Article

Using Mixture Models in Temperament Research

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Abstract

Temperamental characteristics can be conceptualised as continuous dimensions or qualitative categories. The continuous versus categorical question concerns the underlying temperamental characteristics and not the measured variables, which can be recorded in either continuous or categorical forms. This paper argues for a categorical conceptualisation of temperamental characteristics and applies a finite mixture model appropriate to this view to two sets of longitudinal observations of infants and young children. This statistical approach provides a good description of the observed predictive relation between behavioural profiles of children at 4 months and the degree of behavioural signs of fear at 14 months. An advantage of the mixture model approach to this data, relative to more standard approaches to developmental data, is that because it takes into account an a-priori theory, it can be used to address improvements and refinements to theories and experimental designs in a straightforward manner.

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... • Section 3.1: We consider the infant temperament data of Stern et al. (1995), which was also analyzed by Gelman et al. (1996) to illustrate PPCs with realized discrepancies. Following the authors, we fit a multinomial mixture to the data. ...
... Here, the PPN study correctly suggests that PPCA (which assumes linearity) is not adequate to model the data; nonlinear deep generative models provide better fits. Stern et al. (1995) study infant temperament data, which was also analyzed by Gelman et al. (1996) to illustrate PPCs with realized discrepancies. In the study, two cohorts of infants (n = 169, in total) were scored on the (i) degree of motor activity (scored 1-4) and (ii) crying to stimuli (scored 1-3), both at 4 months, and (iii) the degree of fear to unfamiliar stimuli at 14 months (scored 1-3). ...
... i } and their group indicator by z i . Following Stern et al. (1995), we assume that infants in group k will have the same score probabilities, (θ ...
... • Section 3.1: We consider the infant temperament data of Stern et al. (1995), which was also analyzed by Gelman et al. (1996) to illustrate PPCs with realized discrepancies. Following the authors, we fit a multinomial mixture to the data. ...
... Here, the PPN study correctly suggests that PPCA (which assumes linearity) is not adequate to model the data; nonlinear deep generative models provide better fits. Stern et al. (1995) study infant temperament data, which was also analyzed by Gelman et al. (1996) to illustrate PPCs with realized discrepancies. In the study, two cohorts of infants ( = 169, in total) were scored on the (i) degree of motor activity (scored 1-4) and (ii) crying to stimuli (scored 1-3), both at 4 months, and (iii) the degree of fear to unfamiliar stimuli at 14 months (scored 1-3). ...
... For infant , denote their scores in each of the three tests as {x (1) , x (2) , x (3) } and their group indicator by . Following Stern et al. (1995), we assume that infants in group will have the same score probabilities, ( (1) , (2) , (3) ), across the three tests. The multinomial mixture model with groups is: ...
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Bayesian model criticism is an important part of the practice of Bayesian statistics. Traditionally, model criticism methods have been based on the predictive check, an adaptation of goodness-of-fit testing to Bayesian modeling and an effective method to understand how well a model captures the distribution of the data. In modern practice, however, researchers iteratively build and develop many models, exploring a space of models to help solve the problem at hand. While classical predictive checks can help assess each one, they cannot help the researcher understand how the models relate to each other. This paper introduces the posterior predictive null check (PPN), a method for Bayesian model criticism that helps characterize the relationships between models. The idea behind the PPN is to check whether data from one model's predictive distribution can pass a predictive check designed for another model. This form of criticism complements the classical predictive check by providing a comparative tool. A collection of PPNs, which we call a PPN study, can help us understand which models are equivalent and which models provide different perspectives on the data. With mixture models, we demonstrate how a PPN study, along with traditional predictive checks, can help select the number of components by the principle of parsimony. With probabilistic factor models, we demonstrate how a PPN study can help understand relationships between different classes of models, such as linear models and models based on neural networks. Finally, we analyze data from the literature on predictive checks to show how a PPN study can improve the practice of Bayesian model criticism. Code to replicate the results in this paper is available at \url{https://github.com/gemoran/ppn-code}.
