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.     

MULTIPLE IMPUTATION OF INCOMPLETE CATEGORICAL DATA USING LATENT CLASS ANALYSIS

We propose using latent class analysis as an alternative to log-linear analysis for the multiple imputation of incomplete categorical data. Similar to log-linear models, latent class models can be used to describe complex association structures between the variables used in the imputation model. However, unlike log-linear models, latent class models can be used to build large imputation models containing more than a few categorical variables. To obtain imputations reflecting uncertainty about the unknown model parameters, we use a nonparametric bootstrap procedure as an alternative to the more common full Bayesian approach. The proposed multiple imputation method, which is implemented in Latent GOLD software for latent class analysis, is illustrated with two examples. In a simulated data example, we compare the new method to well-established methods such as maximum likelihood estimation with incomplete data and multiple imputation using a saturated log-linear model. This example shows that the proposed method yields unbiased parameter estimates and standard errors. The second example concerns an application using a typical social sciences data set. It contains 79 variables that are all included in the imputation model. The proposed method is especially useful for such large data sets because standard methods for dealing with missing data in categorical variables break down when the number of variables is so large.     

Positive Adult Support and Depression Symptoms in Adolescent Females: The Partially Mediating Role of Eating Disturbances

This study examined linkages between depression symptoms (DEP) and positive adult support (PAS) in female adolescents and the partially mediating influence of eating disturbances (ED). Structural equation modeling was used to establish measurement models for each of the latent constructs, determine the relationships among the latent constructs, and examine the overall model fit of the data. The relationships among the latent constructs of ED, PAS, and DEP were tested using a mediation model. Results indicate that there is a significant, positive relationship between DEP and PAS and that ED are a partial mediator of this relationship. This study provides evidence for the importance of evaluating how ED can influence the trajectory of depression in the lives of adolescent females.     

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 .     

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.     

Capturing temporal dynamics of fear behaviors on a moment‐to‐moment basis

Identifying patterns of fearful behaviors early and accurately is essential to identify children who may be at increased risk for psychopathology. Previous work focused on the total amount of fear by using composites across time. However, considering the temporal dynamics of fear expression might offer novel insights into the identification of children at risk. One hundred and twenty‐five toddlers participated in high‐ and low‐fear tasks. Data were modeled using a novel two‐step approach. First, a hidden Markov model estimated latent fear states and transitions across states over time. Results revealed children's behavior was best represented by six behavioral states. Next, these states were analyzed using sequence clustering to identify groups of children with similar dynamic trajectories through the states. A four‐cluster solution found groups of children varied in fear response and regulation process: “external regulators” (using the caregiver as a regulation tool), “low reactive” (low reaction to stimulus), “fearful explorers” (managing their own internal state with minimal assistance from the caregiver), and “high fear” (fearful/at‐caregiver state regardless of task). The combination of analytic tools enabled fine‐grained examination of the processes of fearful temperament. These insights may help prevention programs target behaviors that perpetuate anxious behavior in the moment.     

DURATION MODELS FOR CREDIT RATING MIGRATION: EVIDENCE FROM THE FINANCIAL CRISIS

We introduce a specific duration model to analyze the prediction of the credit rating migration. We consider hazard rate processes based on multi‐state autoregressive conditional duration models. To take account of the economic context, we model the conditional mean of the duration between two ratings by means of a latent process. To this purpose, a dynamic‐ordered probit model is developed to describe the directions taken by the ratings in the presence of multiple states. As an illustration, we study the migration of credit rating during periods before and after the financial crisis. (JEL C14, C41, G24)     

Extracting a revised labor supply theory from Becker's model of the household

Conflicting assumptions about labor supply behavior lie at the nexus of ideological and theoretical debates regarding the reality of involuntary unemployment, the efficacy of Keynesian macro-policy, and the appropriate nature of welfare policy. This can in part be attributed to the fact that orthodox theory is effectively predicated upon describing the behavior of individuals whose level of affluence enables them to voluntarily withhold their labor from the market. Ironically, a means of resolution appears if we extend Gary Becker's utility producing model of the household to recognize two latent behavioral concerns: (1) the ‘need’ of households for money income in order to produce utility, and (2) the presence of work activity in the home. The resulting generalized labor supply model extends Becker's analysis to explicitly encompass both the behavior of the affluent, and the behavior of the poor who need to work in order to sustain their existence.     

Latent Class Factor and Cluster Models, Bi-Plots, and Related Graphical Displays

We propose an alternative method of conducting exploratory latent class analysis that utilizes latent class factor models, and compare it to the more traditional approach based on latent class cluster models. We show that when formulated in terms of R mutually independent, dichotomous latent factors, the LC factor model has the same number of distinct parameters as an LC cluster model with R+1 clusters. Analyses over several data sets suggest that LC factor models typically fit data better and provide results that are easier to interpret than the corresponding LC cluster models. We also introduce a new graphical "bi-plot" display for LC factor models and compare it to similar plots used in correspondence analysis and to a barycentric coordinate display for LC cluster models. New results on identification of LC models are also presented. We conclude by describing various model extensions and an approach for eliminating boundary solutions in identified and unidentified LC models, which we have implemented in a new computer program.     

