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Using SAS PROC MIXED to fit multilevel models, hierarchical models, and Individual growth models

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Abstract

SAS PROC MIXED is a flexible program suitable for fitting multilevel models, hierarchical linear models, and individual growth models. Its position as an integrated program within the SAS statistical package makes it an ideal choice for empirical researchers and applied statisticians seeking to do data reduction, management, and analysis within a single statistical package. Because the program was developed from the perspective of a "mixed" statistical model with both random and fixed effects, its syntax and programming logic may appear unfamiliar to users in education and the social and behavioral sciences who tend to express these models as multilevel or hierarchical models. The purpose of this paper is to help users familiar with fitting multilevel models using other statistical packages (e.g., HLM, MLwiN, MIXREG) add SAS PROC MIXED to their array of analytic options. The paper is written as a step-by-step tutorial that shows how to fit the two most common multilevel models: (a) school effects models, designed for data on individuals nested within naturally occurring hierarchies (e.g., students within classes); and (b) individual growth models, designed for exploring longitudinal data (on individuals) over time. The conclusion discusses how these ideas can be extended straighforwardly to the case of three level models. An appendix presents general strategies for working with multilevel data in SAS and for creating data sets at several levels.

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... Since bidders' WTP is measured over time, the error terms for bidders are likely to be autocorrelated and heteroscedastic, not independent as required by traditional OLS regressions. To address the research questions at hand with the issues presented by the longitudinal dataset, we opted to employ a multi-level longitudinal modeling approach (Rogosa and Willett, 1985;Singer, 1998;Singer and Willet, 2003 ...
... The above composite multilevel model can also be viewed as a mixed-effects model (Frees, 2006, Singer, 1988, and such a model can be estimated with GLS (generalized least squares) or maximum likelihood estimation method. Following Singer (1998), we opted to use SAS PROC MIXED, which uses maximum likelihood estimation method to estimate parameters. ...
... Maximum likelihood estimates are sometimes preferred because even without normality assumption, they are unbiased, efficient and asymptotically normal with known variance (Singer, 1998, Frees, 2006. ...
... Growth curve analyses can be performed as a special case of hierarchical linear modeling (HLM, also known as multilevel models, random-coefficients models, random-effects models, mixed models, and seemingly unrelated regression (Heo et al., 2003;Raudenbush & Bryk, 2002;Singer, 1998)). HLM is appropriate for growth curve analyses because there are at least two hierarchical levels of analysis: within participant (changes across time for each participant) and across participants (changes to each participant's growth curve intercept and slopes due to covariates). ...
... The hypothesized shapes are coded into four versions of the time variable as shown in Table 1. The baseline value for time in each case is coded as zero to allow for the intercept to have a meaningful interpretation-as the grand mean of baseline outcome values (Biesanz et al., 2004;Mehta & West, 2000;Singer, 1998). For the same reason all explanatory variables (other than group designation) are centered at their grand mean values. ...
... The Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) fit statistics are compared across models to determine which growth curve shape best fit the sample as a whole and each group. Both fit statistics are based on the log likelihood, are in the form of "smaller is better," and penalize the log likelihood for the number of parameters estimated (Raudenbush & Bryk, 2002;Singer, 1998). If the difference between BIC statistics for two models is greater than 10, that can be considered "very strong evidence" that the model with the lower BIC is a better fit to the data (Raftery, 1995). ...
... Due to the limited number of previous studies that used a multi-level analysis to examine variables related to participation in health screenings, regional level variables were selected based on a literature review of studies that examined factors affecting participation in cancer screenings [12,13,21] and studies related to health behaviors [17,19,[22][23][24][25][26][27][28][29]. Regional level variables were selected using the data from the 2017 CHS, and regional indicators for city/county/district units were tak-en from the Korean Statistical Information Service and the National Health Insurance Service (NHIS) website. ...
... The 2017 CHS, which provided the data used in this study, collected multi-level data (hierarchical data) in which sample households were included in each sample region, and each individual was included in each sample household. Each of these groups was characterized by heterogeneity and dependency among individuals within the group [22]. Thus, a multilevel analysis was appropriate for overcoming ecological error. ...
... The high screening rate of participants who lived in singleperson households and were younger than 40 could be attributed to the need to participate in economic activity to maintain their lives as single people, and individuals who are employed likely have more opportunities to attend general health screenings or special screenings for their workplaces. Similarly, among the participants who were aged under 40, the screening rate of those aged 30-39 was higher than that of those aged [19][20][21][22][23][24][25][26][27][28][29]. This result could also likely be attributed to economic activity, though further detailed investigations are needed to confirm these inferences. ...
Article
Objectives: This study divided the factors that affect participation in health screenings into individual, household, and regional levels and conducted a multi-level analysis to identify the factors related to participation in health screenings. Methods: Participants from the 2017 Community Health Survey were classified into 2 groups (under 40 and 40 or older). A multi-level logistic regression analysis was conducted to identify the factors that affected participation in health screenings. Results: The screening rate of the participants was 69.7%, and it was higher among participants aged 40 and older (80.3%) than it was among participants younger than 40 (49.8%). At the individual level, the factors that influenced participation in health screenings included age, economic activity, smoking status, physician-diagnosed hypertension, and a moderate or high physical activity level. At the household level, the odds ratio of participation in health screenings was high for participants who lived in single-person households, lived with a spouse, earned a high monthly household income, and were not beneficiaries of national basic livelihood security. At the regional level, the odds ratio at the 95% confidence interval level of participation in health screenings was high for participants who had trust in the local community and lived in an area with a proportionally high social welfare budget. Conclusions: This study analyzed nationalwide data and confirmed that individual, household, and regional characteristics affected participation in health screenings. Therefore, policies that prioritize the improvement of regional level factors and especially household level factors are likely to be the most effective for improving the screening rate.
... Furthermore, previous studies (Chassin et al., 1990;Choi et al., 1997;Goldade et al., 2012;Sargent et al., 2017) including longitudinal studies largely examined or evaluated cigarette smoking frequency and it correlates without assessing the differences in cigarette smoking frequency between-person and within-person. These within-person and between-person variations in cigarette smoking patterns are important as well because they can help to effectively tailor interventions at individual and national levels (Maruyama et al., 2009;Piasecki et al., 2016;Singer, 1998). Multilevel models are instrumental in examining between-person and within-person variations in cigarette smoking patterns, where repeated measures of cigarette smoking frequency are nested within persons (Belsky et al., 2013;Piasecki et al., 2016;Singer, 1998). ...
... These within-person and between-person variations in cigarette smoking patterns are important as well because they can help to effectively tailor interventions at individual and national levels (Maruyama et al., 2009;Piasecki et al., 2016;Singer, 1998). Multilevel models are instrumental in examining between-person and within-person variations in cigarette smoking patterns, where repeated measures of cigarette smoking frequency are nested within persons (Belsky et al., 2013;Piasecki et al., 2016;Singer, 1998). Thus, these models help to examine changes in cigarette smoking frequency among persons as a function of time. ...
... Data analyses were performed using SAS 9.4 (SAS, 2013), and an alpha level of 0.05 was used to determine significant estimates. We used PROC MIXED, a linear mixed model (LMM) procedure in SAS, to fit the models (Piasecki et al., 2016;Singer, 1998). PROC MIXED was used to model the random and fixed effects as well as accommodate missing data, which are common in longitudinal studies (Piasecki et al., 2016;Singer, 1998). ...
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Background Understanding differences in cigarette smoking patterns such as the frequency between-person and within-person is essential for tailored tobacco health education interventions. Previous studies, however, mostly limited analysis to computation of cigarette smoking frequency and its correlates. This article used multilevel models to examine between-person and within-person variations in cigarette smoking patterns over a 13-year period. Methods We merged the National Longitudinal Study of Adolescent Health public-use data waves 1–4 into one longitudinal dataset for use in this study. Our analysis was based on the past-month’s average number of cigarette smoked per day. We used linear mixed model approach to fit multilevel models. Results The average number of cigarette smoked per day (CPD) among the sample at baseline/wave 1 was 6.92 (SD = 8.18). Time of observation in years (β = 0.455 (p < .001), age (β = 0.355, p < .001), past-year alcohol use frequency (β = −0.329, p < .001), and illicit drug use (β = 1.128, p < .001) were associated with average number of CPD. There were significant variations in the average number of CPD between-person (β = 29.602, p < .001) and within-person (variance = 34.393, p < .001). Conclusions This study demonstrates that rate of change in average number of CPD over years among the study sample could be different between-adolescent and within-adolescent depending on other substance use and demographic factors. Hence, tailored tobacco use educational programs or interventions and policies targeting these adolescents could be designed according to between-adolescent and within-adolescent differences in the average number of CPD trajectories.
