Covariance Models For Latent Structure In Longitudinal Data

We present several approaches to modeling latent structure in longitudinal studies when the covariance itself is the primary focus of the analysis. This is a departure from much of the work on longitudinal data analysis, in which attention is focused solely on the cross-sectional mean and the influence of covariates on the mean. Such analyses are particularly important in policy-related studies, in which the heterogeneity of the population is of interest. We describe several traditional approaches to this modeling and introduce a flexible, parsimonious class of covariance models appropriate to such analyses. This class, while rooted in the tradition of mixed effects and random coefficient models, merges several disparate modeling philosophies into what we view as a hybrid approach to longitudinal data modeling. We discuss the implications of this approach and its alternatives especially on model interpretation. We compare several implementations of this class to more commonly employed mixed effects models to describe the strengths and limitations of each. These alternatives are compared in an application to long-term trends in wage inequality for young workers. The findings provide additional guidance for the model formulation process in both statistical and substantive senses.     

MEANINGFUL REGRESSION AND ASSOCIATION MODELS FOR CLUSTERED ORDINAL DATA

Many proposed methods for analyzing clustered ordinal data focus on the regression model and consider the association structure within a cluster as a nuisance. However, the association structure is often of equal interest—for example, temporal association in longitudinal studies and association between responses to similar questions in a survey. We discuss the use, appropriateness, and interpretability of various latent variable and Markov models for the association structure and propose a new structure that exploits the ordinality of the response. The models are illustrated with a study concerning opinions regarding government spending and an analysis of stability and change in teenage marijuana use over time, where we reveal different behavioral patterns for boys and girls through a comprehensive investigation of individual response profiles.     

Analytic approaches for assessing long-term treatment effects. Examples of empirical applications and findings

Analytic approaches, including the structural equation model (autoregressive panel model), hierarchical linear model, latent growth curve model, survival/event history analysis, latent transition model, and time-series analysis (interrupted time series, multivariate time-series analysis) are discussed for their applicability to data of different structures and their utility in evaluating temporal effects of treatment. Methods are illustrated by presenting applications of the various approaches in previous studies examining temporal patterns of treatment effects. Recent advancements in these longitudinal modeling approaches and the accompanying computer software development offer tremendous flexibility in examining long-term treatment effects through longitudinal data with varying numbers and intervals of assessment and types of measures. A multimethod assessment will contribute to a more complete understanding of the complex phenomena of the long-term courses of substance use and its treatment.     

FOUR USEFUL FINITE MIXTURE MODELS FOR REGRESSION ANALYSES OF PANEL DATA WITH A CATEGORICAL DEPENDENT VARIABLE

This paper describes and contrasts two useful ways to employ a latent class variable as a mixture variable in regression analyses of panel data with a categorical dependent variable. One way is to model unobserved heterogeneity in the trajectory, or change in the distribution, of the dependent variable. Two models that accomplish this are the latent trajectory model and latent growth curve model for a categorical dependent variable having ordered categories. Each latent class here represents a distinct trajectory of the dependent variable. The latent trajectory model introduces covariate effects on the composition of latent classes, while the latent growth curve model introduces covariate effects on both the "intercept" and the "slope" of growth in logit, which may vary among latent classes.
The other useful way is to model unobserved heterogeneity in the state dependence of the dependent variable. Two models that accomplish this are introduced for a simultaneous analysis of response probability and response stability, and the latent class variable is employed to distinguish two latent populations that differ in the stability of responses over time. One of them is the switching multinomial logit model with a time-lagged dependent variable as its separation indicator, and the other is the mover-stayer regression model.
By applying these four models to empirical data, this paper demonstrates the usefulness of these models for panel-data analyses. Example programs for specifying these models based on the LEM program are also provided.     

Latent Class Marginal Models for Cross-Classifications of Counts

The standard latent class model is a finite mixture of indirectly observed multinomial distributions, each of which is assumed to exhibit statistical independence. Latent class analysis has been applied in a wide variety of research contexts, including studies of mobility, educational attainment, agreement, and diagnostic accuracy, and as measurement error models in social research. One of the attractive features of the latent class model in these settings is that the parameters defining the individual multinomials are readily interpretable marginal probabilities, conditional on the unobserved latent variable(s), that are often of substantive interest. There are, however, settings where the local-independence axiom is not supported, and hence it is useful to consider some form of local dependence. In this paper we consider a family of models defined in terms of finite mixtures of multinomial models where the multinomials are parameterized in terms of a set of models for the univariate marginal distributions and for marginal associations. Local dependence is introduced through the models for marginal associations, and the standard latent class model obtains as a special case. Three examples are analyzed with the models to illustrate their utility in analyzing complex cross-classifications.     

