Multilevel Mixture Factor Models

Factor analysis is a statistical method for describing the associations among sets of observed variables in terms of a small number of underlying continuous latent variables. Various authors have proposed multilevel extensions of the factor model for the analysis of data sets with a hierarchical structure. These Multilevel Factor Models (MFMs) have in common that—as in multilevel regression analysis—variation at the higher level is modeled using continuous random effects. In this article, we present an alternative multilevel extension of factor analysis which we call the Multilevel Mixture Factor Model (MMFM). It is based on the assumption that higher level units belong to latent classes that differ in terms of the parameters of the factor model specified for the lower level units. We demonstrate the added value of MMFM compared with MFM, both from a theoretical and applied perspective, and we illustrate the complementarity of the two approaches with an empirical application on students' satisfaction with the University of Florence. The multilevel aspect of this application is that students are nested within study programs, which makes it possible to cluster these programs based on their differences in students' satisfaction.     

Mixture Models of Categorization

Many currently popular models of categorization are either strictly parametric (e.g., prototype models, decision bound models) or strictly nonparametric (e.g., exemplar models) (F. G. Ashby & L. A. Alfonso-Reese, 1995, Journal of Mathematical Psychology, 39, 216-233). In this article, a family of semiparametric classifiers is investigated where categories are represented by a finite mixture distribution. The advantage of these mixture models of categorization is that they contain several parametric models and nonparametric models as a special case. Specifically, it is shown that both decision bound models (F. G. Ashby & W. T. Maddox, 1992, Journal of Experimental Psychology: Human Perception and Performance, 16, 598-612; 1993, Journal of Mathematical Psychology, 37, 372-400) and the generalized context model (R. M. Nosofsky, 1986, Journal of Experimental Psychology: General, 115, 39-57) can be interpreted as two extreme cases of a common mixture model. Furthermore, many other (semiparametric) models of categorization can be derived from the same generic mixture framework. In this article, several examples are discussed and a parameter estimation procedure for fitting these models is outlined. To illustrate the approach, several specific models are fitted to a data set collected by S. C. McKinley and R. M. Nosofsky (1995, Journal of Experimental Psychology: Human Perception and Performance, 21, 128-148). The results suggest that semi-parametric models are a promising alternative for future model development.     

Understanding Materialism Among Youth

As an emerging value, materialism helps explain the consumer behavior of youth. Using a national sample of 9‐ to 14‐year‐olds, in this study we developed a Youth Materialism Scale. The findings suggest that more materialistic youth tend to shop more and save less. They are most interested in new products and most responsive to advertising and promotional efforts. Their parents view them as more expert with regard to products and they wield more purchase influence on their parents. Parents who are more materialistic tend to have children who are more materialistic. This study also reveals a modest negative relation between materialism and liking for school and school performance.     

Social Anxiety Among Adolescents: Linkages with Peer Relations and Friendships

This study examined the utility of modifying the Social Anxiety Scale for Children—Revised (SASC-R) for use with adolescents, and examined associations between adolescents' social anxiety (SA) and their peer relations, friendships, and social functioning. Boys (n = 101) and girls (n = 149) in the 10th through 12th grades completed the Social Anxiety Scale for Adolescents (SAS-A) and measures of social support, perceived competence, and number and quality of their best friendships. Factor analysis of the SAS-A confirmed a three-factor structure: Fear of Negative Evaluation, Social Avoidance and Distress in General, and Social Avoidance Specific to New Situations or Unfamiliar Peers. Girls reported more SA than boys, and SA was more strongly linked to girls' social functioning than boys'. Specifically, adolescents with higher levels of SA reported poorer social functioning (less support from classmates, less social acceptance), and girls with higher levels of SA reported fewer friendships, and less intimacy, companionship, and support in their close friendships. These findings extend work on the SASC-R to adolescents, and suggest the importance of SA for understanding the social functioning and close friendships of adolescents, especially girls.     

Nonlinear Random-Effects Mixture Models for Repeated Measures

A mixture model for repeated measures based on nonlinear functions with random effects is reviewed. The model can include individual schedules of measurement, data missing at random, nonlinear functions of the random effects, of covariates and of residuals. Individual group membership probabilities and individual random effects are obtained as empirical Bayes predictions. Although this is a complicated model that combines a mixture of populations, nonlinear regression, and hierarchical models, it is straightforward to estimate by maximum likelihood using SAS PROC NLMIXED. Many different models can be studied with this procedure. The model is more general than those that can be estimated with most special purpose computer programs currently available because the response function is essentially any form of nonlinear regression. Examples and sample code are included to illustrate the method.     