... Since bidders' WTP is measured over time, the error terms for bidders are likely to be autocorrelated and heteroscedastic, not independent as required by traditional OLS regressions. To address the research questions at hand with the issues presented by the longitudinal dataset, we opted to employ a multi-level longitudinal modeling approach (Rogosa and Willett, 1985;Singer, 1998;Singer and Willet, 2003 ...
... The above composite multilevel model can also be viewed as a mixed-effects model (Frees, 2006, Singer, 1988, and such a model can be estimated with GLS (generalized least squares) or maximum likelihood estimation method. Following Singer (1998), we opted to use SAS PROC MIXED, which uses maximum likelihood estimation method to estimate parameters. ...
... Maximum likelihood estimates are sometimes preferred because even without normality assumption, they are unbiased, efficient and asymptotically normal with known variance (Singer, 1998, Frees, 2006. ...
... In our discussion with the Notes: n = 144; unstandardized coefficients were reported; Pseudo R 2 value indicates the percentage of explainable level 1 variance in the dependent variable. It was calculated according to the formula recommended by Kreft and De Leeuw (1998) and Singer (1998). + p < .10; ...
... However, the direction of the moderating effect of cognitive ability aligned with our expectation: when cognitive ability was low (i.e., one standard deviation below the mean), the curve capturing the Notes: n = 198; unstandardized coefficients were reported; Pseudo R 2 value indicates the percentage of explainable level 1 variance in the dependent variable. It was calculated according to the formula recommended by Kreft and De Leeuw (1998) and Singer (1998). + p < .10; ...
Article
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Drawing on the resource allocation theory, job crafting, and creativity literature, this paper examines a curvilinear (inverted U-shaped) relationship between job crafting and creative performance. Also investigated is how this curvilinear relationship is moderated by individuals’ cognitive ability and time scarcity. Two multi-wave multi-source survey studies conducted in mainland China provide convergent support. In Study 1, using data from 144 editors and their immediate supervisors, we confirmed our prediction that job crafting had an inverted U-shaped relationship with creative performance. In Study 2, the data from 198 matched employee-supervisor pairs replicated the findings in Study 1, while providing further support for the moderating effect of cognitive ability and time scarcity. Specifically, when individuals’ cognitive ability was lower (or time scarcity was higher), the inverted U-shaped relationship between job crafting and creative performance was stronger. We discuss the theoretical and practical implications of these studies.
... Even GEE software emphasizes the longitudinal nature of analysis with users being required to input the clustering or grouping variable using fields such as id or subject, which refer to individuals as the clustering unit. Conversely, MLM books (e.g., Hox et al., 2018;Luke, 2004;Raudenbush & Bryk, 2002) and articles (Singer, 1998) discuss cross-sectional clustered data first and then introduce the concept of growth modeling in later sections. ...
... Compared to a standard GLM, the only additional input required from a researcher to run a model using GEEs is to specify the grouping or clustering variable (e.g., school id) and the working correlation matrix to use, of which there are common types to choose from (e.g., independence, exchangeable). To illustrate the use of GEEs for the modeling of cross-sectionally clustered data, we analyze the High School and Beyond (HSB) data set used by Huang Raudenbush and Bryk (2002) and subsequently by several others in the analysis of clustered data (e.g., Fox, 2016;Huang, 2014;McNeish, 2019;Singer, 1998). An advantage of using such a popular data set is that the data set is readily accessible, 7 is sufficiently large, and researchers who want to learn how to use GEEs can focus on the method rather than the data. ...
Article
The presence of clustered data is common in the sociobehavioral sciences. One approach that specifically deals with clustered data but has seen little use in education is the generalized estimating equations (GEEs) approach. We provide a background on GEEs, discuss why it is appropriate for the analysis of clustered data, and provide worked examples using both continuous and binary outcomes. Comparisons are made between GEEs, multilevel models, and ordinary least squares results to highlight similarities and differences between the approaches. Detailed walkthroughs are provided using both R and SPSS Version 26.
... Because of this modification, we did not conduct an a priori power analysis for multilevel modeling. This is because multilevel models are more robust to issues that reduce power in traditional ANOVA techniques (e.g., missing variables, nonindependent variables, heteroscedasticity; see Singer, 1998;Snijders & Bosker, 1993); thus, multilevel models are as effective, if not more so, at detecting hypothesized effects than ANOVA. Our sample size exceeds minimum sufficient sampling estimates as calculated by simulation studies conducted by Hox (2004, 2005; see also Scherbaum & Ferreter, 2009). ...
... Given the longitudinal nature of our data, we used multilevel modeling to examine the relationship between self-uncertainty, group entitativity, and autonomic stress responses, nesting repeated measurements of SCL or HR (Level 1) within participants (Level 2; Singer, 1998;Hernandez-Lloreda et al., 2004;Kristjansson et al., 2007). As mentioned in 2.1.1, ...
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Groups serve a variety of crucial functions, one of which is the provision of an identity and belief system that impart self-referent information, thereby reducing self-uncertainty. Entitative groups are more attractive for highly uncertain participants seeking groups for identification and self-uncertainty reduction than less entitative groups. The purpose of the current study was to explore how self-uncertainty impacts physiological arousal and stress responses. Using a mixed-methods design (N = 123), we found that self-uncertainty increased physiological arousal (measured via skin-conductance level) and stress responses (measured via heart rate). Furthermore, we found that uncertainty-activated physiological arousal and stress responses were decreased through identification with a high entitativity group. Our findings expand upon uncertainty identity theory by identifying physiological mechanisms that motivate uncertainty reduction.
... Table 3 Study 2-Multilevel polynomial regression results with psychological strain and creative performance as dependent variables Unstandardized coefficients were reported; Pseudo R 2 value indicates the percentage of explainable level 1 variance in the dependent variables. It is calculated according to the formula recommended by Kreft and Leeuw (1998) and Singer (1998) Hypothesis 4 proposed a moderating effect of self-monitoring. In particular, it was predicted that for high self-monitors, the disruptive effect of creative identity asymmetry on psychological strain was stronger than it was for low self-monitors (Hypothesis 4a). ...
... In the table, I represents the creative role identity, R represents the creative reflected appraisal, Z represents the perceived creativity requirement, S represents self-monitoring, and M represents the psychological strain. The pseudo R 2 value indicates the percentage of explainable level 1 variance in the dependent variables and is calculated according to the formula recommended by Kreft and Leeuw (1998) and Singer (1998 Figures 4A and B illustrate the scenarios when selfmonitoring was high versus low. When self-monitoring was high, there was a convex surface, while there was no convex surface when self-monitoring was low, suggesting that the disruptive effect of creative identity asymmetry on psychological strain was strengthened when self-monitoring was high. ...
Article
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Drawing on the identity asymmetry literature, transactional stress theory, and creativity literature, we investigate how a perceived discrepancy between an individual’s creative role identity and others’ views toward his/her creative role identity (i.e., creative identity asymmetry) influences individual’s creative performance via psychological strain. We also examine how perceived creativity requirement and self-monitoring alter the relationships between creative identity asymmetry, psychological strain, and creative performance. Based on two studies (an experimental study and a field study), we found that creative identity asymmetry was positively related to psychological strain and negatively and indirectly related to creative performance. We also found that the effects of negative asymmetry were stronger than positive asymmetry, while perceived creativity requirement and self-monitoring significantly strengthened most of these relationships. Hence, this study contributes to the literature on creativity, identity asymmetry, and stress.
... All analyses were based on 1802 daily units and all analyses used some version of a SAS PROC MIXED statement (Singer, 1998). Ability EI, which varied between subjects, was z-scored (Aiken & West, 1991) and mindfulness, a within-subject predictor, was personcentered, which will focus the analysis on within-person changes in mindfulness rather than between-person differences in mean levels (Enders & Tofighi, 2007). ...
... To examine potential interactive relationships, we performed cross-level model analyses (Singer, 1998). As shown in Table 2, relationships involving mindfulness varied as a function of ability EI levels for both the positive affect and affiliation motivation outcomes. ...
Article
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Relationships between mindfulness and positive affect have been less robust than relationships between mindfulness and negative affect, suggesting that skills in addition to mindfulness may be necessary in transforming mindfulness into a positive psychological force. The present three study program of research (total N = 413) pursued the idea that emotional intelligence (EI), in particular, may infuse mindfulness with social-emotional wisdom, resulting in positive psychological benefits. In Studies 1 and 2, trait-related variations in mindfulness (as assessed by the Mindful Attention Awareness Scale) interacted with an ability-based EI measure to predict positive feelings in employment contexts as well as outcomes related to organizational commitment and citizenship. In Study 3, daily variations in mindfulness interacted with the same ability-based EI measure to predict daily feelings of positive affect and affiliation motivation. These findings highlight synergies among mindfulness and emotional intelligence in supporting positive affect and social engagement.