The longitudinal effects of parental monitoring and self-control on depression in Korean adolescents: A multivariate latent growth approach

The purpose of this study was to examine the longitudinal effects of parental monitoring and self-control on depression. To address this purpose, this study investigated the interrelationships among depression, perceived parental monitoring, and self-control—as well as their developmental changes from the eighth to the twelfth grades—by repeated assessment of 3449 Korean adolescents. The data from Korea Youth Panel Survey (KYPS) of the eighth graders who were followed for five years were analyzed using latent growth modeling. The univariate latent growth models showed that adolescents experience an increase in both parental monitoring and self-control but a decline in depression over the five years. In addition, the multivariate latent growth model suggested that the initial level of parental monitoring had significant effects, both directly and indirectly through self-control, on the initial level of depression. The linear changes in parental monitoring were associated with the linear changes in self-control; likewise, the linear changes in self-control were related to those in depression. These results imply that parental monitoring and self-control need to be emphasized as a strategy in order to prevent or alleviate adolescents' depression.     

Blame It on the Alcohol: The Influence of Alcohol Consumption During Adolescence,the Transition to Adulthood,and Young Adulthood on One-Time Sexual Hookups

Using public-use data from the National Longitudinal Study of Adolescent Health (n = 3,733) and the life-span developmental perspective, the current study sought to determine whether global reports of alcohol use, binge drinking, and drunkenness are best represented as indicators of a latent alcohol consumption construct during adolescence, the transition to adulthood, and young adulthood. We also examined the predictive power of alcohol consumption during each developmental period on the total number of one-time sexual hookups reported in young adulthood. A confirmatory factor analysis revealed alcohol use, binge drinking, and drunkenness are consistent indicators of a latent alcohol consumption variable over time, although the mean levels of the indicators were significantly lower during adolescence. Structural equation modeling analyses found alcohol consumption during the transition to adulthood and young adulthood predicted one-time sexual hookups in young adulthood, but alcohol consumption during the transition to adulthood exhibited the strongest association with hooking up. Implications for research, theory, and practice are discussed.     

In search of the wage-labour/service contract: new evidence on the validity of the Goldthorpe class schema

In this paper we examine new empirical evidence on the coherence and magnitude of the main classes in the Goldthorpe class schema. Particular attention is paid to issues that have recently been a source of academic dispute: the coherence and size of the service class and the distinction between the service class and intermediate classes. Using recently available British data collected by the Office for National Statistics we examine: (i) the extent to which measures of class-relevant job characteristics are empirically discriminated by the categories of the schema; (ii) the structure of a 'contract type' dimension of employment relations conceived of as a categorical latent variable; and (iii) the association between this latent variable and both the Goldthorpe class schema and a related measure socio-economic group (SEG). We find that the data are consistent with the existence of a three category latent 'contract type' variable largely corresponding to the notions of service, intermediate and wage-labour contracts explicit in discussions of the theoretical rationale for the Goldthorpe schema. We further find a substantial degree of fit between the latent 'contract types' and the schema. However, the service class fault line appears to lie within class I and II of the schema rather than between them and the intermediate classes which suggests a revised, smaller service class would better capture the reality of the contemporary British occupational structure.     

Random-Effects Modeling of Categorical Response Data

In many applications observations have some type of clustering, with observations within clusters tending to be correlated. A common instance of this occurs when each subject in the sample undergoes repeated measurement, in which case a cluster consists of the set of observations for the subject. One approach to modeling clustered data introduces cluster-level random effects into the model. The use of random effects in linear models for normal responses is well established. By contrast, random effects have only recently seen much use in models for categorical data. This chapter surveys a variety of potential social science applications of random effects modeling of categorical data. Applications discussed include repeated measurement for binary or ordinal responses, shrinkage to improve multiparameter estimation of a set of proportions or rates, multivariate latent variable modeling, hierarchically structured modeling, and cluster sampling. The models discussed belong to the class of generalized linear mixed models (GLMMs), an extension of ordinary linear models that permits nonnormal response variables and both fixed and random effects in the predictor term. The models are GLMMs for either binomial or Poisson response variables, although we also present extensions to multicategory (nominal or ordinal) responses. We also summarize some of the technical issues of model-fitting that complicate the fitting of GLMMs even with existing software.     

