Showing papers on "Latent variable model published in 1988"

Randomization‐based inferences about latent variables from complex samples

Abstract: Standard procedures for drawing inferences from complex samples do not apply when the variable of interestϑ cannot be observed directly, but must be inferred from the values of secondary random variables that depend onϑ stochastically. Examples are proficiency variables in item response models and class memberships in latent class models. Rubin's “multiple imputation” techniques yield approximations of sample statistics that would have been obtained, hadϑ been observable, and associated variance estimates that account for uncertainty due to both the sampling of respondents and the latent nature ofϑ. The approach is illustrated with data from the National Assessment for Educational Progress.

Latent Structure Models with Direct Effects between Indicators Local Dependence Models

Abstract: A basic assumption of latent structure models is that of local independence: given the score on the latent variable, the scores on the manifest variables are independent of each other. This basic a...

Robustness of normal theory methods in the analysis of linear latent variate models.

Abstract: The structure of the covariance matrix of sample covariances under the class of linear latent variate models is derived using properties of cumulants. This is employed to provide a general framework for robustness of statistical inference in the analysis of covariance structures arising from linear latent variate models. Conditions for normal theory estimators and test statistics to retain each of their usual asymptotic properties under non-normality of latent variates are given. Factor analysis, LISREL and other models are discussed as examples.

The Impact of Specification Error on the Estimation, Testing, and Improvement of Structural Equation Models.

Abstract: The purpose of this paper is to assess the impact of misspecification on the estimation, testing, and improvement of structural equation models. A population study is conducted whereby a prototypical latent variable model is misspecified in various ways. Measurement model and structural model misspecifications are considered separately and together. The maximum likelihood estimator (ML) is compared to a limited information two-stage least squares (2SLS) estimator implemented in LISREL. The ratio of chi-square to its degrees of freedom and power of the likelihood ratio test is assessed for each misspecification. The modification index provided by LISREL is also studied. Results indicate that ML and 2SLS estimates of measurement and structural parameters are both affected by measurement model misspecification. For misspecification of the structural part, ML is shown to propagate errors throughout the structural parameters whereas 2SLS isolates errors only in the parameters of the misspecified equation. Results also show that relying on the ratio of chi-square to degrees of freedom as an index of fit may lead to accepting models with severe parameter bias. Finally, the modification index is shown to be an unreliable indicator of the location of a specification error.

Dimensions of the Need for Cognition: Subscales and Gender Differences

Abstract: The Need for Cognition (Cacioppo & Petty, 1982) scale has been used, predominantly in the persuasion literature, to assess the degree to which individuals tend to engage in elaborative thought. Using both statistically appropriate methods for the factor analysis of dichotomous variables and latent variable models, we report studies which discuss the development and validation of subscales of the NFC. The findings suggest that three subscales (Cognitive Persistence, Cognitive Confidence, and Cognitive Complexity), representing three different domains of elaborative thought, can be identified. A gender difference was obtained consistently on the Cognitive Persistence Scale: Women scored higher than men. Finally, using latent variable modeling methodologies, we present some initial exploratory evidence regarding cohort differences. We find no statistically significant relation between years of education and NFC subscale scores. Implications of the subscales and potential correlates of the gender difference found for Cognitive Persistence are discussed.

Latent Class Models for Measuring

Abstract: Most latent class analysis in contemporary social research is aimed at data reduction or “building clusters for qualitative data” (Formann, 1985, p. 87; see also Aitkin, Anderson, & Hinde, 1981). Some special restricted models in this area have of course been used to represent structural characteristics or behavioral processes (e.g., Clogg, 1981a; Goodman, 1974a). But a careful examination of the latent class models now available shows that none deal in a direct way with measurement, particularly if exacting standards are used to define how measurement should take place. Extensions and modifications of latent class models reported below are intended to remove this deficiency.

