterans with complex post-traumatic stress disorder.
... Goodness of fit for competing confirmatory factor models for the ATTARI-12 (Study 1; US-American MTurk Panelists). χ 2 = Robust test statistic83 , df degrees of freedom, CFI comparative fit index, RMSEA root mean squared error of approximation, SRMR standardized root mean residual, AIC Akaike's information criterion, BIC Bayesian information criterion, Comp. Comparison model, Δχ 2 Scaled chi square difference test statistic 84 .Bifactor S-1 models with one global factor and orthogonal specific factors for …Table 3. Factor loading pattern for the ATTARI-12 (Study 1; US-American MTurk panelists). ...
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Artificial intelligence (AI) has become an integral part of many contemporary technologies, such as social media platforms, smart devices, and global logistics systems. At the same time, research on the public acceptance of AI shows that many people feel quite apprehensive about the potential of such technologies—an observation that has been connected to both demographic and sociocultural user variables (e.g., age, previous media exposure). Yet, due to divergent and often ad-hoc measurements of AI-related attitudes, the current body of evidence remains inconclusive. Likewise, it is still unclear if attitudes towards AI are also affected by users’ personality traits. In response to these research gaps, we offer a two-fold contribution. First, we present a novel, psychologically informed questionnaire (ATTARI-12) that captures attitudes towards AI as a single construct, independent of specific contexts or applications. Having observed good reliability and validity for our new measure across two studies (N1 = 490; N2 = 150), we examine several personality traits—the Big Five, the Dark Triad, and conspiracy mentality—as potential predictors of AI-related attitudes in a third study (N3 = 298). We find that agreeableness and younger age predict a more positive view towards artificially intelligent technology, whereas the susceptibility to conspiracy beliefs connects to a more negative attitude. Our findings are discussed considering potential limitations and future directions for research and practice.
... Third, in the primary analyses, due to the small sample size for the between-level variable (i.e., eight teams), we only tested a model targeting the individual level of analysis. Therefore, a structural equation model (SEM) was completed to test the model hypothesized in this study, using the Mplus COMPLEX instruction to control for the nesting of players within teams, and a multiple linear regression (MLR estimator [47]). Finally, indirect effects were tested using the bias-corrected bootstrap method (10,000 samples with 95% confidence corrected for bias intervals -IC- [48]) with the maximum likelihood procedure (ML; bootstrapping is unavailable when using MLR estimation). ...
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Background In the sports context, coaches must be able to improve their players physically, psychologically, and socially. Hence, a fundamental part of this process is the athlete’s individual resilience (IR). Methods Three hundred and fifteen youth team-sport players (boys: n = 283; Mage = 16.02, SD = 0.56; and girls: n = 32; Mage = 15.92, SD = 0.62) completed the measures of coach’s interpersonal style, individual resilience, perceived performance, and team adherence intention (intention to remain on the same team the following year) twice (Time 1: mid-season; Time 2: end-season). Structural equation modeling was used to test the relationships between variables. Results The results showed that coach support was positively related to IR (p < 0.001) and, in turn, IR to individual (p < 0.01) and team performance (p < 0.05) at Time 1, and to individual performance (p < 0.001) and team adherence intention at Time 2 (p < 0.01). In addition, team performance at Time 2 was positively related to team adherence intention (p < 0.001). Finally, a mediating effect of IR was observed between interpersonal coaching style, individual and team performance, and team adherence intention. Conclusions These results show the importance of a supportive interpersonal coaching style to foster athletes’ levels of resilience, which could have positive consequences in performance (individual and team) and team adherence intention.
... Consistent with Klein and Moosbrugger's (2000) recommendations, we used a two-step approach in order to test the posited moderated mediation model. First, we tested a model without including the latent interactions posited in Figure 1 (Model 0), and using the robust maximum-likelihood estimators recommended for skewed observed variables (Yuan & Bentler, 2000). Next, we tested the posited model including the latent interaction terms (Model 1) estimated with numerical integration. ...
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While a growing body of literature links the stressor of job insecurity (JI) with poor employee well‐being and increased work‐to‐family conflict (WFC), the current study specifically tests WFC as an explanatory mechanism of the relationships between affective JI (i.e., emotional reactions to the perceived threat to one's job) and poor health outcomes (i.e., mental and physical health). Moreover, this study uniquely examines how family–work stereotype threat (FWST; i.e., fears of confirming negative stereotypes about workers with family obligations) may exacerbate the relationship between perceived threats to one's job and employee reports of WFC. Using a cross‐country design, data from 707 employees in the United States (two‐wave) and 763 employees nested within 100 organizations in Italy (multilevel, cross‐sectional) largely supported the hypothesized mediation model. Specifically, WFC explains the association of JI with individual mental and physical health in both countries. Moreover, FWST exacerbates the direct relation of JI with WFC in the United States, but not in Italy. These findings suggest that the fear of losing one's job may prompt employee experiences of WFC and subsequent poorer physical and mental health; additionally, in the United States, this effect is even stronger among employees who reported higher levels of FWST. We interpret these heterogeneous findings in the light of nation‐related factors in managing increasingly insecure employment markets, especially after the COVID‐19 pandemic. Theoretical and practical implications are discussed for improving both health and work–life boundary management of post‐pandemic workers.
... However, semPower 2 also allows one to change the estimator and test statistic employed in a simulated power analysis by setting the lavOptions argument, which is passed to lavaan and thus conforms to the standard lavaan conventions. For instance, lavOptions = list(estimator = 'mlr') leads to a simulated power estimate relying on a corrected test statistic that is asymptotically equivalent to the Yuan & Bentler (2000) statistic, whereas the analytic power estimate is still based on the asymptotically expected distributions based on ML. Repeating the previous example with this additional argument yields less biased distributions of the corrected test statistic under both the H0 and the H1 as compared to the results obtained above using the uncorrected test statistic, Note that the simulated power estimate is still very close to the analytical power estimate: ...