... TIB and age effects on log alpha power were evaluated with mixed effects analysis. Mixed effects analysis is particularly suited for longitudinal studies because it accounts for the inherent correlations of multiple recordings from the same subject [16]. Analyses included TIB as a class measure with three levels (7, 8.5, 10 h) and age as continuous factor centered by subtracting the mean (13.3 y). ...
... Post hoc analyses of neighboring frequency bands, theta (4-8 Hz), and low beta (12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23), determined whether the relations between waking EEG activity and daytime sleepiness were unique to the alpha frequency band. With effects of sleep duration and time of day accounted for, KSS ratings were related to O1 eyes closed low beta (12-23 Hz, F 1,1958 ...
Article
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Study Objectives To understand how sleep need changes across adolescence our laboratory is carrying out a longitudinal dose-response study on the effects of sleep duration on daytime sleepiness and performance. This report focuses on the relation of the waking alpha (8-12 Hz) electroencephalogram (EEG) to prior sleep duration, whether this relation changes with age, and whether decreased waking alpha power is related to changes in daytime sleepiness, vigilance, and executive functioning. Methods Study participants (n=77) entered the study at ages ranging from 9.86 to 13.98 years and were studied annually for 3 years. Each year participants completed each of three time in bed (TIB) conditions (7, 8.5, or 10 hours) for four consecutive nights. Waking EEG was recorded on the day following the fourth night. Results TIB restriction and resultant sleep loss were associated with reduced alpha power with the effect being stronger for the eyes closed condition. TIB restriction altered the power spectrum within the alpha range by increasing the frequency of maximum alpha power. Alpha power decreased with age, but the effect of TIB restriction did not decrease with age. Reduced alpha power was associated with small but significant increases in subjective and objective sleepiness but was not associated with changes in vigilance or executive functioning. Conclusions We interpret the alpha depression following sleep loss as incomplete sleep dependent recuperation that contributes to daytime sleepiness. The absence of a decrease in TIB effects with age indicates that this sleep need measure does not decrease over early to mid-adolescence.
... Multilevel regression properly incorporates predictors associated with both clone and genotype. This allowed us to calculate error terms at the clonal level for trait values and error terms at the genotypic level for plasticity (e.g., Raudenbush & Bryk, 2002;Singer, 1998). Also, we could examine the effects of plasticity predictors on our fitness proxy, independent of any possible correlations between trait values and trait plasticities. ...
Article
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In exploring the roles of phenotypic plasticity in the establishment and early evolution of invading species, little empirical attention has been given to the importance of correlational selection acting upon suites of functionally related plastic traits in nature. We illustrate how this lack of attention has limited our ability to evaluate plasticity's role during invasion and also, the costs and benefits of plasticity. We addressed these issues by transplanting clones of European‐derived Plantago lanceolata L. genotypes into two temporally variable habitats in the species' introduced range in North America. Phenotypic selection analyses were performed for each habitat to estimate linear, quadratic, and correlational selection on phenotypic trait values and plasticities in the reproductive traits: flowering onset and spike and scape lengths. Also, we measured pairwise genetic correlations for our “colonists.” Results showed that (a) correlational selection acted on trait plasticity after transplantation, (b) selection favored certain combinations of genetically correlated and uncorrelated trait values and plasticities, and (c) using signed, instead of absolute, values of plasticity in analyses facilitated the detection of correlational selection on trait value‐plasticity combinations and their adaptive value. Based on our results, we urge future studies on species invasions to (a) measure correlational selection and (b) retain signed values of plasticity in order to better discriminate between adaptive and maladaptive plasticity.
... Effects of CG inclusion on DMI, ADG, G:F ratio, pH, rumen VFA profiles, blood parameters and carcass traits were tested by orthogonal polynomial contrasts. Orthogonal contrasts for equally spaced treatments were done to determine linear and quadratic effects (Singer, 1998). ...
Article
The objective of this experiment was to determine the effects of feeding varying levels of crude glycerine (CG) on dry matter intake (DMI), animal performance, carcass traits and rumen volatile fatty acids (VFA) concentration in meat goats. Twenty-four intact male Boer goats (23.9 ± 1.0 kg initial BW and 4-5 months of age) were randomly assigned to one of four experimental diets (n = 6) containing 30% bermudagrass hay plus 70% concentrate mix with 0, 5, 10 or 15% CG in the diet on an as-fed basis, substituted for the corn portion of the concentrate. Feed offered and refusals were monitored daily for 84 days. Goats were weighed at 28-days interval. Blood and rumen samples were collected on day 84. At the end of the 84-days feeding period, goats were harvested, and carcass characteristics measured. Feed intake, average daily gain (ADG), gain-to-feed ratio (G:F), carcass traits and VFA concentrations were analysed as a completely randomized design. The CG did not influence animal body weight (BW) changes, ADG and G:F ratio but tended to (p = 0.06) decrease DMI. Molar per cent propionic acid increased linearly (p < 0.05) with increasing CG. The acetate: propionate (A:P) ratio decreased (p < 0.05) with increasing amounts of CG in the diet. The CG addition tended to increase (p = 0.09) the longissimus muscle (LM area) in meat goats. In conclusion, CG can replace corn in diet for growing meat goats when fed up to 15% of diet, improving ruminal propionate concentration, but decreasing A:P ratio without affecting animal performance and carcass traits.
... The data analysis strategy used mixed linear models to predict white blood cell ratios based on case-control status, time prior to the case-control reference date and interactions between time and case-control status, time squared and case-control status and time cubed and case-control status [35,36]. The models were fit with random intercepts and random slopes and with blood tests clustered within men [37,38]. Men with at least one eligible WBC measurement were included in the analyses: within this modeling framework, even a single value contributed information to estimating the mean MLR and NLR value at the time of blood test before the reference date. ...
Article
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Systemic inflammation may increase risk for prostate cancer progression, but the role it plays in prostate cancer susceptibility is unknown. From a cohort of over 10,000 men who had either a prostate biopsy or transurethral resection that yielded a benign finding, we analyzed 517 incident prostate cancer cases identified during follow-up and 373 controls with one or more white blood cell tests during a follow-up period between one and 18 years. Multilevel, multivariable longitudinal models were fit to two measures of systemic inflammation, neutrophil-to-lymphocyte ratio (NLR) and monocyte-to-lymphocyte ratio (MLR), to determine NLR and MLR trajectories associated with increased risk for prostate cancer. For both measures, we found no significant differences in the trajectories by case/control status, however in modeling NLR trajectories there was a significant interaction between race (white or Black and case-control status. In race specific models, NLR and MLR values were consistently higher over time among white controls than white cases while case-control differences in NLR and MLR trajectories were not apparent among Black men. When cases were classified as aggressive as compared to non-aggressive, the case-control differences in NLR and MLR values over time among white men were most apparent for non-aggressive cases. For NLR among white men, significant case-control differences were observed for the entire duration of observation for men who had inflammation in their initial prostate specimen. It is possible that, among white men, monitoring of NLR and MLR trajectories after an initial negative biopsy may be useful in monitoring prostate cancer risk.
... At the between-infant level (Level 2), we assessed how time-invariant factors (age at walk onset) accounted for variance in infants' intercept and slope terms. An additional advantage of HLM is that it accommodates missing and unequally spaced data (e.g., Huttenlocher et al., 1991;Singer, 1998 Here, c`oefficients β 01 and β 11 represent the effect that a 1-month increase in the age at walk onset has on infants' intercept and slope terms. ...
Article
Learning to walk allows infants to travel faster and farther and explore more of their environments (e.g., Adolph & Tamis‐LeMonda, 2012). In turn, walking may have a cascading effect on infants’ communication and subsequent responses from caregivers. We tested for an inflection point—a dramatic shift in the developmental progression—in infant communication and caregiver responses when infants started walking. We followed 25 infants longitudinally over 7 months surrounding the onset of walking (Mean walk onset age = 11.76 months, SD = 1.56). After learning to walk, the pace of gesture growth (but not vocalization growth) increased substantially, and infants increasingly coordinated gestures and vocalizations with locomotion (e.g., by walking to a caregiver and showing off a toy bear). Consequently, caregivers had more opportunities to respond contingently to their infants during walking months compared to crawling months (e.g., “What did you find? Is that your bear?”). Changes in communication were amplified for infants who began walking at older ages, compared to younger walkers. Findings suggest that learning to walk marks a point in development when infants actively communicate in new ways, and consequently elicit rich verbal input from caregivers.