Latent Trait Models with Indicators of Mixed Measurement Level

Abstract: In this chapter we deal with the formulation and estimation of simultaneous equation models in metric latent endogenous variables that are connected to observed variables of any measurement level. The literature on this topic has focused on simultaneous equation models with metric (cf. Joreskog & Sorbom, 1984) and ordinal indicators (Muthen, 1984). The use of ordinal indicators is based on an normal theory threshold concept implying an ordinal probit model. Concepts based on normal distribution theory are given up when qualitative variables are used as indicators for a latent metric variable (cf. the multinomial logit latent trait model of Bock, 1972).

A Latent-Variable Model of Quality Determination

Abstract: Because of data difficulties, there has been little empirical work analyzing the determination of the quality of a firm's output. This article constructs a latent variable model for this problem that uses easily obtainable data. The model is developed from the relationship between the firm's input demand functions and reduced-form output functions, and it has a novel multiple indicator multiple cause (MIMIC) interpretation. The model also allows identification of an intercept, implying that an index of quality that is comparable across samples can be constructed. As an example, a latent variable model of nursing-home quality is estimated.

Rating scale analysis with latent class models

Abstract: A general approach for analyzing rating data with latent class models is described, which parallels rating models in the framework of latent trait theory. A general rating model as well as a two-parameter model with location and dispersion parameters, analogous to Andrich's Dislocmodel are derived, including parameter estimation via the EM-algorithm. Two examples illustrate the application of the models and their statisticalcontrol. Model restrictions through equality constrains are discussed and multiparameter generalizations are outlined.

Discovering Heterogeneity: Continuous Versus Discrete Latent Variables

Abstract: In the case of the 2 x 2 x2 table resulting form a three-wave panel study, Converse's "black-and-white" model, with discrete latent classes, and the Rasch continous latent-trait model cannont be distinguished. When the reponse is trichotomous, the resulting 3 x 3 x 3 table provides information on heterogeneity of respondents that is detected in different ways by these two kinds of models. Different kinds of heterogeneity, leading to models with different numbers of latent classes or different numbers of latent traits, can be distinguished within both approaches. The two approaches also yield distinctive accounts of change in response probabilities. Data from the American Panel Study illustrate how comparisons between the two kinds of models can be effected.

A Latent Class Covariate Model with Applications to Criterion-Referenced Testing

Abstract: Modern developments of latent class models as pioneered by Lazarsfeld and Henry (1968) and extended by Proctor (1970), Goodman (1974, 1975), Haberman (1974, 1979), Dayton and Macready (1976, 1980a), and others have found a variety of applications in the social and behavioral sciences. An area of special interest has been criterion referenced testing, where latent class models offer an attractive and powerful alternative to latent trait models (Macready & Dayton, 1980). Latent class models can directly represent mastery/nonmastery status and have the advantage of permitting an objective determination of cutting scores for mastery classification (Macready & Dayton, 1977). Recently, there has been interest in extending latent class models to include information from concomitant variables, or covariates. Although categorical concomitant variables (i.e., variables used to group respondents) can be incorporated systematically into current latent class formulations (Clogg & Goodman, 1984, 1985, 1986; Macready & Dayton, 1980) and estimation carried out using available computer programs (e.g., Clogg, 1977), this chapter develops a more general model in which latent class membership is functionally related to one or more categorical and/or continuous concomitant variables (see Dayton & Macready, 1980b for a restricted model of this type).