... Examples of latent variables in the psychological literature include temperament (Stern, Arcus, Kagan, Rubin, & Snidman, 1995), cognitive ability (Humphreys & Janson, 2000), health behaviors (Maldonado-Molina & Lanza, 2010), and motivation (Coffman, Patrick, Palen, Rhoades, & Ventura, 2007). Knowing that they are imperfect measures, using data from available observed variables provides the best measures of latent variables. ...
... Theory suggests that there are two main temperamental types of children, namely inhibited and uninhibited, characterized by avoidance or approach to unfamiliar situations (Kagan, 1989). Stern et al. (1995) used latent class analysis to test this theory empirically, comparing a model with two temperamental types of children to models with three and four types. Infants in two cohorts of sample sizes 93 and 76 were measured on three categorical variables: motor activity, fret/cry, and fear. ...
Chapter
Often quantities of interest in psychology cannot be observed directly. These unobservable quantities, known as latent variables, tend to be complex, often multidimensional, constructs. In many cases these constructs are categorical, such that individuals belong to mutually exclusive and exhaustive unobservable subgroups. Latent class analysis (LCA) is a statistical approach to modeling a discrete latent variable using multiple, discrete observed variables as indicators. Examples of latent class variables that appear in the psychology literature include temperament type, substance use behavior, teaching style, stages of change in the transtheoretical model, and latent classes of risk. The first section of this chapter provides a conceptual introduction to the concept of a latent class followed by a technical introduction to the mathematical model, including multiple-groups LCA and LCA with covariates. This is followed by a discussion of parameter restrictions, model selection, and goodness-of-fit. The second section demonstrates LCA using the empirical example of depression subtypes in adolescence. Five latent classes were identified based on responses to eight questionnaire items assessing depression symptoms: Non-depressed (characterized by a low probability of reporting all eight depression symptoms), sad, disliked, sad + disliked, and depressed (characterized by a high probability of reporting all eight depression symptoms). The third section presents longitudinal extensions of the model, including repeated-measures LCA and latent transition analysis (LTA). The empirical example is extended to examine change in depression subtypes over time. The final sections describe recent extensions to the latent class model and areas that merit additional research in the future. Keywords: latent class analysis; latent transition analysis; latent variable model; categorical data
... The measurements, however, can give a strong indication of the sex of the individual. In psychology, Stern et al. (1995) used measurements on reactions of infants to strange situations to assign them to high-and low-activity groups. In this paper, responses to sets of survey questions on job preparation and activities are used to cluster respondents into classes. ...
... The Expectation-Maximization algorithm (Dempster, Laird, and Rubin 1977;Stern et al. 1995) can be used to produce maximum likelihood estimates of model parameters without having to pre-classify observations into groups. The EM algorithm alternates between computing the expected value of n lg given current parameter estimates and, holding n lg at current expected values, the maximum likelihood estimates of the π g and π j k k|g probabilities. ...
Article
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The field of Information Technology (IT) has provided extraordinary job growth in the United States over the last two decades; however, women and some minority groups are severely underrepresented in IT occupations, especially in management positions. These groups also on average receive lower salaries than their counterparts. The National Science Foundation's SESTAT database is created from biennial nationally representative surveys of U.S. scientists and engineers. SESTAT provides detailed information, such as employment history, educational background, and demographic characteristics. These data are analyzed here using latent class analysis, which is an exploratory technique that can be used to cluster cases based on categorical variables. The data are from the 1997 Survey of Doctoral Re-cipients. The subset of respondents received Ph.D.'s between 1990 and 1996 in either than physical or biological sciences or in engineering and work at higher educational institutions. There are a few significant differences between men and women in desired work activities, job search resources, and adequacy of doctoral training. There are many large, significant differences in limitations when searching for a job, work activities, and family and career status. Latent class analysis helped identify important subgroups of females and males based on clustering simultaneously on several categorical variables.
... Latent class models assume that the sample observations are drawn from a mixture of qualitatively distinct, internally homogeneous groups of infants. These models are especially useful when it is not possible to identify the group to which a particular subject belongs directly from the observed variables (Clogg, 1995;Stern, Ancus, Kagan, Rubin, & Snidman, 1995), as is the case in the relation between phenotypic handedness and its underlying genotype. Latent class models can incorporate either categorical or continuous measurements. ...
