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.     

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.     

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.     

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.     

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.     

The evaluation and selection of adequate causal models: a compensatory education example

Procedures for ascertaining relative model adequacy in latent variable structural relations models are discussed. Under diverse methods of estimation, this determination may be assessed using the chi square goodness of fit statistic, incremental fit indices for covariance structure models, and latent variable coefficients of determination. An example from evaluation research is taken (cf. Magidson, 1977; Bentler & Woodward, 1978). Numerical sensitivity of parameter estimates under alternative model specifications is demonstrated. Interpretive implications based on these procedures are discussed in terms of parameter sensitivity to alternative model specifications.     

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.     

Object relations family therapy as a model for practice

This paper provides an introduction to a new approach to the practice of family therapy called object relations family therapy. It is viewed as especially appropriate for social work practice due to its ability to combine individual, couple and family modalities. In addition it permits work on multiple levels of latent and manifest content. Its derivatives in the work of the objects relations theorists, Klein, Fairbairn, Guntrip, Winnicott and Bion are described. Illustrative case examples are provided.     

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.     

A propos de l'hétérogénéité des formes organisationnelles de l'économie sociale : isomorphisme versus écologie des organisations en économie sociale

This article addresses the problem of the diversity of social economy organizational forms. Two theoretical approaches (organizational ecology and neo‐institutionalism approach focusing on institutional isomorphism) establish the main forces and determinants of these organizational forms. With data from a survey on Montreal social economy, we use diversified methods (discriminant analysis and latent class analysis) to test these two concurrent theories. As a conclusion, we discuss the established stylized facts. Our results are supportive of the organizational ecology approach, while calling for new empirical investigations.     

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 .     

The spatiality of social relations: an Indian case-study

Using ethnographic information, the paper asserts the significance of space–society relations in rural India. In particular, the paper shows that material interests of classes and other social groups are normally tied to particular geographical areas. So agrarian social relations are local relations. Similarly, given the territorial organization of the state, state–society relations are local relations too. Thus as locally dependent members of classes and other collectivities and as citizens dependent on local branches of the state, people often find themselves predisposed to interact locally. There is also a counter-tendency to this in that people try to escape local dependence and interact with distant places. In either case, social relations are spatial relations, and the fact that social relations are spatial relations makes some difference to the way society works, although the specific ways in which this spatiality makes a difference are place-specific. The paper shows that social processes such as economic development, class conflict, reproduction of caste and kinship relations and performance of public policies can be better understood if we analyse the spatiality of these processes in particular places.     

The same everywhere? Exploring structural homologies of national social fields using the case of journalism

Pierre Bourdieu argued for the existence of general properties and even laws of social fields. In contrast to spaces of class relations and patterns of cultural lifestyles, however, almost no systematic comparative research exists on the homologies of national social fields of a more specialised nature. Also, the large majority of research is done on Western countries, raising concerns about the relevance of the concept for less differentiated societies. Using the field of journalism as a case, typical structures of 67 national fields (n = 27,567) are in this article investigated using a reverse approach: First, the subjective spaces of journalists' experienced constraints and imperatives in their jobs are sketched as a proxy for field structure using variants of multiple correspondence analysis, and second, the distribution of the social and professional properties of journalists are used to suggest capital structures. The results suggest great stability in the fundamental organising principles of fields of journalism around the world, although with considerable variation in their autonomy.     

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.     

Stochastic a posteriori blockmodels: Construction and assessment

In 1983, Holland, Laskey, and Leinhardt, using the ideas of Holland and Leinhardt, and Fienberg and Wasserman, introduced the notion of a stochastic blockmodel. The mathematics for stochastic a priori blockmodels, in which exogenous actor attribute data are used to partition actors independently of any statistical analysis of the available relational data, have been refined by several researchers and the resulting models used by many. Attempts to simultaneously partition actors and to perform relational data analyses using statistical methods that yield stochastic a posteriori blockmodels are still quite rare. In this paper, we discuss some old suggestions for producing such posterior blockmodels, and comment on other new suggestions based on multiple comparisons of model parameters, log-linear models for ordinal categorical data, and correspondence analysis. We also review measures for goodness-of-fit of a blockmodel, and we describe a natural approach to this problem using likelihood-ratio statistics generated from a popular model for relational data.     

Parent–Child Relationships in Stepfather Families and Adolescent Adjustment: A Latent Class Analysis

In the current study the authors drew on Waves I and III from Add Health to examine the closeness of parent–adolescent relationships in married mother–stepfather families (N = 1,934). They used latent class analysis to identify family constellations defined by adolescents' relationships with all of their parents: mothers, stepfathers, and biological nonresident fathers. In particular, the authors (a) identified the most common underlying patterns of adolescent–parent relationships in stepfamilies; (b) determined the background characteristics that predict membership in these groups; and (c) examined how adolescents in these groups fare with respect to depressive symptoms, delinquency, and substance use. The results indicate that adolescents' relationships can be represented with 4 latent classes. Adolescents in these classes differ on measures of adjustment, and many of these differences persist into the early adult years.     

Integrating Survey and Ethnographic Methods For Systematic Anomalous Case Analysis

This paper describes how the salience of research findings can be enhanced by combining survey and ethnographic methods to draw insights from anomalous cases. Using examples from a research project examining the influence of religion on childbearing preferences in Nepal, the author illustrates how survey data can facilitate the selection of ethnographic informants and how semistructured interviews with these deviant cases leads to improved theory, measures, and methods. A systematic sample of 28 informants, whose family size preferences were much larger than a multivariate regression model predicted, were selected from the survey respondent pool for observation and in–depth interviews. The intent was to explore relationships between religion and fertility preferences that may not have been captured in the initial multivariate survey data analyses. Following intensive fieldwork, the author revised theories about religion's influence, coded new measures from the existing survey data, and added these to survey models to improve statistical fit. This paper discusses the author's research methods, data analyses, and resulting insights for subsequent research, including suggestions for other applications of systematic analyses of anomalous cases using survey and ethnographic methods in tandem.     

Settings in Social Networks: A Measurement Model

A class of statistical models is proposed that aims to recover latent settings structures in social networks. Settings may be regarded as clusters of vertices. The measurement model is based on two assumptions. (1) The observed network is generated by hierarchically nested latent transitive structures, expressed by ultrametrics, and (2) the expected tie strength decreases with ultrametric distance. The approach could be described as model–based clustering with an ultrametric space as the underlying metric to capture the dependence in the observations. Bayesian methods as well as maximum–likelihood methods are applied for statistical inference. Both approaches are implemented using Markov chain Monte Carlo methods.