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Structural equation modeling (SEM) is a widespread and commonly used approach to test substantive hypotheses in the social and behavioral sciences. When performing hypothesis tests, it is vital to rely on a sufficiently large sample size to achieve an adequate degree of statistical power to detect the hypothesized effect. However, applications of SEM rarely consider statistical power in informing sample size considerations or determine the statistical power for the focal hypothesis tests performed. One reason is the difficulty in translating substantive hypotheses into specific effect size values required to perform power analyses, as well as the lack of user-friendly software to automate this process. The present paper presents the second version of the R package semPower which includes comprehensive functionality for various types of power analyses in SEM. Specifically, semPower 2 allows one to perform both analytical and simulated a priori, post hoc, and compromise power analysis for structural equation models with or without latent variables, and also supports multigroup settings and provides user-friendly convenience functions for many common model types (e.g., standard confirmatory factor analysis [CFA] models, regression models, autoregressive moving average [ARMA] models, cross-lagged panel models) to simplify power analyses when a model-based definition of the effect in terms of model parameters is desired.
... The study was designed as correlational survey research and a convenience sampling method was utilized. To determine sample size in SEM studies, Yuan and Bentler (2000) and Bandalos (2014) suggested that a sample size of over 400 would be sufficient. In addition, Pituch and Stevens (2015) concluded based on Monte Carlo studies carried out under various conditions that a sample size greater than 400 provides sufficient statistical power for CFA/SEM. ...
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The current study was cross-sectional design and investigated the mediating role of self satisfaction in the relationship between the sense of coherence, family sense of coherence, and psychological distress. A total of 1022 participants adults and emerging adults were included, with a mean age of 27.88 (SD = 9.73). The self satisfaction scale, sense of coherence and family sense of coherence scales, and brief symptom inventory were utilized as data collection tools through the convenience sampling method. Structural equation modeling results indicated that the sense of coherence, family sense of coherence, and self satisfaction was negatively correlated with psychological distress, and the sense of coherence and family sense of coherence were positively correlated with self satisfaction. The mediation analysis showed that self satisfaction fully mediated the relationship between family sense of coherence and psychological distress and partially mediated the relationship between the sense of coherence and psychological distress. Additionally, the bootstrapping process revealed substantial relationships between the sense of coherence, family sense of coherence, and psychological distress through self satisfaction. Competing models indicated that different order variables also supported the structural models. The findings of the study revealed that sense of coherence, family sense of coherence, and self satisfaction play important roles to explain psychological distress, and self satisfaction takes place as a significant mediator between the sense of coherence, family sense of coherence, and psychological distress. This study's results indicated that focusing on and promoting the sense of coherence, family sense of coherence, and self-satisfaction may decrease psychological distress. Limitations and future research were discussed.
... Similar adjustment was not indicated for the DSC model (ICC = 0.007; Ntani et al., 2020). Due to skewed outcome distributions (see Appendix C), we accounted for missing item-level data (7.7%) using maximum likelihood robust estimation (Yuan & Bentler, 2000). We used Mplus v8.2 for analyses (Muthén & Muthén, 2017). ...
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College students’ mental health concerns have dramatically increased in prevalence and severity over the past decade, overwhelming the capacity of counseling centers to meet demand for services. In response, institutions of higher education (IHEs) increasingly emphasize prevention, education, and outreach efforts aimed at improving well-being. Although this focus has prompted an increase in research on student well-being, few studies have investigated the unique contributions of malleable psychosocial factors on student outcomes. This study aims to address this gap in the literature by examining the relative impact of an array of psychosocial factors—adaptive and maladaptive perfectionism, coping self-efficacy, social connectedness, perceived burdensomeness, grit, resilience, and meaning in life—on academic performance and distress and suicidality in a sample of 7505 students from 15 U.S. IHEs. Controlling for institutional selectivity and non-malleable aspects of students’ identities and pre-college experiences, facets of perfectionism, grit, and emotion-focused coping self-efficacy were the psychosocial factors most strongly associated with GPA, and perceived burdensomeness, social connectedness, emotion-focused coping self-efficacy, and resilience were most strongly associated with distress and suicidality. Among non-malleable factors, race/ethnicity explained the most variance in GPA and gender identity explained the most variance in distress and suicidality. Results are discussed in light of persistent, identity-based disparities in academic achievement and suicide risk and the potential of psychosocial factors as intervention targets to improve academic performance and reduce suicide risk.
... Because these procedures have been outlined in detail elsewhere and are extensions of well-known complete data correctives, further details are omitted for the sake of brevity. Interested readers are encouraged to consult Yuan and Bentler (2000) for technical details on these methods. ...
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A Monte Carlo simulation examined full information maximum-likelihood estimation (FIML) in structural equation models with nonnormal indicator variables. The impacts of 4 independent variables were examined (missing data algorithm, missing data rate, sample size, and distribution shape) on 4 outcome measures (parameter estimate bias, parameter estimate efficiency, standard error coverage, and model rejection rates). Across missing completely at random and missing at random patterns, FIML parameter estimates involved less bias and were generally more efficient than those of ad hoc missing data techniques. However, similar to complete-data maximum-likelihood estimation in structural equation modeling, standard errors were negatively biased and model rejection rates were inflated. Simulation results suggest that recently developed correctives for missing data (e.g., rescaled statistics and the bootstrap) can mitigate problems that stem from nonnormal data.
... Indirect effects and 95% confidence intervals were also computed". To account for skewness, all models were estimated using the robust maximum likelihood (MLR) estimator, which utilizes a sandwich estimator to compute standard errors robust to non-normality and a chi-square test statistic asymptotically equivalent to the Yuan-Bentler T2 test statistic (Yuan & Bentler, 2000). The initial model specification included correlations between predictors, between mediators, and between outcomes, as well as all possible regression paths within the causal chains of interest. ...