... The latent class analysis was repeated under a variety of assumptions about the number of groups, and then the ®ts of the models were examined. Because latent class models are not nested models, a chi-square test cannot be used to determine whether the two-class model provides a better ®t than that of the alternative three-class model (Stern et al., 1995). Therefore, we evaluated the models based on the stability of the parameter estimates and whether the estimates have clear interpretations. ...
Article
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Infant hand-use preferences for apprehending objects were assessed three times at 7, 9, and 11 months of age for 154 infants (79 males) using a reliable and valid procedure. Two classification procedures (differing in Type I classification error rates) were used to identify an infant's preference (right, left, no preference) at each age, and these data were examined using two- and three-group latent class analysis models. These analyses revealed the importance of using a handedness classification procedure with low Type I error rates and evidence of a right-shift factor similar to that expressed in child and adult handedness. Thus, infant hand-use preferences for apprehending objects are likely a developmental precursor of adult handedness. The relation of the right-shift factor to increased susceptibility to social influences during development and the evolution of human abilities also is discussed.
... Muthén and Shedden [37] improved the models that identified latent growth trajectory class membership in longitudinal data based on individual growth trajectories and were estimated by the EM algorithm. Stern et al. [38] applied LCA in studying the two main temperamental types of children: inhibited and uninhibited. LCMs have been used to investigate the initiation of substance use habits throughout adolescence, such as alcohol, caffeine, and tobacco [39]. ...
Article
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We investigate the association of a sensitive characteristic or latent variable with observed binary random variables by the randomized response (RR) technique of Warner in his publication (Warner, S.L. J. Am. Stat. Assoc.1965, 60, 63–69) and a latent class model. First, an expectation-maximization (EM) algorithm is provided to easily estimate the parameters of the null and alternative/full models for the association between a sensitive characteristic and an observed categorical random variable under the RR design of Warner’s paper above. The likelihood ratio test (LRT) is utilized to identify observed categorical random variables that are significantly related to the sensitive trait. Another EM algorithm is then presented to estimate the parameters of a latent class model constructed through the sensitive attribute and the observed binary random variables that are obtained from dichotomizing observed categorical random variables selected from the above LRT. Finally, two classification criteria are conducted to predict an individual in the sensitive or non-sensitive group. The practicality of the proposed methodology is illustrated with an actual data set from a survey study of the sexuality of first-year students, except international students, at Feng Chia University in Taiwan in 2016.
... LCA is advantageous because there are no assumptions about the distributions of the indicators (e.g., normality). LCA has also been applied in several domains [11,[15][16][17][18][19]. In the present study, we use LCA to identify subgroups within the larger population of children in the US based on indicators of EF, SE traits, stuttering, and developmental typicality. ...
Article
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A growing body of research has reported associations between weaker Executive Functions (EF), the set capacities that are needed to manage and allocate one’s cognitive resources during cognitively challenging activities and various neurodevelopmental conditions, including stuttering. The majority of this research has been based on variable-centered approaches, which have the potential to obscure within-population heterogeneity. Person-centered analyses are essential to understanding multifactorial disorders where relationships between indicators have been elusive, such as stuttering. The current study addressed gaps in the literature by using latent class analysis (LCA), a person-centered approach, to identify homogenous subgroups within the National Health Interview Survey (2004–2018) publicly available data set. Using this exploratory approach, we examined the hypothesis that there exist distinct classes (or subgroups) of children based on parent reports of EF, Socioemotional (SE) traits, developmental atypicality, and stuttering. Our analyses revealed distinct subgroups with substantially different likelihoods of parent-reported stuttering behaviors and developmental atypicality. For children with both EF and SE difficulties, the likelihood of parental report of stuttering and atypical development was even higher, in fact this likelihood (of stuttering and not-typically developing) was highest among all subgroups. In contrast, children without difficulties were the least likely to be reported with stuttering or not-typically developing. Our findings are consistent with theoretical frameworks for stuttering, which cite EF as a crucial component in the disorder. Additionally, our findings suggest within-population heterogeneity among children with EF difficulties and, specifically, EF and SE heterogeneity among children who stutter.