Structural Equation Modeling of Travel Choice Dynamics

Abstract: This research has two objectives The first objective is to explore the use of the modeling tool called "latent structural equations" (structural equations with latent variables) in the general field of travel behavior analysis and the more specific field of dynamic analysis of travel behavior The second objective is to apply a latent structural equation model in order to determine the causal relationships between income, car ownership, and mobility Many transportation researchers might be unfamiliar with latent structural equation modeling, which is also known as "latent structural analysis," "causal analysis," and "soft modeling" However, most researchers will be quite familiar with techniques that are special cases of latent structural equations: eg, conventional multiple regression and simultaneous equations, path analysis, and (confirmatory) factor analysis Furthermore, recent advances in estimation techniques have made it possible to incorporate discrete choice variables and other non-normal variables in structural equations models Thus, probit choice models (binomial, ordered, and multinomial) can be incorporated within the general model framework The empirical analysis reported here involves dynamic travel demand data from the Dutch National Mobility Panel for the three years 1984 through 1986 All variables in the model, with the exception of income level in the first year, are endogenous: income is treated as an ordinal (four category) variable; car ownership is treated as either an ordinal (ordered probit) or a categorical (multinomial probit) choice variable; and mobility, in terms of car trips and public transport trips, is treated as two censored (tobit) continuous variables The model fits the data well, but only scratches the surface of the potential of latent structural equation modeling with panel data Some possible extensions are outlined The methodological discussion is not intended as a comprehensive overview of structural equation modeling with latent variables Rather, the aim is to explore the technique in comparison to conventional methods of travel behavior analysis Many extensive overviews are available, due to the popularity of the technique in the fields of sociology and psychology, and more recently in marketing research The technique as described here has been in use since the early 1970s, but, because of recent rapid developments, current overviews are more relevant to transportation researchers Such overviews are provided by Bentler (1980), Bentler and Weeks (1985), Fornell and Larcker (1981), Hayduk (1987), and Joreskog and Wold (1982), among others In particular, Hayduk (1897) provides an extensive bibliography Historical developments are reviewed in Bentler (1986) and Bielby and Hauser (1977) The author is aware of three computer programs for latent structural equation modeling: LISREL (Joreskog and Sorbom, 1984; 1987), EQS (Bentler, 1985), and LISCOMP (Muthen, 1987) Each program is based on a different approach to estimation and testing and each has its advantages and disadvantages The three approaches are briefly reviewed in Section 6 on estimation methods The application results presented here were obtained using the LISCOMP program It is also possible to replicate the approaches of these programs by implementing several separate estimation procedures (eg, maximum likelihood estimations of probit models and tobit models, and generalized least square and maximum likelihood estimations of siumultaneous equations) in sequential and recursive order, but this is inefficient in view of the available comprehensive packages

LCAG — Loglinear Modelling with Latent Variables: a Modified LISREL Approach

Abstract: In order to explicate the potentialities of loglinear modelling Goodman introduced the phrases ‘modified multiple regression approach’ and ‘modified path analysis approach’ (Goodman, 1972, 1975, 1973). As he pointed out, the loglinear techniques are not exactly identical with the classical regression techniques, but there is indeed a rather striking analogy between the two (see also Brier, 1979). As such, these phrases were very aptly chosen. They convey the general impression that the questions to be answered by the analyses of data measured at a nominal scale are essentially the same as the questions one tries to answer while analysing interval or ratio level data.

Latent class models for nonmonotone dichotomous items

Abstract: Starting from perfectly discriminating nonmonotone dichotomous items, a class of probabilistic models with or without response errors and with or without intrinsically unscalable respondents is described. All these models can be understood as simply restricted latent class analysis. Thus, the estimation and identifiability of the parameters (class sizes and item latent probabilities) as well as the chi-squared goodness-of-fit tests (Pearson and likelihood-ratio) are free of the problems. The applicability of the proposed variants of latent class models is demonstrated on real attitudinal data.

Test Theory with Qualitative and Quantitative Latent Variables

Abstract: Latent trait models and latent class models can be considered as two alternative, mutually complementary approaches to analyzing data obtained from tests and questionnaires. Data of this type are characterized by the fact that a larger number of manifest variables, that is, the items, are observed and that all manifest variables refer to the same aspect of personality of the individuals and are designed to measure it. The ultimate aim of a test analysis is to make comparative statements about the individuals by representing them on a scale, that is, by allocating them values of a latent variable. In the case of latent trait models, this latent person variable is quantitative, the persons are represented on a metric scale. In the case of latent class models the latent person variable is qualitative, the persons are mapped into a set of categories or classes.

Linear dynamic errors in variable models: some structure theory

Abstract: In the paper we give a survey on identifiability problems in linear dynamic errors-in-variables systems, where emphasis is put on the case of mutually uncorrelated errors.