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In explaining the “parenting – callous-unemotional traits – antisocial behavior” axis, recent theoretical advances postulate a critical role for affiliative reward. Existing empirical studies focus on early childhood and the appetitive phase of the reward process (i.e. affiliation-seeking behavior) rather than the consummatory phase (i.e. affective rewards). This study focuses on experienced affiliative reward (i.e. companionship, intimacy, affection, and worth) in relation to parents and best friends in early adolescence. The Alabama Parenting Questionnaire, Network of Relationships Inventory, Inventory of Callous and Unemotional Traits, and Youth Self Report were completed by 1132 12-year-olds and analyzed via structural equation models. In this cross-sectional sample, parent-related affiliative reward mediated the path from perceived parenting practices to callousness and further to aggression and rule-breaking. Parent-related affiliative reward was also related to uncaring traits and further to aggression and rule-breaking. In contrast, friend-related affiliative reward was not a mediator in this theoretical causal chain and largely not related to perceived parenting practices or CU traits. Low parent-related experienced affiliative reward is a mechanism through which corporal punishment, poor monitoring, and low involvement translate into callousness, and therefore to aggression and rule-breaking. Friend-related affiliative reward does not yet play a role in early adolescence.
... We used Mplus Version 8.5 (Muth en & Muth en, 1998-2017) for all analyses. Models were estimated using maximum likelihood robust standard error correction estimator for unbiased estimates (i.e., MLR; Yuan & Bentler, 2000), and missing data were handled with the Full information maximum likelihood method. We used the sandwich estimator (i.e., command TYPE ¼ COMPLEX) to account for clustering effects (i.e., youth nested within families. ...
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Objectives: We investigated whether the self-system belief of fear of abandonment mediated the effects of intervention-induced change in 2 protective factors-positive parenting and adaptive coping-and one risk factor-stressful events-on youth mental health problems and maladaptive grief. This study extends prior research on fear of abandonment in youth who experience parental death by examining pathways through which a program reduced fear of abandonment and, in turn, affected subsequent pathways to child mental health problems in the context of a randomized experiment. Methods: This is a secondary data analysis study. We used data from the 4-wave longitudinal 2-arm parallel randomized controlled trial of the Family Bereavement Program conducted between 1996 and 1999 in a large city in the Southwestern United States. The sample consisted of 244 offspring between 8 and 16 at the pretest. They were assessed again at posttest, 11-month follow-up, and 6-year follow-up. Offspring, caregivers, and teachers provided data. Results: Mediation analyses indicated that intervention-induced reductions in stressful events were prospectively associated with a lower fear of abandonment. For girls, fear of abandonment was related to self-reported maladaptive grief and teacher-reported internalizing problems 6 years later. Conclusions: This study extends prior research on the relation between intervention-induced changes in risk and protective factors and improvements in outcomes of bereaved youth. The findings support the reduction of stressful events as a key proximal target of prevention programs for bereaved children.
... Sandwich Estimator. Mplus offers a so-called robust standard error (Huber, 1967;Satorra & Bentler, 1994;White, 1982;Yuan & Bentler, 2000). More specifically, the LMS approach in Mplus employs a sandwich type estimator, which calculates the sampling variability of an estimate through the utilization of the Fisher information as derived from the principles of maximum likelihood theory. ...
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In multilevel nonlinear structural equation modeling via latent moderated structural equations, the homoscedasticity assumption is typically made; that is, it is assumed that the variances within higher-level units are equal across these units. However, this assumption is frequently violated in research, potentially leading to inaccuracies in standard errors and inferences. In this article, we present an extensive Monte Carlo simulation study that provides evidence that the robust standard errors for moderation effects as obtained from the commonly employed sandwich estimator in Mplus can be suboptimal when samples are small to medium-sized, and intraclass correlations are low. This outcome holds true not only in scenarios characterized by substantial heteroscedasticity but also, albeit to a lesser degree, when homoscedasticity is upheld but the number of integration points per dimension is suboptimal. As a remedy, we propose a computationally efficient delete-d type jackknife and a variant thereof. The two jackknife techniques tended to outperform the sandwich estimator. Therefore, we caution users not to apply the sandwich estimator in challenging conditions and suggest that a jackknife technique be preferred.
... It should be said that robust ML is a very good choice when continuous data lacks normality. It should also be noted that EQS, which decreased its popularity in the second period and became the second most widely used SEM program, provides a wide range of residual-based X 2 tests which are very versatile in studies based on smaller samples (Yuan & Bentler, 2000). ...
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Structural equation modeling (SEM), as a flexible and versatile multivariate statistical technique, has been growingly used since its introduction in the 1970s. This article presents a methodological synthesis of the characteristics of the use of SEM in L2 research by examining the reporting practices in light of the current SEM literature to eventually provide some empirically grounded recommendations for future research. A total of 722 instances of SEM found in 145 empirical reports published in 16 leading L2 journals across two periods of 1981-2008 and 2009-2020 were systematically reviewed. Each study was coded for a wide range of analytic and reporting practices. The results indicate that despite the growing popularity of SEM in L2 research, there was a wide variation and inconsistency in its uses and reports within and across the two periods in regard to the underlying assumptions, variables and models, model specification and estimation, and fit statistics. Drawing on the current SEM literature, we will discuss the findings and research implications for future use and reporting of SEM in L2 research.
... Sample sizes were determined according to requirements for confirmatory factor analyses (CFA, see 2.5.3): computing a CFA with a maximum likelihood robust to non-normality of data and missing values requires a minimum number of 400 participants ( [33], cited by [34]), which was (almost) the case for the participating countries. ...