... A number of empirical research studies have used LCA to classify individuals into the categories of a (latent) categorical variable on the basis of the observed variable values. For example, in psychology, LCA has been used to assess temperament (Stern, Arcus, Kagan, Rubin, & Snidman, 1995) and depression (Lanza, Flaherty, & Collins, 2003). In educational studies, teaching style has been modeled using LCA (e.g., Aitkin, Anderson, & Hinde, 1981). ...
... A number of empirical research studies have used LCA to classify individuals into the categories of a (latent) categorical variable on the basis of the observed variable values. For example, in psychology, LCA has been used to assess temperament (Stern, Arcus, Kagan, Rubin, & Snidman, 1995) and depression (Lanza, Flaherty, & Collins, 2003). In educational studies, teaching style has been modeled using LCA (e.g., Aitkin, Anderson, & Hinde, 1981). ...
Article
Latent class analysis (LCA) is a statistical method used to group individuals (cases, units) into classes (categories) of an unobserved (latent) variable on the basis of the responses made on a set of nominal, ordinal, or continuous observed variables. In this article, we introduce LCA in order to demonstrate its usefulness to early adolescence researchers. We provide an application of LCA to empirical data collected from a national survey carried out in 2010 in Italy to assess mathematics and reading skills of fifth-grade primary school pupils (10 years in age). The data were used to measure pupils’ supplies of cultural capital by specifying a latent class model. This article aims to describe and interpret results of LCA, allowing users to replicate the analysis. All LCA examples included in the text are illustrated using the Latent GOLD package, and command files needed to reproduce all analyses with SAS and R are available as supplemental online appendix files along with the example data files.
... Latent class analysis (LCA) is one such statistical technique that is widely used to identify subgroups using unsupervised analysis. [12][13][14][15][16] Within musculoskeletal research, the use of LCA has increased during the last decade, [17][18][19] and its strengths compared to other clustering approaches are becoming more evident. 20 In LBP research, LCA has mainly been applied to the analysis of outcome trajectories. ...
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Background Latent class analysis (LCA) is increasingly being used in health research, but optimal approaches to handling complex clinical data are unclear. One issue is that commonly used questionnaires are multidimensional, but expressed as summary scores. Using the example of low back pain (LBP), the aim of this study was to explore and descriptively compare the application of LCA when using questionnaire summary scores and when using single items to subgrouping of patients based on multidimensional data. Materials and methods Baseline data from 928 LBP patients in an observational study were classified into four health domains (psychology, pain, activity, and participation) using the World Health Organization’s International Classification of Functioning, Disability, and Health framework. LCA was performed within each health domain using the strategies of summary-score and single-item analyses. The resulting subgroups were descriptively compared using statistical measures and clinical interpretability. Results For each health domain, the preferred model solution ranged from five to seven subgroups for the summary-score strategy and seven to eight subgroups for the single-item strategy. There was considerable overlap between the results of the two strategies, indicating that they were reflecting the same underlying data structure. However, in three of the four health domains, the single-item strategy resulted in a more nuanced description, in terms of more subgroups and more distinct clinical characteristics. Conclusion In these data, application of both the summary-score strategy and the single-item strategy in the LCA subgrouping resulted in clinically interpretable subgroups, but the single-item strategy generally revealed more distinguishing characteristics. These results 1) warrant further analyses in other data sets to determine the consistency of this finding, and 2) warrant investigation in longitudinal data to test whether the finer detail provided by the single-item strategy results in improved prediction of outcomes and treatment response.
... That is, the LC to which someone belonged did not change. This static nature of the class memberships is a common feature of many typological theories, for example temperament (Stern, Arcus, Kagan, Rubin, & Snidman, 1995) and attachment (Ainsworth & Bell, 1970). However, one can also view the LC variable as dynamic (Collins & Cliff, 1990) and examine changes in class memberships over time (called latent transition analysis, LTA, or latent Markov models; Collins & Wugalter, 1992;Langeheine, 1994). ...
