Estimating Latent Structure Models with Categorical Variables: One-Step Versus Three-Step Estimators
Tóm tắt
We study the properties of a three-step approach to estimating the parameters of a latent structure model for categorical data and propose a simple correction for a common source of bias. Such models have a measurement part (essentially the latent class model) and a structural (causal) part (essentially a system of logit equations). In the three-step approach, a stand-alone measurement model is first defined and its parameters are estimated. Individual predicted scores on the latent variables are then computed from the parameter estimates of the measurement model and the individual observed scoring patterns on the indicators. Finally, these predicted scores are used in the causal part and treated as observed variables. We show that such a naive use of predicted latent scores cannot be recommended since it leads to a systematic underestimation of the strength of the association among the variables in the structural part of the models. However, a simple correction procedure can eliminate this systematic bias. This approach is illustrated on simulated and real data. A method that uses multiple imputation to account for the fact that the predicted latent variables are random variables can produce standard errors for the parameters in the structural part of the model.
Từ khóa
Tài liệu tham khảo
Steiger, 1978, Theory Construction and Data Analysis in Behavioral Sciences, 136
Lazarsfeld, 1950a, Measurement and Prediction, 413
Vermunt, 1997a, Loglinear Models for Event History Analysis
Croon, 2002, Latent Variable and Latent Structure Models, 195
Heinen, 1996, Latent Class and Discrete Latent Trait Models: Similarities and Differences
Bolck, 1997, On the Use of Latent Scores in Causal Models for Categorical Variables
Bartholomew, 1999, Latent Variable Models and Factor Analysis
Haberman, 1979, Analysis of Qualitative Data: New Developments, 2
Hagenaars, 1990, Categorical Longitudinal Data: Log-Linear Panel, Trend and Cohort Analysis
Lazarsfeld, 1950b, Measurement and Prediction, 362
Vermunt, 2000, Latent Gold; User's Guide
These models are also denoted as DLM (Directed Loglinear Models) with latent variables.
Lazarsfeld, 1968, Latent Structure Analysis
Bentler, 1996, Latent Variable Modeling and Applications to Causality, 259
Van de Pol, 1996, PANMARK 3 User's Manual
Whittaker, 1990, Graphical Models in Applied Multivariate Statistics
Occasionally a third approach is proposed in which, first, an appropriate “stand-alone” measurement model is defined and its parameters are estimated. In the next step, the parameters of the causal model are estimated with the parameters of the measurement model fixed to their values obtained in the first step. This two-step approach will not be discussed further in this paper.
Croon, 1997, On the Use of Factor Scores in Structural Equations Models
Vermunt, 1997b, ℓEM: A General Program for the Analysis of Categorical Data
Hagenaars Jacques A. , McCutcheon Allan L. 2002. Applied Latent Class Analysis. Cambridge: Cambridge University Press.