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Background Healthcare professionals (HCPs) play an important role in vaccination; those with low confidence in vaccines are less likely to recommend them to their patients and to be vaccinated themselves. The study’s purpose was to adapt and validate long- and short-form versions of the International Professionals’ Vaccine Confidence and Behaviors (I-Pro-VC-Be) questionnaire to measure psychosocial determinants of HCPs’ vaccine confidence and their associations with vaccination behaviors in European countries. Research design and methods After the original French-language Pro-VC-Be was culturally adapted and translated, HCPs involved in vaccination (mainly GPs and pediatricians) across Germany, Finland, France, and Portugal completed a cross-sectional online survey in 2022. A 10-factor multigroup confirmatory factor analysis (MG-CFA) of the long-form (10 factors comprising 34 items) tested for measurement invariance across countries. Modified multiple Poisson regressions tested the criterion validity of both versions. Results 2,748 HCPs participated. The 10-factor structure fit was acceptable to good everywhere. The final MG-CFA model confirmed strong factorial invariance and showed very good fit. The long- and short-form I-Pro-VC-Be had good criterion validity with vaccination behaviors. Conclusion This study validates the I-Pro-VC-Be among HCPs in four European countries; including long- and short-form tools for use in research and public health.
... Model estimation is performed using the lavaan package in R (Rosseel 2012). We use a maximum likelihood estimator with robust standard errors and test statistics (mlr; Satorra and Bentler 1994;Yuan and Bentler 2000) and treat missing values using full information maximum likelihood (FIML) estimation. We present the annotated R code and output at the end of our supporting information. ...
Article
Previous explanations regarding transnational solidarity in the European Union (EU) have mainly focussed on factors including left–right self-placement, support for European integration and European identity. We expand this model by considering deeper psychological determinants of transnational solidarity: values, operationalised as Schwartz’s basic human values of universalism and security. We expect them to exert (1) direct effects on transnational solidarity – measured as support for pan-European social benefits – and (2) indirect effects via the three aforementioned factors. We test and find evidence to support our theoretical framework using multigroup structural equation modelling and data from the European Social Survey. We further show that the effect size of the value of universalism on preferences for an EU social benefit scheme in each country is positively moderated by that country’s net contribution to the EU budget, highlighting the interaction between material interests and psychological value motivations.
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Objective: the present study evaluated the factorial validity, measurement invariance, reliability and graded response model of the WAST in a sample of female victims and non-victims of intimate partner violence. Method: A total of 285 Peruvian women participated (59.6were victims of intimate partner violence and 40.4were not victims of intimate partner violence), with ages ranging from 18 to 64 years and an average age of 31.73 years for victims of intimate partner violence and 26.54 years for non-victims. The confirmatory factor analysis (CFA) suggested a two-factor model that was significantly adjusted for the group of female victims of IPV and non-victims of IPV. Results: The multigroup CFA supported factorial invariance according to female IPV and non-IPV victims of the WAST. Reliability was adequate and was calculated using the omega coefficient. Finally, the WAST items showed adequate discrimination indexes and a correct ordering of the difficulty thresholds. Conclusion: The results showed that the WAST possesses good evidence of validity, reliability, invariance and graded response model in women victims and non-victims of IPV.
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Hyperphosphorylated tau accumulation is seen in the noradrenergic locus coeruleus from the earliest stages of Alzheimer’s disease onwards and has been associated with symptoms of agitation. It is hypothesized that compensatory locus coeruleus-noradrenaline system overactivity and impaired emotion regulation could underlie agitation propensity, but to our knowledge this has not previously been investigated. A better understanding of the neurobiological underpinnings of agitation would help the development of targeted prevention and treatment strategies. Using a sample of individuals with amnestic mild cognitive impairment and probable mild Alzheimer’s disease dementia from the German Center for Neurodegenerative Diseases (DZNE)-Longitudinal Cognitive Impairment and Dementia (DELCODE) study cohort (N = 309, aged 67–96 years, 51% female), we assessed cross-sectional relationships between a latent factor representing the functional integrity of an affect-related executive regulation network and agitation point prevalence and severity scores. In a subsample of individuals with locus coeruleus MRI imaging data (N = 37, aged 68–93 years, 49% female), we also investigated preliminary associations between locus coeruleus MRI contrast ratios (a measure of structural integrity, whole or divided into rostral, middle, and caudal thirds) and individual affect-related regulation network factor scores and agitation measures. Regression models controlled for effects of age and clinical disease severity and, for models including resting-state functional MRI connectivity variables, grey matter volume and education years. Agitation point prevalence showed a positive relationship with a latent factor representing the functional integrity (and a negative relationship with a corresponding structural measure) of the affect-related executive regulation network. Locus coeruleus MRI contrast ratios were positively associated with agitation severity (but only for the rostral third, in N = 13) and negatively associated with the functional affect-related executive regulation latent factor scores. Resting-state functional connectivity between a medial prefrontal cortex region and the left amygdala was related to locus coeruleus MRI contrast ratios. These findings implicate the involvement of locus coeruleus integrity and emotion dysregulation in agitation in Alzheimer’s disease and support the presence of potential compensatory processes. At the neural level, there may be a dissociation between mechanisms underlying agitation risk per se and symptom severity. Further studies are needed to replicate and extend these findings, incorporating longitudinal designs, measures of autonomic function and non-linear modelling approaches to explore potential causal and context-dependent relationships across Alzheimer’s disease stages.
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Introduction Despite recent efforts to understand the possible impact of contextual factors on adolescents’ involvement in ethnic bullying, most existing studies have focused on the effects of one context at a time. As adolescents are simultaneously exposed to the influence of multiple socialization agents, the aim of this study was to investigate whether teachers’ and classmates’ tolerance towards ethnic minorities could buffer the effect of perceived parental prejudice on adolescents’ involvement in ethnic bullying. Methods Data were collected between January and February 2020 from 9th grade adolescents (N = 582; Mage = 15.23; SD = 0.65; 50.9% female; 30.7% with an immigrant background), and their teachers (N = 72; aged between 27 and 65 years; 79% female), belonging to 37 classrooms located in Italy. Results A cross‐sectional multilevel analysis showed that teachers’ tolerance moderated the effect of perceived parental prejudice on adolescents’ involvement in ethnic bullying. Specifically, we found that in classrooms with low levels of teachers’ tolerance, perceived parental prejudice was significantly associated with students’ involvement in ethnic bullying. Conversely, in classrooms with high levels of teachers’ tolerance, parental prejudice was no longer associated with ethnic bullying. Furthermore, classmates’ tolerance was not significantly associated with students’ involvement in ethnic bullying and did not moderate the association between perceived parental prejudice and adolescents’ engagement in ethnic bullying. Conclusions Findings are discussed highlighting the important role of school as a context to promote positive multicultural relations and the unique role played by teachers in affecting adolescents’ behaviors.