... In this case, it is unlikely that the sample averaged estimates are very meaningful or accurately reflect associations among phenomena of interest (Flaherty, submitted). Applications of latent class and latent profile models include: temperament types in young children (Sanson et al., 2009;Stern, Arcus, Kagan, Rubin, & Snidman, 1995), children's disruptive behavior problems (Degnan, Calkins, Keane, & Hill-Soderlund, 2008), adolescent socialization (Cumsille, Darling, Flaherty & Martínez, 2006) and patterns of substance use (Flaherty, 2002;O'Connor & Colder, 2005). ...
... The procedure was videotaped and the total number of frets and cries was recorded. Previous studies have demonstrated high interrater reliability, and predictive validity, such that infants who show high frequencies of irritability (crying and fretting) and activity show higher levels of fear, inhibition, anxiety, and social withdrawal at later ages (Kagan et al., 1999;Stern, Arcus, Kagan, Rubin, & Snidman, 1995). Coding was supervised by Dr. Snidman and Dr. Kagan. ...
Article
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The purpose of the current study was to examine the unique and interactive contributions of infant negative emotionality and family risk factors in the development of internalizing-only, externalizing-only, and co-occurring behavior problems in early childhood. The sample included 412 infants and their primary caregivers. Interviews and temperament assessments took place when infants were 5-7 months old, and primary caregivers completed child behavior ratings at ages 2 1/2 and 5 years. Mixed-effects multinomial logistic regression was used to examine associations between infant risk factors and "pure" and co-occurring child behavior problems, and test whether these associations changed over time. The results of this study showed that hostile parenting during infancy increased the likelihood that children would develop internalizing-only problems, whereas infants who were highly distressed in response to novelty were at increased risk of developing externalizing-only problems. Multiple risk factors, including maternal anxious and depressive symptoms, family conflict, and younger maternal age, independently predicted early childhood co-occurring problems. Additionally, there was a significant interaction between infant anger/frustration and hostile parenting: In the context of hostile parenting, infants high in anger were at increased risk of developing early co-occurring problems, though this association faded by age 5. These findings point to the importance of considering the infant's family context, and differentiating between "pure" and co-occurring behaviors when examining the etiology of early childhood behavior problems. (PsycINFO Database Record (c) 2015 APA, all rights reserved).
... where p 1 , p 2 , and (1 2 p 1 2 p 2 ) specify the proportion s of the binomial components, which are determined by the probabilities of a correct response (q 1 , q 2 , q 3 ). Furthermore, the application of mixture models is not restricted to investigation s concerning performance data, but is always useful, if hypotheses about qualitative categories are exam ined, as, for example, in temperament research (Stern, Arcus, Kagan, Rubin, & Snidman, 1995). ...
Article
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This paper reports on modelling six frequency distributions representing the analogical reasoning performance of four different samples of elementary schoolchildren. A two-component model outperformed a one-component model in all investigated data sets, discriminating accurate performers with high success probabilities and inaccurate performers with low success probabilities, whereas for two data sets a three-component model provided the best fit. In a treatment-control group data set, the treatment group comprised a larger proportion of accurate performers than the control group, whereas the success probabilities of the two latent classes were nearly identical in both groups. In a repeated-measures data set, both the success probabilities of the two latent classes and the proportion of accurate performers increased from the first to the second test session. The results provided a first indication of a transition in the development of analogical reasoning in elementary schoolchildren.
... A final person-centered approach that has been increasingly used is latent class analysis (LCA; Goodman, 1974; Lazarsfeld & Henry 1968). LCA has been used with a variety of constructs, including child temperament (Stern, Arcus, Kagan, Rubin, & Snidman, 1995), problem behavior (Lanza, Collins, Schafer, & Flaherty, 2005), depression (Lanza, Flaherty, & Collins, 2003; Sullivan, Kessler, & Kendler, 1998), and substance use (Chung, Park, & Lanza, 2005; Guo, Collins, Hill, & Hawkins, 2000; Lanza & Collins, 2002). More recently, LCA has been used to identify profiles of early risk associated with behavior and academic outcomes (Lanza, Rhoades, Nix, Greenberg, & CPPRG, in press). ...