USING INSTRUMENTAL VARIABLE TESTS TO EVALUATE MODEL SPECIFICATION IN LATENT VARIABLE STRUCTURAL EQUATION MODELS

Structural equation modeling (SEM) with latent variables is a powerful tool for social and behavioral scientists, combining many of the strengths of psychometrics and econometrics into a single framework. The most common estimator for SEM is the full-information maximum likelihood (ML) estimator, but there is continuing interest in limited information estimators because of their distributional robustness and their greater resistance to structural specification errors. However, the literature discussing model fit for limited information estimators for latent variable models is sparse compared with that for full-information estimators. We address this shortcoming by providing several specification tests based on the 2SLS estimator for latent variable structural equation models developed by Bollen (1996) . We explain how these tests can be used not only to identify a misspecified model but to help diagnose the source of misspecification within a model. We present and discuss results from a Monte Carlo experiment designed to evaluate the finite sample properties of these tests. Our findings suggest that the 2SLS tests successfully identify most misspecified models, even those with modest misspecification, and that they provide researchers with information that can help diagnose the source of misspecification.     

Conditionally Independent Dyads (CID) network models: A latent variable approach to statistical social network analysis

Latent variable network models that accommodate edge correlations implicitly, by assuming an underlying latent factor, are increasing in popularity. Although, these models are examples of what is a growing body of research, much of the research is focused on proposing new models or extending others. There has been very little work on unifying the models in a single framework. In this paper, we present a complete framework that organizes existing latent variable network models within an integrative generalized additive model. Our framework is called Conditionally Independent Dyad (CID) models, and includes existing network models that assume dyad (or edge) independence conditional on latent variables and other components in the model. We further discuss practical aspects of model fitting such as posterior parameter estimation via MCMC, identifiability of parameters, approaches to handle missing data and model selection via cross-validation, for the proposed additive CID models. Finally, by presenting several data examples, we illustrate the utility of the proposed framework and provide advice on selecting components for building new CID models.     

Evaluation of HIV risk reduction intervention programs via latent growth model

The latent growth model (LGM) has drawn increasing attention in behavioral studies using longitudinal data. The LGM captures the level and trajectory of behavior change, variation in both the initial status and the trend of behavior change, as well as the time-ordered covariation between the initial status and change. This study demonstrates how the LGM can be applied in the evaluation of intervention programs targeting HIV risk behavior among drug users. Multi-group piecewise latent growth models were fit to longitudinal data with three repeated response measures.     

ON THE ASSIGNMENT OF INDIVIDUALS TO LATENT CLASSES

Consider an m-way cross-classification table (for m = 3, 4, … ) of m dichotomous variables that describes (1) the 2 ^m possible response patterns to a set of m questions (where the response to each question is binary), and (2) the number of individuals whose responses to the m questions can be described by a particular response pattern, for each of the 2 ^m possible response patterns. Consider the situation where the data in the cross-classification table are analyzed using a particular latent class model having T latent classes (for T = 2, 3, …), and where this model fits the data well. With this latent class model, it is possible to estimate, for an individual who has a particular response pattern, what is the conditional probability that this individual is in a particular latent class, for each of the T latent classes. In this article, the following question is considered: For an individual who has a particular response pattern, can we use the corresponding estimated conditional probabilities to assign this individual to one of the T latent classes? Two different assignment procedures are considered here, and for each of these procedures, two different criteria are introduced to help assess when the assignment procedure is satisfactory and when it is not. In addition, we describe here the particular framework and context in which the two assignment procedures, and the two criteria, are considered. For illustrative purposes, the latent class analysis of a classic set of data, a four-way cross-classification of some survey data, obtained in a two-wave panel study, is discussed; and the two different criteria introduced herein are applied in this analysis to each of the two assignment procedures .     

Political and economic determinants of expenditure on day services for persons with intellectual disabilities or autism

This study investigates whether the Swedish national entitlement legislation, which is known to be one of the most developed in Europe for persons with intellectual disabilities or autism, accomplishes its aim to provide equal quality of day services independent of location. We estimated a reduced-form model of demand and supply-side determinants of a latent quality variable for day-service programmes using panel data on expenditure per attendee for the 290 Swedish municipalities 2004–2012. We found that expenditure per attendee is among others affected by changes of the local tax base and outcome in elections to the local assemblies. These results imply that rights of persons with intellectual disabilities with regard to equal quality of day services independent of where they live are not fully honoured in budget allocation decisions made by local governments.     