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Objective This study has examined the indirect role of perceived teaching quality in the relationship between TSRs and academic grades, further considered the moderating effects of students' mental health symptoms. Methods Utilizing Structural Equation Modelling, this study collected academic grades at three distinct time points to examine the associations among Teacher-Student Relationships, perceived teaching quality, and mental health symptoms with academic grades. Results The findings reveal that perceived teaching quality plays a statistically significant indirect role in the relationship between Teacher-Student Relationships and student academic grades. Additionally, the size of this indirect effect is moderated by students' mental health symptoms. Conclusion While Teacher-Student Relationships may not be directly associated with students' academic grades, they are significantly linked to perceived teaching quality, which in turn is closely related to academic grades. The extent of this indirect effect is moderated by students' mental health symptoms, suggesting that the relationship between perceived teaching quality and academic grades is influenced by students' mental health status. These findings empirically indicate that Teacher-Student Relationships are important for both teaching and learning activities, underscoring their essential role in improving educational outcomes.
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Researchers may have at their disposal the raw data of the studies they wish to meta-analyze. The goal of this study is to identify, illustrate, and compare a range of possible analysis options for researchers to whom raw data are available, wanting to fit a structural equation model (SEM) to these data. This study illustrates techniques that directly analyze the raw data, such as multilevel and multigroup SEM, and techniques based on summary statistics, such as correlation-based meta-analytical structural equation modeling (MASEM), discussing differences in procedures, capabilities, and outcomes. This is done by analyzing a previously published collection of datasets using open source software. A path model reflecting the theory of planned behavior is fitted to these datasets using different techniques involving SEM. Apart from differences in handling of missing data, the ability to include study-level moderators, and conceptualization of heterogeneity, results show differences in parameter estimates and standard errors across methods. Further research is needed to properly formulate guidelines for applied researchers looking to conduct individual participant data MASEM.
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Missing Not at Random (MNAR) and nonnormal data are challenging to handle. Traditional missing data analytical techniques such as full information maximum likelihood estimation (FIML) may fail with nonnormal data as they are built on normal distribution assumptions. Two-Stage Robust Estimation (TSRE) does manage nonnormal data, but both FIML and TSRE are less explored in longitudinal studies under MNAR conditions with nonnormal distributions. Unlike traditional statistical approaches, machine learning approaches do not require distributional assumptions about the data. More importantly, they have shown promise for MNAR data; however, their application in longitudinal studies, addressing both Missing at Random (MAR) and MNAR scenarios, is also underexplored. This study utilizes Monte Carlo simulations to assess and compare the effectiveness of six analytical techniques for missing data within the growth curve modeling framework. These techniques include traditional approaches like FIML and TSRE, machine learning approaches by single imputation (K-Nearest Neighbors and missForest), and machine learning approaches by multiple imputation (micecart and miceForest). We investigate the influence of sample size, missing data rate, missing data mechanism, and data distribution on the accuracy and efficiency of model estimation. Our findings indicate that FIML is most effective for MNAR data among the tested approaches. TSRE excels in handling MAR data, while missForest is only advantageous in limited conditions with a combination of very skewed distributions, very large sample sizes (e.g., n larger than 1000), and low missing data rates.
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Sexuality education (SE) can be acquired through different sources. In a cross-sectional online study with Spanish and Portuguese participants (N = 595), we examined differences between formal traditional sources (i.e., mandatory SE received in schools), formal modern sources (e.g., SE received in courses), informal traditional sources (e.g., talks with friends and family), and informal modern sources (e.g., pornography and online content) and their contribution to sexual health and well-being outcomes. Results showed that sexual and reproductive health were among the most addressed topics across all sources. Nearly all participants received SE from informal sources, whereas more than two-thirds received SE from formal traditional sources. Results of a linear regression model showed that participants who perceived more influence from formal traditional sources reported using condoms more often, were more focused on disease prevention, and enacted more sexual health communication, but were also less sex-positive. Participants who perceived more influence from both types of informal sources attributed more importance to SE topics but reported having condomless sex more frequently and were more focused on pleasure promotion. Still, participants who perceived more influence from informal traditional sources also endorsed more internal/external consent, were more sexually satisfied, were more sex-positive, and enacted more sexual health practices. Lastly, participants who perceived more influence from informal modern sources were also more likely to have been diagnosed with a sexually transmitted infection. Only a small proportion of participants received SE from formal modern sources and had to be excluded from this analysis. Some differences between Spain and Portugal are discussed. Taken together, our findings highlight the need to consider different sources for a more comprehensive and inclusive SE, in articulation with sociocultural and political contexts.
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Food and nutrition are important issues of interest to policy makers, practitioners, and academics around the world due to the far-reaching consequences for society, households and individuals, and guidelines related to food consumption have been included in several policies both nationally and internationally. This study identifies household ‘typologies’ with regard to household food consumption of ‘marker’ food groups, and examines related associations with household demographics, analysing quantitative data on households (n = 4144) from the most recently available Northern Ireland Health Survey (2014/2015). Latent Class Analysis identified five household typologies; ‘Hedonistic Households (19%), Healthier Households (13%), General Households (42%), Unhealthier Households (3%), Balanced Households (23%)’, which individually vary in their adherence to recommended guidelines, and in their demographic composition. The study provides insight into how households’ dietary consumption patterns accord with government recommendations, and findings have implications for policy, for example through informing decision-making related to promoting behavioural change, and informing future collection of data related to ‘marker’ food groups.