Article
The primary goal of this study was to compare several variable-centered and person-centered methods for modeling multiple risk factors during infancy to predict the quality of caregiving environments at six months of age. Nine risk factors related to family demographics and maternal psychosocial risk, assessed when children were two months old, were explored in the understudied population of children born in low-income, non-urban communities in Pennsylvania and North Carolina (N = 1047). These risk factors were (1) single (unpartnered) parent status, (2) marital status, (3) mother's age at first child birth, (4) maternal education, (5) maternal reading ability, (6) poverty status, (7) residential crowding, (8) prenatal smoking exposure, and (9) maternal depression. We compared conclusions drawn using a bivariate approach, multiple regression analysis, the cumulative risk index, and latent class analysis (LCA). The risk classes derived using LCA provided a more intuitive summary of how multiple risks were organized within individuals as compared to the other methods. The five risk classes were: married low-risk; married low-income; cohabiting multiproblem; single low-income; and single low-income/education. The LCA findings illustrated how the association between particular family configurations and the infants' caregiving environment quality varied across race and site. Discussion focuses on the value of person-centered models of analysis to understand complexities of prediction of multiple risk factors.
... Although LCA has been applied to many multidimensional constructs, including temperament (Stern, Arcus, Kagan, Rubin, & Snidman, 1995), depression (Lanza, Flaherty, & Collins, 2003), teaching style (Dewilde, 2004), and alcohol use behavior (Lanza, Collins, Lemmon, & Schafer, 2007), it has not been well demonstrated in the literature, as applied to the study of multiple risks. Only very recently has this type of approach been proposed for modeling multiple risks. ...
Article
This study identified profiles of 13 risk factors across child, family, school, and neighborhood domains in a diverse sample of children in kindergarten from four US locations (n = 750; 45% minority). It then examined the relation of those early risk profiles to externalizing problems, school failure, and low academic achievement in Grade 5. A person-centered approach, latent class analysis, revealed four unique risk profiles, which varied considerably across urban African American, urban White, and rural White children. Profiles characterized by several risks that cut across multiple domains conferred the highest risk for negative outcomes. Compared to a variable-centered approach, such as a cumulative risk index, these findings provide a more nuanced understanding of the early precursors to negative outcomes. For example, results suggested that urban children in single-parent homes that have few other risk factors (i.e., show at least average parenting warmth and consistency and report relatively low stress and high social support) are at quite low risk for externalizing problems, but at relatively high risk for poor grades and low academic achievement. These findings provide important information for refining and targeting preventive interventions to groups of children who share particular constellations of risk factors.
... The only intimation of a discrete category in the anxiety disorder spectrum relates to social phobia, with one unpublished study [36] finding ambiguous evidence for a taxon of socially anxious individuals marked by extreme fears of public scrutiny. The existence of a taxon in this domain is rendered more plausible by taxometric evidence [37], replicated with mixture modelling [38], that inhibited temperament in childhood reflects a latent category. However, a finding that avoidant attachment style falls on a continuum in adults and infants [39,40] also counts against this possibility. ...
Article
To review studies of the categorical versus dimensional status of mental disorders that employ taxometric methodology. A comprehensive qualitative review of all published taxometric studies of psychopathology. Categorical and dimensional models each receive well-replicated support for some groups of mental disorders. Studies favour categorical models for melancholia, eating disorders, pathological dissociation, and schizotypal and antisocial personality disorders. Dimensional models tend to be favoured for the broad neurotic spectrum--general depression, generalized anxiety, posttraumatic stress disorder--and for borderline personality disorder. Taxometric research clarifies the latent structure of psychopathology in ways that have implications for the classification, assessment, explanation and conceptualization of mental disorder.
... Since that initial work, the latent class model has been applied to many research areas. Stern, Arcus, Kagan, Rubin, and Snidman (1995) presented a latent class analysis of infant temperament. In this work, several measures of temperament are given to a sample of infants and then it is determined whether a small number of latent classes (corresponding to different temperament types) can account for the observed relations among the items. ...