... These latter analyses offer a sensitive technique for modeling change in continuous variables and use maximum likelihood estimation to accommodate missing data (Singer, 1998). fMRI data analysis. ...
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We tested if we could replicate the main effect relations of elevated striatum and lateral orbitofrontal cortex (OFC) response to high-calorie food stimuli to weight gain reported in past papers in six prospective datasets that used similar fMRI paradigms. Participants in Study 1 (N = 37; M age = 15.5), Study 2 (N = 160; M age = 15.3), Study 3 (N = 130; M age = 15.0), Study 4 (N = 175; M age = 14.3), Study 5 (N = 45; M age = 20.8), and Study 6 (N = 49; M age = 31.1) completed fMRI scans at baseline and had their BMI and body fat (Studies 4 and 6 only) measured at baseline and over follow-ups. Elevated striatal response to palatable food images predicted BMI gain in Studies 1 and 6 and body fat gain in Study 6. Lateral OFC activation did not predict weight gain in any of the six studies. Results provide limited support for the hypothesis that elevated reward region responsivity to palatable food images predicts weight gain. Factors that make replication difficult are discussed and potential solutions considered.
... As in the previous study [15], SAS mixed-effects analysis was used to evaluate the effects of the three TIB sleep schedules and age on sleep duration measures, EEG power and EEG energy. Mixed-effects analysis is particularly suited for longitudinal data because it accounts for the correlation between multiple observations on the same subject [21]. We treated TIB as a categorical measure and age as a continuous measure. ...
Article
Study Objectives This report describes findings from an ongoing longitudinal study of the effects of varied sleep durations on wake and sleep electroencephalogram (EEG) and daytime function in adolescents. Here, we focus on the effects of age and time in bed (TIB) on total sleep time (TST) and nonrapid eye movement (NREM) and rapid eye movement (REM) EEG. Methods We studied 77 participants (41 male) ranging in age from 9.9 to 16.2 years over the 3 years of this study. Each year, participants adhered to each of three different sleep schedules: four consecutive nights of 7, 8.5, or 10 h TIB. Results Altering TIB successfully modified TST, which averaged 406, 472 and 530 min on the fourth night of 7, 8.5, and 10 h TIB, respectively. As predicted by homeostatic models, shorter sleep durations produced higher delta power in both NREM and REM although these effects were small. Restricted sleep more substantially reduced alpha power in both NREM and REM sleep. In NREM but not REM sleep, sleep restriction strongly reduced both the all-night accumulation of sigma EEG activity (11–15 Hz energy) and the rate of sigma production (11–15 Hz power). Conclusions The EEG changes in response to TIB reduction are evidence of insufficient sleep recovery. The decrease in sigma activity presumably reflects depressed sleep spindle activity and suggests a manner by which sleep restriction reduces waking cognitive function in adolescents. Our results thus far demonstrate that relatively modest TIB manipulations provide a useful tool for investigating adolescent sleep biology.
... To determine the unique effects of each combination on a given day on consumption and consequences, we conducted a series of generalized linear mixed-effects models (GLMMs) using SAS PROC GLIMMIX and Laplace approximation for missing data. GLMMs, an extension of multilevel modeling, are necessary to account for clustering that is inherent for nested data that would violate the assumption of independent errors in ordinary least squares regression (Curran and Bauer, 2011;Hox et al., 2017;Raudenbush and Bryk, 2002;Singer, 1998). For each reference group, we analyzed three outcomes, which were not normally distributed: (1) any negative consequence (binomial distribution), (2) number of drinks (count; negative binomial distribution), and (3) number of cannabis uses (count; negative binomial distribution). ...
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Background Alcohol and marijuana/cannabis are frequently used simultaneously (i.e., SAM use). SAM use is complex, and the ways in which alcohol and cannabis are simultaneously used may reveal differential effects. The purpose of this study was to examine day‐level effects of distinct alcohol and cannabis product combinations on simultaneous use and consequences on that day. Methods College student SAM users (N = 274; 50% women; Mage = 19.82 years) were recruited to complete 54 days of data collection, including 5 repeated daily surveys each day. We identified 12 distinct product combinations reported during SAM‐use days. We tested 4 reference groups, with one reflecting the most common use pattern and 3 potentially risky use patterns. We considered 3 outcomes (negative consequences, number of drinks, and number of cannabis uses) and used generalized linear mixed‐effects models disentangling within‐ from between‐person effects in all analyses. Results Using multiple products (≥2) of alcohol was consistently linked to higher odds of experiencing a negative consequence. Combining beer with only one cannabis product (leaf or concentrate) was consistently associated with lower odds of a consequence. Combining cannabis with multiple alcohol products was associated with heavier alcohol consumption. Using dual cannabis products also was associated with heavier cannabis consumption, but this pattern was not significantly different than using concentrate only on a given day. Conclusion This is the first study to examine day‐level influences of distinct alcohol and cannabis product combinations on consumption and consequences among young adult SAM users. Findings suggest that mixing alcohol products confers greater risk for negative consequences and heavier consumption, whereas there is little difference in cannabis consumption when using concentrate only vs. 2 cannabis products on a given day, except for concentrate + beer. Our findings support existing protective strategies of not mixing alcohol products and avoiding use of cannabis concentrate for SAM use as well.
... Because randomization occurred on a clinic-byclinic basis, yet measures were taken on individual participants, hierarchical models were necessary to account for the correlated nature of the repeated measures and clustering of participants within sites. 44,45 Thus, categorical outcome data were analyzed using logistic regression with estimation via generalized estimating equations (SAS PROC GLIMMIX) and continuous outcome data were analyzed using linear mixed models with repeated measures (SAS PROC MIXED). The within-subject, fixed factor was intervention vs control status; participant and clinic were treated as random effects. ...
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Background Bottle-fed infants are at greater risk for overfeeding and rapid weight gain (RWG); evidence-based strategies for promoting healthy bottle-feeding practices are needed. Objective Our aim was to assess whether policy, systems, and environmental (PSE) strategies for promoting responsive bottle-feeding practices within the Special Supplemental Nutrition Program for Women, Infants, and Children (WIC) were associated with lower risk for RWG. Design We conducted a matched-pair cluster randomized trial. PSE strategies were implemented at 3 WIC clinics in Los Angeles County. PSE clinics were compared with 3 matched control clinics. Mothers and infants were assessed when infants were newborn and 3 months and 6 months of age. Participants/setting Participants were mothers (n = 246) who enrolled their newborn infants (younger than 60 days) into WIC between May and August 2019. Main outcome measures Infant weight was assessed and standardized to sex- and age-specific z scores. RWG was defined as weight-for-age z score change > 0.67. Mothers completed questionnaires assessing responsive and pressuring feeding styles, breast- and bottle-feeding patterns, and perceptions of WIC experiences. Statistical analyses performed Logistic regression with estimation via generalized estimating equations and linear mixed models with repeated measures assessed effects of PSE strategies on categorical and continuous outcomes, respectively. Results Infants in PSE clinics had significantly lower likelihood of exhibiting RWG (P = .014) than infants in control clinics. Mothers in PSE and control clinics reported similar levels of responsive and pressuring feeding style and similar prevalence of breastfeeding and bottle-feeding. Mothers in PSE clinics trended toward feeling better supported with respect to their decision to bottle-feed (P = .098) and had more stable intentions to stay in the WIC program (P = .002) compared with mothers in control clinics. Conclusions PSE strategies focused on promoting more inclusive assessment of infant feeding, tailored bottle-feeding counseling, and increased education and support for responsive bottle-feeding were associated with lower risk for RWG among WIC infants.
... 7 This tool is employed to calculate the probability that a patient will develop coronary heart condition in 5 or 10 years and has been widely integrated into disorder prevention and management throughout the planet. [8][9][10][11][12] Risk algorithms are widely recommended by medical societies for appropriate identification of patients that may have the benefit of specific interventions. This is often exemplified in clinical guidelines for pharmacologic interventions like cholesterol-lowering medications. ...
... 2.1 Data generating process Our notation may be described as the composite form for nested multilevel structure Singer and Willett 2003;Singer 1998). We use subscript i to index the individual (sometimes known as varying at level 1) and j for the group index (level 2). ...
... These multi-level analyses were run with Proc Mixed in SAS 9.3 (SAS Institute, Inc; Cary, NC, USA), which is suited for data with repeated measures, correlations amongst observations within an individual subject and missing data. The response of individual subjects is first modeled, and then, the estimates for each individual are combined in a group analysis (Singer 1998;Ballinger 2004;Diggle et al. 1996;Gibbons et al. 1993;Kreft and De Leeuw 1998). Tukey's post hoc tests compared active doses to placebo. ...