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Background Uterine fibroids are the leading cause of hysterectomies among women of childbearing age. This study aims to elicit the knowledge, attitude and perceptions of childbearing women towards uterine fibroids in order to provide empirical evidence informing relevant interventions oriented toward health promotion in this regard. Methods A quantitative, cross-sectional descriptive design was used and data were collected from a sample of 362 women of reproductive age residing in a selected township in KwaZulu-Natal, South Africa. Ethical approval to conduct the study was obtained from the Durban University of Technology’s Institutional Research Ethics’ Committee (IREC – Ref No. BIREC 014/21). A pre-tested survey was conducted to gather data on knowledge, attitudes, and perceptions concerning uterine fibroids. The collected data were analyzed using SPSS version 27, employing descriptive statistics. Inferential statistics were also conducted to examine associations between key variables and respondents who self-reported being diagnosed with uterine fibroids. Results Most participants, 73.8% (n=267), had no awareness of uterine fibroids. Participants also demonstrated poor knowledge regarding the aetiology and symptoms of the condition. However, most participants, 49.2% (n=178), perceived uterine fibroids to be of spiritual origin, citing evil spirits and witchcraft as the cause. Participants subsequently reported that treatment would require herbal approaches and consultation with spiritualists such as traditional healers and seers. In summary, the study highlights various factors influencing self-reporting behaviours, including age, education level, employment status, marital status, number of children, awareness of the condition, perception of requiring treatment, family history, and symptom severity. Discussion and conclusion The study findings seem to suggest that women in the selected township lack accurate knowledge about uterine fibroids. These insights are valuable for shaping targeted health interventions and policies. Recognizing the complexities of self-reporting is crucial for improving health outcomes through early detection and tailored interventions
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This study aimed to explore the underlying mechanism of childhood psychological maltreatment and self-satisfaction through serial mediation involving self-critical rumination and self-compassion. The study employed a cross-sectional design with 528 participants (343 females, 185 males), including young adults and adults aged 18 to 59. The convenience sampling method was used, and to collect data, the participants completed the self-satisfaction scale, childhood trauma questionnaire, self-critical rumination, and self-compassion scale. Structural equation modeling results indicated that, controlling for age and gender effects, childhood psychological maltreatment was negatively correlated with self-satisfaction and self-compassion and positively correlated with self-critical rumination. The serial mediation analysis revealed that self-critical rumination explains a unique variance beyond the influence of self-compassion. Furthermore, even when controlling for the effects of self-critical rumination and self-compassion, childhood psychological maltreatment still directly affected self-satisfaction. The bootstrapping process revealed substantial relationships between childhood psychological maltreatment and self-satisfaction through self-critical rumination. An important result of this study indicated that childhood psychological maltreatment may impair individual’s subjective well-being even during adulthood. To enhance the self-satisfaction of these individuals, interventions should focus especially on decreasing self-critical rumination and increasing self-compassion. Public health professionals should make efforts to prevent children from experiencing psychological maltreatment, which can adversely impact their subjective well-being in adulthood. The study acknowledges its limitations, and suggestions for future research are highlighted in light of the existing literature.
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Monte Carlo computer simulations were used to investigate the performance of three χ–2 test statistics in confirmatory factor analysis (CFA). Normal theory maximum likelihood χ–2 (ML), Browne's asymptotic distribution free χ–2 (ADF), and the Satorra-Bentler rescaled χ–2 (SB) were examined under varying conditions of sample size, model specification, and multivariate distribution. For properly specified models, ML and SB showed no evidence of bias under normal distributions across all sample sizes, whereas ADF was biased at all but the largest sample sizes. ML was increasingly overestimated with increasing nonnormality, but both SB (at all sample sizes) and ADF (only at large sample sizes) showed no evidence of bias. For misspecified models, ML was again inflated with increasing nonnormality, but both SB and ADF were underestimated with increasing nonnormality. It appears that the power of the SB and ADF test statistics to detect a model misspecification is attenuated given nonnormally distributed data. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
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Asymptotically distribution-free efficient estimates are obtained for a large class of models and estimators, all based on a postulate of the form: V T(s - converges in law to a multivariate normal distribution with s+= u(O) being a function of a set of structural parameters under the null hypothesis. First, we deal with minimum x2 or nonlinear generalized least squares estimation under nonlinear constraints and con- sider the problems of consistency, asymptotic normality and efficiency, bias, and tests of fit and restrictions. Thereafter, we develop the parallel theory for an estimator obtained by linearization of the structural model as well as constraint functions on the parameters. Linearized estimators and tests based on a one-step improvement from an initial consistent estimator are shown to have the same optimal statistical proper- ties as their fully iterated counterparts. The classical psychometric factor analytic model, the econometric simultaneous equation system, and related models provide illustrations of the theory. A number of new estimators and their asymptotic distributions are described. New perspectives on old estimators are also offered.
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A nonlinear mean- and covariance-structure model for one or more groups is constructed. The model subsumes the usual linear model considered in the literature. It is then shown how to estimate the parameters of the model and the asymptotic covariance matrix of the parameter estimates using pseudo-maximum likelihood (PML) estimation. The resulting estimates are strongly consistent under general regularity conditions, provided only that the model for the first two moments is correctly specified. Nevertheless, because the data are not necessarily drawn from a multivariate normal distribution, the usual likelihood ratio tests for model comparisons in mean- and covariance-structure models do not apply. Wald tests and Lagrange multiplier tests may be used to implement such comparisons. Next, the standard results on ML estimation with missing data are extended to the case of PML estimation with missing data, and the results are applied to the model. The approach to the missing-data problem adopted, which decomposes the pseudo-log-likelihood function from normal theory into a sum of individual components, cannot generally be implemented by using existing mean- and covariance-structure programs. In some important instances, however, the approach can be implemented by using one of the standard programs (e.g., LISREL). Finally, an example is used to illustrate the approach used. In particular, data from various sources are combined to circumvent an omitted-variables problem in a linear system of equations. The example is somewhat novel because there is no complete data sample from which the model could be estimated. Comments are made on other research situations where data can be combined from multiple sources in the absence of a complete data sample to estimate models that could not otherwise be considered.