Testing a Latent Trait Model

Abstract: Within the domain of latent trait models the Rasch model (Rasch, 1960) takes a prominent place. This fact can be accounted for by the special characteristics of the model deriving from specific objectivity. As a consequence, this one-parameter logistic model, as it is also called, has been studied extensively for the past decade. Also with respect to model testing the Rasch model has been studied more thoroughly than other latent trait models. For this reason we will concentrate in the present paper on testing the Rasch model. Most of the points made with respect to the Rasch model apply to other latent trait models as well.

Latent variable models for the analysis of medical data with repeated measures of binary variables.

Abstract: Consideration of within-subject dependencies is a key issue in modelling binary repeated measures medical data. Borrowing from recent developments in sociology and psychology, we demonstrate the applicability of a latent variable approach to the analysis of such data. In particular we present the Rasch model as a basic model for representing the relationship of subject and treatment parameters. The latent variable approach is useful in providing a theoretical framework for specifying dependencies exactly and also as a base for considering more complicated relationships between repeated measures variables.

Developing and Testing an Expanded Model of Survivor Responses to Layoffs: A Longitudinal Field Study.

Abstract: This longitudinal field study develops and tests a multivariate latent variable model of survivor responses to a layoff. The model was tested with structural equations modeling. Procedural justice,...

Comparison of Latent Structure Models

Abstract: In this chapter we shall by means of two examples compare different models for the same data set. The purpose is to illustrate various models as regards their capability to explain essential structures in the given data. The first example is concerned with consumer complaint behavior. The data consist of the responses for 600 individuals on six questions each with two answer categories. In the second example we consider two dichotomous questions; both questions have been answered by 3398 schoolboys on two occasions.

Log-Linear Modeling, Latent Class Analysis, or Correspondence Analysis Which Method Should Be Used for the Analysis of Categorical Data?

Abstract: Data collected by social and behavioral scientists very often consist of large multidimensional tables of subjects cross-classified according to the values or states of several categorical variables. For example, Table 1 shows a set of data on suicide victims in which the method of committing suicide is cross-classified by sex and age group (Van der Heijden & de Leeuw, 1985) and Table 2 shows counts of subjects resulting from a survey of the political attitudes of a sample from the British electorate (Butler & Stokes, 1974). The analysis of such data should clearly depend on the substantive questions posed by the researcher involved, although in many cases these questions will be rather vague. The research worker may be interested in such notions as “pattern” and “structure” but it will often be left to the statistician to clarify what is meant by such concepts and whether they are present in the investigator’s data. Finally, the statistician has the often difficult task of explaining the results.

On the validity of the indeterminate latent variables in the lisrel model

Abstract: The language of abstract vector spaces is used to show that the latent variables and errors of the Lisrel model can always be constructed so as to predict any criterion perfectly,including all those that are entirely uncorrelated with the observed variables.

Loglinear modelling with latent variables: The case of mobility tables

Abstract: In this chapter mobility tables of Denmark and Britain will be reanalysed. Following Clogg’s earlier work (Clogg, 1981a, 1981b), a loglinear analysis with latent variables will be presented. The methodology is embedded in the latent structure analysis, developed by Paul F. Lazarsfeld (Lazarsfeld, 1950a, 1950b, 1954, 1959; Lazarsfeld and Henry, 1968). Besides Lazarsfeld’s and Clogg’s work, papers by Leo Goodman (1974a, 1974b), Jacques Hagenaars (1976, 1978), and my own unpublished work (Luijkx, 1983) are the basis of this chapter.

A Procedure on Parameter Estimation in Latent Class Analysis

Abstract: The present paper is to give a new procedure of parameter estimation in a latent class model by rneans of maxipaum likelihood. Since current methods of parameter estimation haveL occurred frequently improper solutions, the new procedure depends on the result of Gibson's method and, if the solution is not satisfied, the methods of maximum likelihood estimation are applied. In order to realize such an improved procedure, several functions are newly developed, i. e. contour map of the likelihood function, determination of direction vectors.