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AimsIntravenous (IV) misuse of the µ opioid analgesic oxymorphone has caused significant public health harms; however, no controlled data on its IV abuse potential are available. The primary aims of this pilot study were to directly compare IV oxymorphone to IV oxycodone, morphine, and hydromorphone on a subjective measure of drug liking and to assess relative potency.Methods Participants (n = 6) with opioid use disorder, physical dependence, and current IV use completed this two-site, within-subject, double-blind, placebo-controlled, inpatient pilot study. During each session, one IV dose (mg/70 kg) was administered: oxymorphone (1.8, 3.2, 5.6, 10, 18, 32), hydromorphone (1.8, 3.2, 5.6, 10, 18), oxycodone (18, 32, 56), morphine (18, 32), and placebo. Data were collected before and for 6 h after dosing. Primary outcomes included safety/physiological effects, subjective reports of drug liking, and relative potency estimates.ResultsAll active test drugs produced prototypical, dose-related µ opioid agonist effects (e.g., miosis). Oxymorphone was more potent than the comparator opioids on several measures, including drug liking and respiratory depression (p < 0.05). Across abuse-related subjective outcomes, oxymorphone was 2.3–2.8-fold more potent than hydromorphone and 12.5–14-fold more potent than oxycodone (p < 0.05).Conclusions Despite the relatively small sample size, this pilot study detected robust oxymorphone effects. Oxymorphone was far more potent than the comparator opioids, particularly on abuse potential outcomes. Overall, these findings may help explain surveillance reports that demonstrate, after adjusting for prescription availability, oxymorphone is injected at the highest frequency, relative to other prescription opioids.
... Descriptive statistics were used to summarize baseline characteristics and study variables. Multilevel regression was used to analyze the temporal course of SWB and other repeated measures with adjustment for missing data pattern, which could explore intra-and inter-individual differences in baseline and trajectories of study variables [32]. The outcome variables are conceptualized to be nested within individuals, and the growth modeling of change in these variables has two levels. ...
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PurposeAlthough spiritual well-being (SWB) is gaining increasing attention within the international palliative care (PC) guidelines, a lack of insight exists into the correlates and course of SWB among cancer patients. We therefore conducted a prospective observational study to capture trend of SWB and to identify their predictors in Chinese inpatients with terminal cancer receiving short-term PC.MethodsA prospective observational study was conducted of terminal cancer inpatients in the hospice ward, Shengjing Hospital of China Medical University. A total of 108 patients completed self-report questionnaires on Functional Assessment of Chronic Illness Therapy-Spiritual Well-being, Hospital Anxiety and Depression Scale, Numerical Rating Scales, and Life Orientation Scale-Revised anonymously at baseline; SWB, depression, anxiety, and pain were subsequently assessed at 1-week interval. Multilevel regression was used to analyze the temporal course and predictors of SWB.ResultsPatients’ existential well-being (B = − 0.99, p = 0.008; 95%CI = − 1.72 to − 0.26) and meaning dimension (B = − 0.87, p < 0.001; 95% CI = − 1.29 to − 0.43) significantly decreased after admission to the PC unit, but peace and faith did not change over time. Increases in depression and pain were related to lower existential well-being, particularly in the meaning dimension. Optimism–pessimism moderated the linear trend of existential well-being and meaning domain, such that those with higher optimism and lower pessimism paired with a decrease in outcomes.Conclusions Terminal cancer patients experienced worsening existential well-being, particularly in the meaning facet while hospitalized, indicating that PC should include content that targets the existential concerns of spirituality in China. These findings also supported the need for an integrated PC to address personality traits and emotional and physical distress in this population.
... The modelling strategy was as follows (Hox, 1995;Singer, 1998;Wang et al., 2011). First, a two-level logistic regression empty model (without any explanatory variables) with random intercept was fitted to the data: embryos (level 1) were clustered within couples (level 2). ...
Article
Research question What are the prevalence of embryo abnormal early cleavages (AC) identified by time-lapse and patient- and treatment- related factors that explain AC occurrence? Design This project was a single-center, retrospective cohort study (Reproductive Department, AP-HP, Paris). We collected data on all IVF cycles for which embryos were observed in the EmbryoScope® from December 2015 to August 2017. Only diploid zygotes cleaved on Day-2 were included. The study included 318 cycles, (250 couples and 1343 embryos). Embryo videos were retrospectively analyzed for AC. The prevalence of each type of AC was recorded. The influence of clinical factors (whether they were intrinsic to patients or specific to IVF treatment) on AC occurrence was analyzed in multivariate multilevel mixed-effect logistic regression analysis. Results A high prevalence of AC was observed: 37.6% (505/1343) of embryos presented at least one AC, 22.8% (306/1343) a trichotomous mitosis (TM), 25.8% (347/1343) a rapid cleavage (RaC), 6.7% (90/1343) a cell fusion (CF), and ≥ 2 AC (mAC, 16.1%). Part of the variation (12 to 25%) in AC occurrence could be explained by embryo origin. TM and mAC phenotypes were less likely to occur in women with endometriosis or tubal pathology and tubal pathology alone, respectively. No factor related to IVF cycles was found to be statistically associated with AC occurrence. Conclusions Our findings emphasize the importance of considering embryo origin when interpreting studies focusing on embryo characteristics and factors that could impact their quality. The present study is limited by a small sample size of known embryo implantations and monocentric criterion.
... Hierarchical models were used for all inferential analyses to account for the correlated nature of clustering of participants within clinics; clinic was treated as a random effect in all models. 42 Because infant negative affectivity was only measured at 6 months, models examined concurrent associations between PSE strategies, infant negative affectivity at 6 months, feeding practices at 6 months, and weight status at 4-6 months. In models examining whether infant negative affectivity moderated associations between PSE strategies and mothers' reported feeding practices or infant weight-for-age percentiles, infant negative affectivity was mean-centred and moderation was tested by including main and interactive effects of temperament and intervention group. ...
Article
The aim of this study was to explore associations between parenting stress, feeding practices, and perceptions of children's eating behaviors during the COVID-19 pandemic. Parents (n = 284) of children aged 4-6 years completed a cross-sectional online survey during the onset of pandemic-related stay-at-home mandates in the U.S. Parents reported current levels of parenting stress, feeding practices, and child eating behaviors. Parents also reported whether parenting stress had increased, stayed the same, or decreased since prior to the onset of pandemic-related stay-at-home mandates. Greater levels of parenting stress were associated with less desirable feeding practices, including greater odds of high use of food for emotional regulation (OR = 1.05, 95% CI = 1.03-1.08), food as a reward (OR = 1.05, 95% CI = 1.02-1.08), and pressure to eat (OR = 1.03, 95% CI = 1.01-1.06), and low use of encouraging a balanced diet (OR = 1.03, 95% CI = 1.01-1.06). Greater levels of parenting stress were also associated with greater perceptions that children exhibited problematic eating behaviors, including greater odds of high food fussiness (OR = 1.05, 95% CI = 1.02-1.08) and low enjoyment of food (OR = 1.05, 95% CI = 1.02-1.07). For parents who reported their parenting stress had increased, greater parenting stress was associated with more frequent use of pressure to eat (p = .009) and less frequent monitoring their child's diet (p = .028). In conclusion, parenting stress during the pandemic was associated with use of food for emotional and behavioral regulation and perceptions that children exhibited problematic eating behaviors. Further research is needed to understand how to mitigate parenting stress and promote healthy feeding practices during times of crisis.
... To examine aggression across the 16 trials, multilevel models were constructed, which permitted control of within-person response variability across trials and, for exploratory purposes, examination of trajectories of response across trials. Analyses were conducted using SAS PROC MIXED (Wolfinger, 1997;Singer, 1998). ...
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Reactive aggression, a hostile retaliatory response to perceived threat, has been attributed to failures in emotion regulation. Interventions for reactive aggression have largely focused on cognitive control training, which target top-down emotion regulation mechanisms to inhibit aggressive impulses. Recent theory suggests that mindfulness training (MT) improves emotion regulation via both top-down and bottom-up neural mechanisms and has thus been proposed as an alternative treatment for aggression. Using this framework, the current pilot study examined how MT impacts functional brain physiology in the regulation of reactive aggression. Participants were randomly assigned to 2 weeks of MT (n = 11) or structurally equivalent active coping training (CT) that emphasizes cognitive control (n = 12). Following training, participants underwent functional magnetic resonance imaging (fMRI) during a retaliatory aggression task, a 16-trial game in which participants could respond to provocation by choosing whether or not to retaliate in the next round. Training groups did not differ in levels of aggression displayed. However, participants assigned to MT exhibited enhanced ventromedial prefrontal cortex (vmPFC) recruitment during punishment events (i.e., the aversive consequence of losing) relative to those receiving active CT. Conversely, the active coping group demonstrated greater dorsomedial prefrontal cortex (dmPFC) activation when deciding how much to retaliate, in line with a bolstered top-down behavior monitoring function. The findings suggest that mindfulness and cognitive control training may regulate aggression via different neural circuits and at different temporal stages of the provocation-aggression cycle. Trial Registration: identification no. NCT03485807.