Mothers' depression and educational attainment and their children's academic trajectories

In this study, we take a dynamic approach to studying the connections among mothers' education, their depression, and their children's academic trajectories during elementary school. Applying latent growth curve modeling to longitudinal data from the National Institute of Child Health and Human Development's Study of Early Child Care and Youth Development (N = 1,012), we find that maternal depression does not mediate the association between mothers' education and children's achievement. Instead, maternal education moderates the association between maternal depression and children's achievement. Specifically, maternal depression only predicted lower achievement for children of women who did not pursue higher education. These results highlight the role of mothers' mental health in the intergenerational linkage between mothers' and children's educational experiences.     

Regression Analysis of Multivariate Binary Response Variables Using Rasch-Type Models and Finite-Mixture Methods

A model is considered for the regression analysis of multivariate binary data such as repeated-measures data (for example, panel data) or multiple-indicators with measures of some underlying characteristic such as attitude or ability (for example, surveys or tests). The model is related to the usual Rasch model, the usual latent-class model, and other familiar models such as logistic regression. In addition to a regression specification, the model includes parameters that describe heterogeneity not accounted for by the predictors. In contrast to most other approaches, a nonparametric specification of the latent mixing distribution is used, leading to a formulation based on scaled latent classes. We examine the relationship between this model and several other models, give a tractable formulation of the likelihood function and likelihood equations, present an algorithm for maximum-likelihood estimation, and analyze marginal and conditional latent structures. The approach is illustrated with longitudinal data from the German Socioeconomic Panel.     

Längsschnittdaten und Mehrebenenanalyse

In the present article a few basic multilevel models for longitudinal data are introduced and applied to the Household Income and Labor Dynamics in Australia Survey 10 (HILDA) for demonstrational purposes. The covered models are adaptions of the random-intercept-only model, the random-intercept models and the random- intercept random-slope model with and without level-1 and level-2 predictors to longitudinal data. The modeling of contextual effects is covered. One particularity in longitudinal data is the fact that persons (level-2) may be regarded as the context of the time-varying observations on level-1. To incorporate the macro-level of sociology, it is necessary to expand the model to a third level. A model with three levels is introduced and in addition a simple growth curve model and a multivariate multilevel model are presented.     

Longitudinal Pathways From Shyness in Early Childhood to Personality in Adolescence: Do Peers Matter?

Temperamental shyness in childhood is theorized to be an important contributor for adolescent personality. However, empirical evidence for such pathways is scarce. Using longitudinal data (N = 939 children, 51% boys) across 17 years, the aim of this study was to examine how shyness development throughout childhood predicted personality traits in adolescence, and the role of peers in these associations. Results from piecewise latent growth curve modeling showed early shyness levels to predict lower emotional stability and openness in adolescence, whereas early shyness levels and growth across childhood predicted lower extraversion. Peer problems in early adolescence accounted for these associations. This study is the first to demonstrate the role of childhood shyness and peer relations for adolescents’ personality development.     

Log-Multiplicative Association Models As Latent Variable Models For Nominal and/or Ordinal Data

Associations between multiple discrete measures are often due to collapsing over other variables. When the variables collapsed over are unobserved and continuous, log-multiplicative association models, including log-linear models with linear-by-linear interactions for ordinal categorical data and extensions of Goodman's (1979, 1985) RC(M) association model for multiple nominal and/or ordinal categorical variables, can be used to study the relationship between the observed discrete variables and the unobserved continuous ones, and to study the unobserved variables. The derivation and use of log-multiplicative association models as latent variable models for discrete variables are presented in this paper. The models are based on graphical models for discrete and continuous variables where the variables follow a conditional Gaussian distribution. The models have many desirable properties, including having schematic or graphical representations of the system of observed and unobserved variables, the log-multiplicative models can be read from the graphs, and estimates of the means, variances, and covariances of the latent variables given values on the observed variables are a function of the log-multiplicative model parameters. To illustrate some of the advantageous aspects of these models, two examples are presented. In one example, responses to items from the General Social Survey (Davis and Smith 1996) are modeled, and in the other example, panel data from two groups (Coleman 1964) are analyzed.