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Covariance structure analysis uses χ–2 goodness-of-fit test statistics whose adequacy is not known. Scientific conclusions based on models may be distorted when researchers violate sample size, variate independence, and distributional assumptions. The behavior of 6 test statistics was evaluated with a Monte Carlo confirmatory factor analysis study. The tests performed dramatically differently under 7 distributional conditions at 6 sample sizes. Two normal-theory tests worked well under some conditions but completely broke down under other conditions. A test that permits homogeneous nonzero kurtoses performed variably. A test that permits heterogeneous marginal kurtoses performed better. A distribution-free test performed spectacularly badly in all conditions at all but the largest sample sizes. The Santorra-Bentler scaled test performed best overall. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
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An investigation of the distributional characteristics of 440 large-sample achievement and psychometric measures found all to be significantly nonnormal at the alpha .01 significance level. Several classes of contamination were found, including tail weights from the uniform to the double exponential, exponential-level asymmetry, severe digit preferences, multimodalities, and modes external to the mean/median interval. Thus, the underlying tenets of normality-assuming statistics appear fallacious for these commonly used types of data. However, findings here also fail to support the types of distributions used in most prior robustness research suggesting the failure of such statistics under nonnormal conditions. A reevaluation of the statistical robustness literature appears appropriate in light of these findings. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
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The analysis of moment structures originated with the factor analysis model and with some simple pattern hypotheses concerning equality of elements of mean vectors and covariance matrices. They have more recently received considerable attention and been expanded to incorporate a variety of additional models. Covariance structures, some with associated mean structures, occur in psychology, economics, education, marketing, sociology, biometrics, and other disciplines. Most models involving covariance structures that are in current use are related to the factor analysis model in some way, either by being special cases with restrictions on parameters or, more commonly, extensions incorporating additional assumptions.
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Monte Carlo computer simulations were used to investigate the performance of three χ2 test statistics in confirmatory factor analysis (CFA). Normal theory maximum likelihood χ2 (ML), Browne's asymptotic distribution free χ2 (ADF), and the Satorra-Bentler rescaled χ2 (SB) were examined under varying conditions of sample size, model specification, and multivariate distribution. For properly specified models, ML and SB showed no evidence of bias under normal distributions across all sample sizes, whereas ADF was biased at all but the largest sample sizes. ML was increasingly overestimated with increasing nonnormality, but both SB (at all sample sizes) and ADF (only at large sample sizes) showed no evidence of bias. For misspecified models, ML was again inflated with increasing nonnormality, but both SB and ADF were underestimated with increasing nonnormality. It appears that the power of the SB and ADF test statistics to detect a model misspecification is attenuated given nonnormally distributed data.
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The use of sample covariance matrices constructed with pairwise deletion for data missing completely at random (SPW) is addressed in a simulation study based on 3 sample sizes (n = 200, 500, 1,000) and 5 levels of missing data (%miss = 0, 1, 10, 25, and 50). Parameter estimates were unbiased, parameter variability was largely explicable in terms of the number of nonmissing cases, and no sample covariance matrices were nonpositive definite except when %miss was 50 and the sample size was 200. However, nominal χ test statistics (and, thus, fit indices based on χs) were substantially biased by %miss and its interaction with N. Corrected χs based on the minimum, mean, and maximum number of nonmissing cases per measured variables and cases per covariance term (NPC) reduced but did not eliminate the bias. Empirically derived power functions did substantially better but may not generalize to other situations. Whereas the minimum NPC (the default in the SPSS version of LISREL) is probably better than most simple alternatives in many applications, the problem of how to assess fit for models fit to SPWS has no simple solution; caution is recommended, and there is need for further research with more suitable methods for this problem.
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The t distribution provides a useful extension of the normal for statistical modeling of data sets involving errors with longer-than-normal tails. An analytical strategy based on maximum likelihood for a general model with multivariate t errors is suggested and applied to a variety of problems, including linear and nonlinear regression, robust estimation of the mean and covariance matrix with missing data, unbalanced multivariate repeated-measures data, multivariate modeling of pedigree data, and multivariate nonlinear regression. The degrees of freedom parameter of the t distribution provides a convenient dimension for achieving robust statistical inference, with moderate increases in computational complexity for many models. Estimation of precision from asymptotic theory and the bootstrap is discussed, and graphical methods for checking the appropriateness of the t distribution are presented.
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Contents: Preface Frequently Used Symbols and Notation List of Figures and Tables CHAPTER 1: Linear Regression and Classical Path Analysis Overview and Key Points. Linear Ordinary Least Squares Regression. Classical Path Analysis. Summary. Exercises. Recommended Readings. CHAPTER 2: Confirmatory Factor Analysis. Overview and Key Points. Specification and Identification of a CFA Model. Data-Model Fit. Model Modification. Validity and Reliability from a CFA Perspective. Summary. Exercises. Recommended Readings. CHAPTER 3: General Structural Equation Modeling. Overview and Key Points. Specification and Identification of a General Structural Equation Model. The Direct, Indirect, and Total Structural Effect Components. Parameter Estimation. The Structural Equation Modeling Process: An Illustrated Review and Summary. Conclusion. Exercises. Recommended Readings. APPENDIX A: The Simplis Command Language. APPENDIX B: Location, Dispersion and Association. APPENDIX C: Matrix Algebra APPENDIX D: Descriptive Statistics for the SES Analysis. APPENDIX E: Descriptive Statistics for the HBI Analysis. References. Index.
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This paper proposes an extension of generalized linear models to the analysis of longitudinal data. We introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence. The estimating equations are derived without specifying the joint distribution of a subject's observations yet they reduce to the score equations for niultivariate Gaussian outcomes. Asymptotic theory is presented for the general class of estimators. Specific cases in which we assume independence, m-dependence and exchangeable correlation structures from each subject are discussed. Efficiency of the pioposecl estimators in two simple situations is considered. The approach is closely related to quasi-likelihood.