... The smaller the deviance score, the better the model fit. In addition, to better estimate effect sizes at different levels, we adopted Kreft and de Leeuw's (1998) and Singer's (1998) formulation of pseudo R 2 , which is based on the proportional reduction of variance at each level due to the inclusion of predictors, as well as the total proportional reduction of variance of all levels. Table 2 presents the descriptive statistics and correlations for the focal study variables. ...
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To understand the conditions that support employee green behavior across cultures, we develop and test a conceptual model that describes how normative cues from work team leaders and peers in combination with country cultural norms shape discretionary green workplace behavior. Data from 1,605 employees in five countries indicate that power distance moderates the positive relationships observed between the discretionary green workplace behavior of leaders and their subordinates. In addition, an observed positive relationship between team green advocacy and individual discretionary green workplace behavior held across both collectivistic and individualistic cultures, contrary to our predictions. By taking macro-level cultural context into account and examining its interplay with lower-level work team norms, the study makes a significant contribution to understanding and intervening employees’ discretionary green behavior at work.
... First, we estimated the null model (with no predictors involved) and found significant level-2 and level-3 variation (0.6757 and 0.1675 intraclass correlations, respectively), which corroborates the necessity of multi-level modelling. Second, in developing the fixed and random portions of the model, we followed Singer (1998), Bliese and Ployhart (2002), and Holcomb et al. (2010) recommendations to use theory and fit indices (Akaike Information Criterion-AIC and Bayesian Information Criterion-BIC each assess goodness-of-fit of successive models) to produce the most parsimonious, yet best fitting, model. This approach indicated that the best models (lowest AIC and BIC) include time, male/female, and racial category as fixed factors with random intercepts at the board and director levels. ...
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A corporate board’s work is largely dependent on the collective contributions of individual directors. Thus, greater board diversity, with its commensurate knowledge complementarity, should stimulate better board discussions when members actively participate. Without the participation of underrepresented directors, however, the potential benefits of board diversity are lost. Herein we examine the drivers of underrepresented directors’ participation in board meetings. Departing from prior studies that often used a single‐level, compositional view of board diversity, we explore the antecedents of individual underrepresented director participation with a multi‐level, multi‐theoretic model. We find strong empirical support for our model, derived from detailed board of director meeting transcripts, offering several theoretical contributions to the literature.
... Table 1 presents means and standard deviations of all variables by culture and genre. We conducted a 2 (culture: Western vs. Asian) x 2 (genre: fiction vs. memoir) mixed-model analysis on each variable with chapter being the unit of analysis, where culture and genre were betweensubjects factors and subject (i.e., book) was a random factor (Singer, 1998). Adjusted means from the models are presented with results of relevant analyses. ...
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The present study compared ways of storytelling in Western and Asian literature. Content analysis was performed on Amazon.com and New York Times best-selling fictions and memoirs (N = 102) by Western and Asian authors. Although authors of the two cultural groups described similar numbers of event episodes per chapter, Western authors depicted the episodes in greater detail than Asian authors in both fictions and memoirs. Asian authors, on the other hand, described more frequently repeated events than Western authors in fictions. These findings highlight the important role of literature in reflecting as well as perpetuating cultural ways of storytelling.
... Hierarchical models were used for all inferential analyses to account for the correlated nature of clustering of participants within clinics; clinic was treated as a random effect in all models. 42 Because infant negative affectivity was only measured at 6 months, models examined concurrent associations between PSE strategies, infant negative affectivity at 6 months, feeding practices at 6 months, and weight status at 4-6 months. In models examining whether infant negative affectivity moderated associations between PSE strategies and mothers' reported feeding practices or infant weight-for-age percentiles, infant negative affectivity was mean-centred and moderation was tested by including main and interactive effects of temperament and intervention group. ...
Article
Background: Infants with greater temperamental negative affectivity are at higher risk for overfeeding and excess weight gain. Objective: To examine whether strategies to promote responsive bottle-feeding within WIC promoted healthier maternal feeding practices and infant weight status among infants with greater negative affectivity. Methods: Secondary analysis of data from a matched-pair cluster randomized trial. Policy, systems and environmental change (PSE) strategies to promote responsive bottle-feeding were implemented at three WIC clinics; these clinics were compared with three matched control clinics. Linear mixed models tested whether infant negative affectivity interacted with PSE strategies to predict feeding and weight outcomes when infants were 4-6 months old. Results: Significant interactions between infant negative affectivity and PSE strategies were noted. Among infants with high negative affectivity, mothers in PSE clinics reported less frequent use of food to soothe (p = 0.009) compared with mothers in control clinics. Among infants with moderate (p = 0.008) or high (p = 0.029) negative affectivity, infants in PSE clinics had healthier weight status compared with infants in control clinics. Conclusions: Promotion of responsive bottle-feeding is an effective way to support WIC mothers and reduce risk for overfeeding and excess weight gain, particularly for mothers of infants with greater negative affectivity.
... A random intercept was included in all the models to allow 235 individual differences to be captured. Finally, due to a lack of assumption with respect to the error 236 structure an unstructured covariance matrix was assumed (Singer, 1998 Twelve out of twenty participants, seven males and five females, felt that they were interacting 248 ...
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The impact of automated vehicles (AV) on pedestrians’ crossing behavior has been the topic of some recent studies, but findings are still scarce and inconclusive. The aim of this study is to determine whether the drivers’ presence and apparent attentiveness in a vehicle influences pedestrians’ crossing behavior, perceived behavioral control, and perceived risk, in a controlled environment, using a Head-mounted Display in an immersive Virtual Reality study. Twenty participants took part in a road-crossing experiment. The VR environment consisted of a single lane one-way road with car traffic approaching from the right-hand side of the participant which travelled at 30 kmph. Participants were asked to cross the road if they felt safe to do so. The effect of three driver conditions on pedestrians’ crossing behavior were studied: Attentive driver, distracted driver, and no driver present. Two vehicles were employed with a fixed time gap (3.5 s and 5.5s) between them to study the effects of time gaps on pedestrians’ crossing behavior. The manipulated vehicle yielded to the pedestrians in half of the trials, stopping completely before reaching the pedestrian’s position. The crossing decision, time to initiate the crossing, crossing duration, and safety margin were measured. The main findings show that the vehicle’s motion cues (i.e. the gap between the vehicles, and the yielding behavior of the vehicle) were the most important factors affecting pedestrians’ crossing behavior. Therefore, future research should focus more on investigating how AVs should behave while interacting with pedestrians. Distracted driver condition leads to shorter crossing initiation time but the effect was small. No driver condition leads to smaller safety margin. Findings also showed that perceived behavioral control was higher and perceived risk was significantly lower when the driver appeared attentive. Given that drivers will be allowed to do other tasks while AVs are operating in the future, whether explicit communication will be needed in this situation should be further investigated.
... 3. It is not possible to calculate r 2 in a multilevel modeling context. However, it is possible to calculate pseudo R 2 statistics that estimate the proportion of the variance in the outcome variable that is associated with the explanatory variables based on the following formula (Kreft & de Leeuw, 1998;Singer, 1998) Pseudo R 2 = 1 -(restricted error variance / unrestricted error variance). These statistics can be calculated for each level in a multilevel model. ...
Article
It is widely understood that teachers are plagued by a myriad of challenges that ultimately affect their stress levels, job satisfaction, and effectiveness at work. Teacher stress can lead to burnout, lowered occupational commitment, and an eventual decision to leave the field. An important question for the field is how best to understand which teachers are most vulnerable to stress. This study used Lazarus and Folkman's transactional theory, which is the dominant model within the stress literature, to examine teachers’ stress vulnerability.
... We analyzed the data we collected with SAS version 9.2 and its PROC MIXED procedure for hierarchical linear modeling (HLM) (Raudenbush & Bryk, 2002;Singer, 1998). Of the 307 questionnaires that we sent to potential respondents, we received 248 (81%) completed questionnaires in return. ...
... (6) SAS. SAS provided no GUI, and multilevel model analysis is implemented using the "MIXED program" command, and the parameter estimation method is REML by default [9]. ...