School: One world or two worlds? Children's perspectives

The interlinguistic and intercultural comparability of school satisfaction as a component of subjective well-being (SWB) is analysed using a sample of 11 to 14-year-olds extracted from the Children's Worlds international database, which includes 15 countries (N = 17,246). To this end, two multi-item scales and one single-item scale on overall life satisfaction were adopted as indicators of SWB. Six items on satisfaction with different facets of school life were included as subjective indicators of school satisfaction.Previous analyses conducted by different authors in several countries were replicated by means of multiple regression analysis in order to explore which items could be better used to test models which alternatively use one or two latent variables. Different options were considered and analysed using Structural Equations Modelling (SEM) to estimate the most appropriate model for a cross-country comparison of school satisfaction as a component of SWB. Multi-group SEM was used on six items regarding school-related satisfaction, related alternatively to one and two latent variables. We propose a multi-group model with two latent variables for school-related satisfaction related to the SLSS and OLS for the purposes of cross-cultural comparison; the model displays excellent fit indexes.     

Work orders: Analysing employment histories using sequence data

The analysis of employment histories has been facilitated recently by advances in survey methodology, statistical processes and computing power. While much work has focused on transitions between states and time spent in one state, the potential of analysing a series of states (i.e. careers) has largely been ignored. A concentration on movement between two states, whilst allowing relevant contextual covariates to be controlled for, often ignores valuable data both prior to and after the episode in question. Analysis of extended sequences of employment states is better able to describe employment trajectories. Furthermore, comparison of sequences permits either allocation to theoretical categories, or the identification of latent groupings using cluster analysis. The resulting typology of careers can then be used in inferentially based analyses. This paper explores sequence analysis using Optimal Matching Analysis (OMA). OMA is explained in relation to one broad substantive issue: the relationship between employment trajectories and gender.     

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.     

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.     

ELECTRIC AND PLUG‐IN HYBRID VEHICLE DEMAND: LESSONS FOR AN EMERGING MARKET

Understanding demand in the new plug‐in hybrid electric vehicle (PHEV) market is critical to designing more effective adoption policies. We use stated preference data from an innovative choice experiment to estimate demand for PHEVs relative to battery electric vehicles (BEVs) and to explore heterogeneity in demand for these vehicles. We find the gap between willingness to pay for PHEVs and their price premium over conventional vehicles is on the order of current subsidies, while that of BEVs is an order of magnitude larger. We use a latent class model to show PHEVs draw a different consumer segment into the market. (JEL Q5, R41)     

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.     

A PARTIAL INDEPENDENCE ITEM RESPONSE MODEL FOR SURVEYS WITH FILTER QUESTIONS

In many surveys, responses to earlier questions determine whether later questions are asked. The probability of an affirmative response to a given item is therefore nonzero only if the participant responded affirmatively to some set of logically prior items, known as "filter items." In such surveys, the usual conditional independence assumption of standard item response models fails. A weaker "partial independence" assumption may hold, however, if an individual's responses to different items are independent conditional on the item parameters, the individual's latent trait, and the participant's affirmative responses to each of a set of filter items. In this paper, we propose an item response model for such "partially independent" item response data. We model such item response patterns as a function of a person-specific latent trait and a set of item parameters. Our model can be seen as a generalized hybrid of a discrete-time hazard model and a Rasch model. The proposed procedure yields estimates of (1) person-specific, interval-scale measures of a latent trait (or traits), along with person-specific standard errors of measurement; (2) conditional and marginal item severities for each item in a protocol; (3) person-specific conditional and marginal probabilities of an affirmative response to each item in a protocol; and (4) item information and total survey information. In addition, we show here how to investigate and test alternative conceptions of the dimensionality of the latent trait(s) being measured. Finally, we compare our procedure with a simpler alternative approach to summarizing data of this type.     

Financing long-term care with limited resources: combining the resources of the public and private sectors

Under Connecticut's recently implemented public/private partnership to finance long-term care, individuals will no longer need to impoverish themselves in order to receive Medicaid assistance. To encourage those people who can afford to buy a private long-term care insurance policy to do so, the state promises to shield one dollar in assets from Medicaid "spend-down" rules for every dollar a private policy pays out for Medicaid-covered services. This article describes the Partnership, shows how dwindling resources and budget constraints affected the development of this model, and then contrasts Connecticut's experience with that of other states and describes what can be learned from this demonstration.     

Lattice analysis and the representation of handicap associations

A main goal of this paper is to show how lattice analysis and the computer program GLAD can help in understanding the associations among psychological/somatic handicaps for a population of children excluded from school because of those handicaps. The lattices can be taken as a conceptual as well as an implicational model of multiple handicaps because of their capacity for formalizing the definitions of disorders in terms of extensions or intensions. Certain substructures of the lattice, weighted by the frequencies of the subject groups, can display the assessed associations between handicaps, thus addressing quite directly the research questions of the health services.     

For Better or For Worse? State-Level Marital Formation and Risk Sharing

Why do some U.S. states have higher levels of marital formation than others? This paper introduces an economic model wherein a state’s representative individual may choose to marry in order to diversify his or her idiosyncratic income risk. The paper demonstrates that such a diversification motive is enhanced for some utility functions when a state’s level of undiversifiable risk becomes larger, and when a state’s initial income is lower. A test of the model’s predictions, using cross-sectional data for the 50 U.S. states, provides some suggestive evidence for a risk sharing motive in marriage formation and joint spouse labor participation.     

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.