Regularized Finite Mixture Models for Probability Trajectories

Finite mixture models are widely used in the analysis of growth trajectory data to discover subgroups of individuals exhibiting similar patterns of behavior over time. In practice, trajectories are usually modeled as polynomials, which may fail to capture important features of the longitudinal pattern. Focusing on dichotomous response measures, we propose a likelihood penalization approach for parameter estimation that is able to capture a variety of nonlinear class mean trajectory shapes with higher precision than maximum likelihood estimates. We show how parameter estimation and inference for whether trajectories are time-invariant, linear time-varying, or nonlinear time-varying can be carried out for such models. To illustrate the method, we use simulation studies and data from a long-term longitudinal study of children at high risk for substance abuse. This work was supported in part by NIAAA grants R37 AA07065 and R01 AA12217 to RAZ.     

Detecting Social Desirability Bias Using Factor Mixture Models

Based on the conceptualization that social desirable bias (SDB) is a discrete event resulting from an interaction between a scale's items, the testing situation, and the respondent's latent trait on a social desirability factor, we present a method that makes use of factor mixture models to identify which examinees are most likely to provide biased responses, which items elicit the most socially desirable responses, and which external variables predict SDB. Problems associated with the common use of correlation coefficients based on scales' total scores to diagnose SDB and partial correlations to correct for SDB are discussed. The method is demonstrated with an analysis of SDB in the Attitude toward Interprofessional Service-Learning scale with a sample of students from health-related fields.     

Analyzing Job Analysis Data Using Mixture Rasch Models

An important piece of validity evidence to support the use of credentialing exams comes from performing a job analysis of the profession. One common job analysis method is the task inventory method, where people working in the field are surveyed using rating scales about the tasks thought necessary to safely and competently perform the job. This article describes how mixture Rasch models can be used to analyze these data, and how results from these analyses can help to identify whether different groups of people may be responding to job tasks differently. Three examples from different credentialing programs illustrate scenarios that can be found when applying mixture Rasch models to job analysis data. Discussion of what these results may imply for the development of credentialing exams and other analyses of job analysis data is provided.     

Nonlinear Structured Growth Mixture Models in Mplus and OpenMx

Growth mixture models (GMMs; B. O. Muthén & Muthén, 2000; B. O. Muthén & Shedden, 1999) are a combination of latent curve models (LCMs) and finite mixture models to examine the existence of latent classes that follow distinct developmental patterns. GMMs are often fit with linear, latent basis, multiphase, or polynomial change models because of their common use, flexibility in modeling many types of change patterns, the availability of statistical programs to fit such models, and the ease of programming. In this article, we present additional ways of modeling nonlinear change patterns with GMMs. Specifically, we show how LCMs that follow specific nonlinear functions can be extended to examine the presence of multiple latent classes using the Mplus and OpenMx computer programs. These models are fit to longitudinal reading data from the Early Childhood Longitudinal Study–Kindergarten Cohort to illustrate their use.     

Assessing the Robustness of Mixture Models to Measurement Noninvariance

Abstract

Recent work reframes direct effects of covariates on items in mixture models as differential item functioning (DIF) and shows that, when present in the data but omitted from the fitted latent class model, DIF can lead to overextraction of classes. However, less is known about the effects of DIF on model performance—including parameter bias, classification accuracy, and distortion of class-specific response profiles—once the correct number of classes is chosen. First, we replicate and extend prior findings relating DIF to class enumeration using a comprehensive simulation study. In a second simulation study using the same parameters, we show that, while the performance of LCA is robust to the misspecification of DIF effects, it is degraded when DIF is omitted entirely. Moreover, the robustness of LCA to omitted DIF differs widely based on the degree of class separation. Finally, simulation results are contextualized by an empirical example.     

Investigating Individual Differences in Toddler Search with Mixture Models

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.     

Models of Development: Understanding Risk in Adolescence

In this paper, we review developmental models for understanding adolescence as they might be applied to emerging sexuality and the challenges and risks that may be associated with different sexual orientations and identities. Models have been identified as: cumulative events or simultaneous change, accentuation, or trajectory models. Inclusion of risk and protective factors and considering the extent of balance between these elements of an adolescent's life is also discussed in terms of predicting mental health outcomes. These models have been particularly useful in the study of the development of psychopathology and clearly relate to the broader issue of understanding suicide risk during adolescence.     