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Multilevel model methodology is widely used in social science. There are many textbooks and h papers introducing the principles and methods of multilevel model. However, most of them are simply a brief instruction how to apply statistical software to run multilevel model, which brings some obstacles for beginners in empirical research. To address this gap, this paper aims to help beginners and common users to grasp the operation skills of multilevel model in these statistical software. Firstly, the operation procedure of multilevel model in eight statistical software are introduced. Secondly, this paper systematically compares the output results of multilevel models of these statistical software. Finally, some operational guidelines and suggestions are put forward for the empirical application of multilevel model.
... This would manifest itself in terms of a feeling by attention interaction with respect to avatar placements. Both analyses were conducted using multilevel modeling (MLM) procedures, using the SAS PROC MIXED function (Singer, 1998). ...
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Individuals are thought to differ in the extent to which they attend to and value their feelings, as captured by the construct of attention to emotion. The well-being correlates of attention to emotion have been extensively studied, but the decision-making correlates have not been. A three study program of research (total N = 328) sought to examine relationships between stimulus-specific feelings and decisions concerning those stimuli in the context of high levels of within-subject power. Evidence for the pleasure principle was robust, in that individuals placed a virtual self closer to stimuli that they found more pleasant (Study 1) and they wished to re-view such stimuli more frequently (Studies 2 & 3). These relationships, however, were more pronounced at higher levels of attention to emotion. The findings affirm the importance of feelings in decision-making while highlighting ways in which individual differences in attention to emotion operate.
... A random intercept was included in all the models to allow individual differences to be captured. Finally, due to a lack of assumption with respect to the error structure an unstructured covariance matrix was assumed (Singer, 1998). ...
Article
The impact of automated vehicles (AV) on pedestrians’ crossing behavior has been the topic of some recent studies, but findings are still scarce and inconclusive. The aim of this study is to determine whether the drivers’ presence and apparent attentiveness in a vehicle influences pedestrians’ crossing behavior, perceived behavioral control, and perceived risk, in a controlled environment, using a Head-mounted Display in an immersive Virtual Reality study. Twenty participants took part in a road-crossing experiment. The VR environment consisted of a single lane one-way road with car traffic approaching from the right-hand side of the participant which travelled at 30 kmph. Participants were asked to cross the road if they felt safe to do so. The effect of three driver conditions on pedestrians’ crossing behavior were studied: Attentive driver, distracted driver, and no driver present. Two vehicles were employed with a fixed time gap (3.5 s and 5.5 s) between them to study the effects of time gaps on pedestrians’ crossing behavior. The manipulated vehicle yielded to the pedestrians in half of the trials, stopping completely before reaching the pedestrian’s position. The crossing decision, time to initiate the crossing, crossing duration, and safety margin were measured. The main findings show that the vehicle’s motion cues (i.e. the gap between the vehicles, and the yielding behavior of the vehicle) were the most important factors affecting pedestrians’ crossing behavior. Therefore, future research should focus more on investigating how AVs should behave while interacting with pedestrians. Distracted driver condition leads to shorter crossing initiation time but the effect was small. No driver condition leads to smaller safety margin. Findings also showed that perceived behavioral control was higher and perceived risk was significantly lower when the driver appeared attentive. Given that drivers will be allowed to do other tasks while AVs are operating in the future, whether explicit communication will be needed in this situation should be further investigated.
Article
Background: Transcranial focused ultrasound (tFUS) is a noninvasive brain stimulation method that may modulate deep brain structures. This study investigates whether sonication of the right anterior thal-amus would modulate thermal pain thresholds in healthy individuals. Methods: We enrolled 19 healthy individuals in this three-visit, double-blind, sham-controlled, crossover trial. Participants first underwent a structural MRI scan used solely for tFUS targeting. They then attended two identical experimental tFUS visits (counterbalanced by condition) at least one week apart. Within the MRI scanner, participants received two, 10-min sessions of either active or sham tFUS spread 10 min apart targeting the right anterior thalamus [fundamental frequency: 650 kHz, Pulse repetition frequency: 10 Hz, Pulse Width: 5 ms, Duty Cycle: 5%, Sonication Duration: 30s, Inter-Sonication Interval: 30 s, Number of Sonications: 10, ISPTA. 0 995 mW/cm2, ISPTA. 3 719 mW/cm2, Peak rarefactional pressure 0.72 MPa]. The primary outcome measure was quantitative sensory thresholding (QST), measuring sensory, pain, and tolerance thresholds to a thermal stimulus applied to the left forearm before and after right anterior thalamic tFUS. Results: The right anterior thalamus was accurately sonicated in 17 of the 19 subjects. Thermal pain sensitivity was significantly attenuated after active tFUS. The pre-post x active-sham interaction was significant (F(1,245.95) ¼ 4.03, p ¼ .046). This interaction indicates that in the sham stimulation condition , thermal pain thresholds decreased 1.08 C (SE ¼ 0.28) pre-post session, but only decreased .51 C (SE ¼ 0.30) pre-post session in the active stimulation group. Conclusions: Two 10-min sessions of anterior thalamic tFUS induces antinociceptive effects in healthy individuals. Future studies should optimize the parameter space, dose and duration of this effect which may lead to multi-session tFUS interventions for pain disorders.
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Introduction Managing Cancer and Living Meaningfully (CALM) is a novel, brief and manualised psychotherapeutic intervention intended to treat and prevent depression and end-of-life distress in patients with advanced cancer. This phase 2 trial aims to assess the feasibility and preliminary efficacy of CALM in Japanese patients with cancer. Methods and analysis This study is a single-arm clinical trial. All patients involved in the study are ≥18 years of age, have been diagnosed with advanced or metastatic solid-tumour cancer, and their expected survival is at least 6 months. CALM comprises three to six individual therapy sessions, each lasting approximately 45–60 min, provided over 3– 6 months. The participants will be asked to complete questionnaires at baseline (t0), 3 months (t1) and 6 months (t2). The primary outcomes are rates of completion of the intervention and of the outcome measures and improvement of depressive symptoms measured using the Patient Health Questionnaire-9 between t0 and t2. The criteria for the successful rate of completion is that at least 70% participants who participate in at least three sessions will complete measures at t2. The secondary outcomes are the improvement in scores on: (1) the Quality of Life at the End of Life-Cancer Scale, (2) the Experiences in Close Relationships scale, (3) the Death and Dying Distress Scale and (4) the Clinical Evaluation Questionnaire. Ethics and dissemination This study was approved by the Research Ethics Committee of The University of Tokyo, Cancer Institute Hospital of Japanese Foundation for Cancer Research and Yamaguchi University. We will conduct the study in accordance with the Declaration of Helsinki and the Ethical Guidelines for Medical and Health Research Involving Human Subjects. The results of this study will be submitted for peer-reviewed publication and presentation at local, national and international scientific meetings and conferences. Trail registration number UMIN000040032; Pre-results.
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Background: The World Health Organization (WHO) recommends the WHO Disability Assessment Schedule (WHODAS) 2.0 as a generic assessment instrument to collect data on functioning and disability. The questionnaire was developed specifically to capture the activities and participation domain as defined by the International Classification of Functioning, Disability and Health (ICF). Evidence on the most relevant factors predicting WHODAS 2.0 outcome in the context of musculoskeletal injuries are controversial. This study aims to assess change in functioning of patients with severe musculoskeletal injuries undergoing inpatient rehabilitation over time. Methods: A longitudinal multicentre study was conducted, following up 571 participants with severe musculoskeletal injuries over the course of a first inpatient rehabilitation stay until 3 months after discharge. At admission, data on sociodemographic, health-related aspects, functioning and contextual factors were collected. WHODAS 2.0 assessed functioning. Data were analysed using a multilevel model approach. Results: The mean WHODAS 2.0 declined from admission to discharge and 3-month follow-up, indicating an improvement in functioning. Multilevel analyses revealed age, duration of inpatient rehabilitation, severity of the injury, injury localizations, number of comorbidities, emotional functioning, pain, being informed about the injury, subjective prognosis on return to work and agreement on treatment targets as factors influencing change in functioning over time. Conclusions: In a rehabilitation setting, a healthcare professional can promote an increase in functioning, for example, by ensuring that there are treatment targets defined and agreed on with the patient and that the patient feels sufficiently informed about the injury. The identified factors could potentially be used for a short screening at admission to rehabilitation to estimate the patient’s change of functioning over time. Trial registration number and date of registration: DRKS00014857; July 04, 2018.