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Developmental research often involves studying change across 2 or more processes or constructs simultaneously. A natural question in this work is whether change in these 2 processes is related or independent. Associative latent transition analysis (ALTA) was designed to test hypotheses about the degree to which change in 2 discrete latent variables is related. The ALTA model is a type of latent class model, which is a categorical latent variable model based on categorical indicators. In the ALTA approach, level and change on 1 variable is predicted by level and change in another. Two types of hypotheses are discussed: (a) broad hypotheses of dependence between the 2 discrete latent variables and (b) targeted hypotheses comparing specific patterns of change between levels of the discrete variables. Both types of hypotheses are tested via nested model comparisons. Analyses of relations between psychological state and substance use illustrate the model. Recent psychological state and recent substance use were found to be associated cross-sectionally and longitudinally, implying that change in recent substance use was related to change in recent psychological state.
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The documented importance of temperament in explaining individual variability in development and adjustment continues to spur interest in research even as contrasting theoretical perspectives are being debated. This review examines unresolved conceptual issues in the measurement of temperament. Despite many psychometric problems and conceptual shortcomings of measures derived from various perspectives that are available to assess temperament, the constructs themselves have important implications for the practice of psychology.
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A Monte Carlo evaluation of four procedures for detecting taxonicity was conducted using artificial data sets that were either taxonic or nontaxonic. The data sets were analyzed using two of Meehl's taxometric procedures, MAXCOV and MAMBAC, Ward's method for cluster analysis in concert with the cubic clustering criterion and a latent variable mixture modeling technique. Performance of the taxometric procedures and latent variable mixture modeling were clearly superior to that of cluster analysis in detecting taxonicity. Applied researchers are urged to select from the better procedures and to perform consistency tests.
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Children's performance on cognitive tasks is often described in categorical terms in that a child is described as either passing or failing a test, or knowing or not knowing some concept. We used binomial mixture models to determine whether individual children could be classified as passing or failing two search tasks, the DeLoache model room task and the Berthier et al. door task. The data support categorical classification of the children and suggest that the increase in average proportion correct with age is the result of an increasing proportion of children who can solve the tasks. Performance on the two tasks was concordant, and improving performance could be due to advances in a single psychological ability, such as cognitive control. Copyright © 2014 John Wiley & Sons, Ltd.
Article
Mixture models are appropriate for data that arise from a set of qualitatively different subpopulations. In this study, latent class analysis was applied to observational data from a laboratory assessment of infant temperament at four months of age. The EM algorithm was used to fit the models, and the Bayesian method of posterior predictive checks was used for model selection. Results show at least three types of infant temperament, with patterns consistent with those identified by previous researchers who classified the infants using a theoretically based system. Multiple imputation of group memberships is proposed as an alternative to assigning subjects to the latent class with maximum posterior probability in order to reflect variance due to uncertainty in the parameter estimation. Latent class membership at four months of age predicted longitudinal outcomes at four years of age. The example illustrates issues relevant to all mixture models, including estimation, multi-modality, model selection, and comparisons based on the latent group indicators.
Chapter
Often quantities of interest in psychology cannot be observed directly. These unobservable quantities are known as latent variables. By using multiple items as indicators of the latent variable, we can obtain a more complete picture of the construct of interest and estimate measurement error. One approach to latent variable modeling is latent class analysis, a method appropriate for examining the relationship between discrete observed variables and a discrete latent variable. The present chapter will introduce latent class analysis, its extension to repeated measures, and recent developments further extending the latent class model. First, the concept of a latent class and the mathematical model are presented. This is followed by a discussion of parameter restrictions, model fit, and the measurement quality of categorical items. Second, latent class analysis is demonstrated through an examination of the prevalence of depression types in adolescents. Third, longitudinal extensions of the latent class model are presented. This section also contains an empirical example on adolescent depression types, where the previous analysis is extended to examine the stability and change in depression types over time. Finally, several recent developments that further extend the latent class model are introduced. Keywords: categorical variables; depression types; latent class analysis; latent transition analysis; latent variables; longitudinal
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Unpublished doctoral dissertation
  • D M Arcus