混合IRT潜在模型及其应用轨迹

项目反应理论是测量被试潜在特质的现代测量理论, 潜在类别分析是基于模型的潜在特质分类技术。混合项目反应理论将项目反应理论与潜在类别分析相结合, 能够同时对被试分类并量化其潜在特质。在阐述混合项目反应理论概念、原理的基础上, 介绍了MRM、mNRM和mPCM等几种常见混合模型及其参数估计方法, 并从心理与行为特征分类、项目功能差异检测、测验效度评价等方面评述了其在心理测验中的应用发展轨迹。     

Detecting Multiple Random Changepoints in Bayesian Piecewise Growth Mixture Models

Piecewise growth mixture models are a flexible and useful class of methods for analyzing segmented trends in individual growth trajectory over time, where the individuals come from a mixture of two or more latent classes. These models allow each segment of the overall developmental process within each class to have a different functional form; examples include two linear phases of growth, or a quadratic phase followed by a linear phase. The changepoint (knot) is the time of transition from one developmental phase (segment) to another. Inferring the location of the changepoint(s) is often of practical interest, along with inference for other model parameters. A random changepoint allows for individual differences in the transition time within each class. The primary objectives of our study are as follows: (1) to develop a PGMM using a Bayesian inference approach that allows the estimation of multiple random changepoints within each class; (2) to develop a procedure to empirically detect the number of random changepoints within each class; and (3) to empirically investigate the bias and precision of the estimation of the model parameters, including the random changepoints, via a simulation study. We have developed the user-friendly package BayesianPGMM for R to facilitate the adoption of this methodology in practice, which is available at https://github.com/lockEF/BayesianPGMM. We describe an application to mouse-tracking data for a visual recognition task.     

Interrelations Among Models For The Analysis Of Moment Structures

Factor analysis in several populations, covariance structure models, three-mode factor analysis, structural equation systems with measurement model, and analysis of covariance with measurement model are all shown to be specializations of a general moment structure model published previously in this journal. Some new structured linear models are also described; they may be considered either generalizations or special cases of existing models. Simple representations are developed for complex linear models, and some applications to behavioral data are cited.     

The Propositional vs. Hermeneutic Models of Cross-Cultural Understanding

Abstract

What the authors attempts to address in this paper is a Kantian question: not whether, but how is cross-cultural understanding possible? And specifically, what is a more effective approach for cross-cultural understanding? The answer lies in an analysis of two different models of cross-cultural understanding, that is, propositional and hermeneutic understanding. To begin with, the authors presents a linguistic interpretation of culture, i.e., a culture as a linguistically formulated and transmitted symbolic system with its conceptual core as a scheme of basic cultural presuppositions. Such a symbolic system is referred to as a cultural language. After exploring the essential role of cultural presuppositions in cross-cultural understanding, the authors discusses the traditional model of cross-cultural understanding, namely, the propositional model. Through critically examining the two popular versions of the propositional model, i.e., the projective approach and the adoptive approach to cross-cultural understanding, it is found that cross-cultural propositional understanding is doomed to failure. To move us beyond the absolutism-relativism trap embedded within propositional understanding, the authors first introduces and discusses Hans-Georg Gadamer’s hermeneutic understanding, and then applies Hans-Georg Gadamer’s hermeneutic model of understanding to cross-cultural understanding. It is finally concluded that cross-cultural understanding is essentially hermeneutic – including the case of cultural learning, not propositional. Therefore, cross-cultural understanding is hermeneutically possible.     

On Inclusion of Covariates for Class Enumeration of Growth Mixture Models

In this article, we directly question the common practice in growth mixture model (GMM) applications that exclusively rely on the fitting model without covariates for GMM class enumeration. We provide theoretical and simulation evidence to demonstrate that exclusion of covariates from GMM class enumeration could be problematic in many cases. Based on our findings, we provide recommendations for examining the class enumeration by the fitting model without covariates and discuss the potential of covariate inclusion as a remedy for the weakness of GMM class enumeration without including covariates. A real example on the development of children's cumulative exposure to risk factors for adolescent substance use is provided to illustrate our methodological developments.     

Observations on the Use of Growth Mixture Models in Psychological Research

Psychologists are applying growth mixture models at an increasing rate. This article argues that most of these applications are unlikely to reproduce the underlying taxonic structure of the population. At a more fundamental level, in many cases there is probably no taxonic structure to be found. Latent growth classes then categorically approximate the true continuum of individual differences in change. This approximation, although in some cases potentially useful, can also be problematic. The utility of growth mixture models for psychological science thus remains in doubt. Some ways in which these models might be more profitably used are suggested.     

Longitudinal Linkages Between Posttraumatic Stress Disorder Symptoms and Violent Behaviors Among Chinese Adolescents Following the Wenchuan Earthquake

This study was conducted to examine the longitudinal relations between posttraumatic stress disorder (PTSD) symptoms and violent behaviors. In this study, 415 adolescent survivors of the Wenchuan earthquake in China (May 12, 2008) were assessed by using self-report questionnaires 1 year (T1), 1.5 years (T2), and 2 years (T3) after the earthquake. The findings suggested that from 1 to 1.5 years after the earthquake, only intrusive symptoms of PTSD were a risk factor for violent behaviors, whereas violent behaviors were a risk factor for all 3 PTSD symptom clusters. Furthermore, 1.5 to 2 years after the earthquake, avoidance symptoms of PTSD were a risk factor for violent behaviors and hyperarousal symptoms of PTSD had no significant relation with violent behaviors.