Chapter
Chronic nonspecific low back pain is a frequent clinical condition affecting the general population and influencing disability level and quality of life. We performed a single-blinded, randomized, and controlled study to compare the effectiveness of manual pressure release (MPR) and electrical neuromodulation (ENM) treatments in the management of chronic low back pain. There were 20 patients with chronic low back pain randomly assigned to 6 treatment sessions with either technique. Both groups were treated for 2 days a week for 3 weeks. Myofascial trigger points (MTrPs) were identified and skin conductance, pressure-pain threshold, postural changes, and the Oswestry Disability Index were assessed before and after each treatment session, along with the protocol-end data compared against the baseline data in each group. We found an outstanding and about equal deactivation of MTrPs from pre- to post-treatment in both groups, reducing disability in patients with chronic low back pain. The study highlights the ENM as a reliable tool for the evaluation of MTrPs, given a high agreement with the MPR. The effect on the neuromuscular condition of treating the “key trigger points” found in this study advances the knowledge of medical rehabilitation.
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Background: Chronic spinal pain is prevalent and long-lasting. Although provider-based nonpharmacologic therapies, such as chiropractic care, have been recommended, healthcare and coverage policies provide little guidance or evidence regarding long-term use of this care. Objective: To determine the relationships between visit frequency and outcomes for patients using ongoing chiropractic care for chronic spinal pain. Study design: Observational 3-month longitudinal study. Setting: Data collected from patients of 124 chiropractic clinics in 6 United States regions. Methods: We examined the impact of visit frequency and patient characteristics on pain (pain 0-10 numeric rating scale) and functional outcomes (Oswestry Disability Index [ODI] for low-back pain and Neck Disability Index [NDI] for neck pain, both 0-100 scale) using hierarchical linear modeling (HLM) in a large national sample of chiropractic patients with chronic low back pain (CLBP) and/or chronic neck pain (CNP). This study was approved by the RAND Human Subjects Protection Committee and registered under ClinicalTrials.gov Identifier: NCT03162952. Results: One thousand, three hundred, sixty-two patients with CLBP and 1,214 with CNP were included in a series of HLM models. Unconditional (time-only) models showed patients on average had mild pain and function, and significant, but slight improvements in these over the 3-month observation period: back and neck pain decreased by 0.40 and 0.44 points, respectively; function improved by 2.7 (ODI) and 3.0 points (NDI) (all P < 0.001). Adding chiropractic visit frequency to the models revealed that those with worse baseline pain and function used more visits, but only visits more than once per week for those with CLBP were associated with significantly better improvement. These relationships remained when other types of visits and baseline patient characteristics were included. Limitations: This is an observational study based on self-reported data from a sample representative of chiropractic patients, but not all patients with CLBP or CNP. Conclusions: This 3-month window on chiropractic patients with CLBP and/or CNP revealed that they were improving, although slowly; may have reached maximum therapeutic improvement; and are possibly successfully managing their chronic pain using a variety of chiropractic visit frequencies. These results may inform payers when building coverage policies for ongoing chiropractic care for patients with chronic pain.
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The global trend of increasing age diversity in workforces has called for research on understanding and managing age differences to better integrate employees across the lifespan into organizations. Integrating aging and lifespan development research and inclusion work, we conduct a daily diary study to investigate age differences in employees’ responses to inclusion experience on a daily basis. In light of socioemotional selectivity theory, we argue that older workers exhibit stronger affective shifts (i.e., increase or upshift in positive affect and decrease or downshift in negative affect) in response to inclusion experience because they are likely to put higher value on social relationships, such that the daily effects of inclusion experience on changes in positive and negative affect are stronger for older (vs. younger) workers through the mediating mechanism of relationship value. We tested our hypotheses by surveying 128 employees from a manufacturing company for 10 consecutive workdays (N = 1,248). We found that the daily effects of inclusion experience on affective changes were stronger for older workers through the mediation of higher relationship value. Changes in positive and negative affect, in turn, related to employees’ work engagement over the course of a workday. Our study serves as an important initial step that examines age differences in affective responses to daily inclusion and sheds light on the importance of promoting workplace inclusion for older workers in particular. This article is protected by copyright. All rights reserved
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As environmental concerns continue to draw attention from governments, businesses, and citizens worldwide, the so-called green behaviors of employees are being recognized as important for both the successful implementation of environmental management policies and as sources of upward influence that can hasten managerial responsiveness to environmental concerns. This three level study sought to replicate and extend prior research by examining how cultural collectivism shapes the dynamics through which personal attributes and the proximal social context within work teams and firms influence the dynamic processes that shape discretionary green behavior, green advocacy and organizational self-esteem. Results based on data from 1,117 individuals organized in 263 work teams in 17 firms and 8 industries and located in 5 countries (Austria, Brazil, China, India, and Germany) indicate that moral attentiveness, firm environmental practices and social cues from leaders and work team members all influence the discretionary green behaviors of employees working in firms, with the influence of social cues being stronger for employees in firms with more collectivistic cultures. The results point to the importance of accounting for cultural influence in studies of environmental behavior and suggest the value of leader authenticity in firms seeking to improve their environmental performance.
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Purpose This study develops a cross-level moderated mediating model based on expectation-value theory to extend the knowledge on how and when organizational culture motivates employee radical creativity. Design/methodology/approach Based on longitudinal, multisource data for 584 R&D employees in 73 organizations, the research hypotheses were tested by a multilevel analysis using hierarchical linear model. Findings The results showed that error management culture had a positive effect on employees' psychological safety and radical creativity; psychological safety mediated the effect of error management culture on employee radical creativity. Further, moderated path analysis revealed that employees' promotion focus moderated the positive effect of psychological safety on employee radical creativity and thus strengthened the indirect effect of error management culture on employee radical creativity via psychological safety. Originality/value Literature on how organizational culture motivates workplace creativity pays little attention to employees' radical creativity. This study fills this gap by empirically examining the role of error management culture as a critical organizational culture that secures employee radical creativity. It also provides a novel mechanism, i.e., an expectancy-value mechanism to explain the link between organizational context and radical creativity by elucidating the underlying psychological process whereby error management culture drives employee radical creativity and identifying the pivotal moderating role of employees' regulatory focus in the function of error management culture.
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Few studies examine how neighborhood structural factors (e.g., socioeconomic status [SES] and diversity) and perceived disorder may influence the messages parents communicate to their youth about race/ethnicity. Guided by the integrative model and social disorganization theory, this study examines how parents' ethnic–racial socialization messages (ERS) are shaped by the broader environment. Data come from the MacArthur Studies of Diversity in Midlife. Latinx and African American parents N = 508 (Mage = 39) with a child between 6- and 17-years old living in two urban US cities were included. Cultural perceptions were assessed at both the individual level (e.g., perceived discrimination and ethnic affirmation) and neighborhood level along with demographic and structural neighborhood characteristics at the individual and neighborhood level, respectively. Multilevel analyses revealed that at both the individual level and neighborhood levels, perceived neighborhood problems were associated with more frequent messages about ethnicity and race (e.g., cultural socialization and preparation for bias). In addition, neighborhood-level affirmation promoted cultural messages; in contrast, neighborhood-level discrimination experiences positively impacted preparation for unfair treatment. Results reveal how parents' ERS is informed by their own characteristics as well as neighborhood factors. Further, cross-level interactions were found. Findings are discussed in terms of contextual and cultural-developmental theorizing about parenting. Key points • Neighborhood problems were associated with more frequent messages about ethnicity and race. • Neighborhood-level racial–ethnic group affirmation promoted cultural messages. • Neighborhood-level discrimination experiences positively impacted preparation for unfair treatment. • Cross-level interactions showed that cultural socialization frequency varied.
Presentation
Xenobalanus globicipitis is an epibiont of cetaceans that typically attaches on the edge of fins. Recent evidence showed that its distribution on the tail flukes of striped dolphins, Stenella coeruleoalba, was non-random; most barnacles occurring on the dorsal side, and the central third, of the trailing edge of the flukes. These patterns were interpreted based on functional demands regarding barnacle structural integrity and/or filtering performance. The present study provides evidence that this seemingly preferential use of some fluke areas may actually be a consequence of dolphin hydrodynamics. We performed an analysis of the distribution and aggregation of X. globicipitis on the flukes of 55 Mediterranean striped dolphins, and interpreted the patterns obtained using published evidence on swimming dolphin models based on computational fluid dynamics. Nearest neighbor analysis strongly suggested that new barnacle recruits actively seek placements along the trailing edge beside already settled individuals, presumably to facilitate copulation. However, the gross distribution of X. globicipitis on the flukes was directly related with cetacean hydrodynamics, preferentially settling on areas of higher pressure and lower shear stress. Accordingly, these results suggest that X. globicipitis could be used as a natural tag to shed light on cetacean hydrodynamics.
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Students studying hierarchical models are often confronted with multiple notational representations. The purpose of this note is to illustrate the relationship between HLM notation and mixed model notation. This is accomplished by explicitly mapping the parameters across notations for a concrete example involving the hierarchical modeling of change.