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An asymptotic theory for canonical correlation analysis is given for multivariate populations with finite fourth moments. The asymptotic distributions of the sample canonical correlation coefficients and of statistics used for testing hypotheses about the population coefficients involve the fourth order cumulants of the parent population and are sensitive to departures from normality. These asymptotic distributions have surprisingly simple forms in the case of elliptical populations; here a modified test statistic with a chi-squared approximation can be used for testing the hypothesis that some of the population coefficients are zero. Finally we note that, when sampling from elliptical populations, the asymptotic distributions of test statistics used in some other multivariate procedures are similarly simple.
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Influence functions are derived for the parameters in covariance structure analysis, where the parameters are estimated by minimizing a discrepancy function between the assumed covariance matrix and the sample covariance matrix. The case of confirmatory factor analysis is studied precisely with a numerical example. Comparing with a general procedure called one-step estimation, the proposed procedure has two advantages:1) computing cost is cheaper, 2) the property that arbitrary influence can be decomposed into a fi-nite number of components discussed by Tanaka and Castano-Tostado(1990) can be used for efficient computing and the characterization of a covariance structure model from the sensitivity perspective. A numerical comparison is made among the confirmatory factor analysis and some procedures of ex-ploratory factor analysis by using the decomposition mentioned above.
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This article examines the adjustment of normal theory methods for the analysis of covariance structures to make them applicable under the class of elliptical distributions. It is shown that if the model satisfies a mild scale invariance condition and the data have an elliptical distribution, the asymptotic covariance matrix of sample covariances has a structure that results in the retention of many of the asymptotic properties of normal theory methods. If a scale adjustment is applied, the likelihood ratio tests of fit have the usual asymptotic chi-squared distributions. Difference tests retain their property of asymptotic independence, and maximum likelihood estimators retain their relative asymptotic efficiency within the class of estimators based on the sample covariance matrix. An adjustment to the asymptotic covariance matrix of normal theory maximum likelihood estimators for elliptical distributions is provided. This adjustment is particularly simple in models for patterned covariance or correlation matrices. These results apply not only to normal theory maximum likelihood methods but also to a class of minimum discrepancy methods. Similar results also apply when certain robust estimators of the covariance matrix are employed.
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Methods of D. B. Rubin [Iteratively reweighted least squares. Entry in S. Kotz, N. L. Johnson and C. B. Read (eds.), Encyclopedia of statistical sciences, Vol. 4 (1983; Zbl 0585.62002)] for robust estimation of a mean and covariance matrix and associated parameters are extended to analyse data with missing values. The methods are maximum likelihood (ML) for multivariate t and contaminated normal models. ML estimation is achieved by the EM algorithm, and involves minor modifications to the EM algorithm for multivariate normal data. The methods are shown to be superior to existing methods in a simulation study, using data generated from a variety of models. Model selection and standard error estimation are discussed with the aid of two real data examples.
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Incomplete or missing data are routinely encountered in structural equation problems. Although current literature supports the use of a direct approach for modeling the missing values in a structural equation model, many situations are not applicable for the effective use of this approach. This leaves the use of an indirect approach for dealing with missing information. There is a general lack of knowledge regarding the efficacy of the use of the indirect approach in structural equation modeling. This article assesses the efficacy of five indirect methods for estimating parameters in a structural equation model with various levels of missing data.
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The structure of the covariance matrix of sample covariances under the class of linear latent variate models is derived, using properties of cumulants. This derivation is employed to provide a general framework for robustness of statistical inference in the analysis of covariance structures arising from linear latent variate models. Conditions for normal theory estimators and test statistics to retain each of their usual asymptotic properties under nonnormality of latent variates are given. Factor analysis and LISREL analysis are discussed as examples. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
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A condition is given by which optimal normal theory methods, such as the maximum likelihood methods, are robust against violation of the normality assumption in a general linear structural equation model. Specifically, the estimators and the goodness of fit test are robust. The estimator is efficient within some defined class, and its standard errors can be obtained by a correction formula applied to the inverse of the information matrix. Some special models, like the factor analysis model and path models, are discussed in more detail. A method for evaluating the robustness condition is given.
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Several test statistics for covariance structure models derived from the normal theory likelihood ratio are studied. These statistics are robust to certain vi-olations of the multivariate normality assumption underlying the classical method. In order to explicitly model the behavior of these statistics, two new classes of nonnormal distributions are defined and their fourth-order moment matrices are obtained. These nonnormal distributions can be used as alternatives to elliptical symmetric distributions in the study of the robustness of a multivariate statisti-cal method. Conditions for the validity of the statistics under the two classes of nonnormal distributions are given. Some commonly used models are considered as examples to verify our conditions under each class of nonnormal distributions. It is shown that these statistics are valid under much wider classes of distributions than previously assumed. The theory also provides an explanation for previously reported Monte-Carlo results on some of the statistics.
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Analysis of Ordinal Categorical Data Alan Agresti Statistical Science Now has its first coordinated manual of methods for analyzing ordered categorical data. This book discusses specialized models that, unlike standard methods underlying nominal categorical data, efficiently use the information on ordering. It begins with an introduction to basic descriptive and inferential methods for categorical data, and then gives thorough coverage of the most current developments, such as loglinear and logit models for ordinal data. Special emphasis is placed on interpretation and application of methods and contains an integrated comparison of the available strategies for analyzing ordinal data. This is a case study work with illuminating examples taken from across the wide spectrum of ordinal categorical applications. 1984 (0 471-89055-3) 287 pp. Regression Diagnostics Identifying Influential Data and Sources of Collinearity David A. Belsley, Edwin Kuh and Roy E. Welsch This book provides the practicing statistician and econometrician with new tools for assessing the quality and reliability of regression estimates. Diagnostic techniques are developed that aid in the systematic location of data points that are either unusual or inordinately influential; measure the presence and intensity of collinear relations among the regression data and help to identify the variables involved in each; and pinpoint the estimated coefficients that are potentially most adversely affected. The primary emphasis of these contributions is on diagnostics, but suggestions for remedial action are given and illustrated. 1980 (0 471-05856-4) 292 pp. Applied