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Estimating Latent Structure Models with Categorical Variables: One-Step Versus Three-Step Estimators

Published online by Cambridge University Press:  04 January 2017

Annabel Bolck ,
Marcel Croon  and
Jacques Hagenaars
Annabel Bolck
Affiliation:
Netherlands Forensic Institute, 2288 GD Rijswijk, The Netherlands. e-mail: a.bolck@nfi.minjus.nl
Marcel Croon
Affiliation:
Department of Statistics and Methodology, Faculty of Social Sciences, Tilburg University, 5000 LE Tilburg, The Netherlands. e-mail: m.a.croon@uvt.nl
Jacques Hagenaars
Affiliation:
Department of Statistics and Methodology, Faculty of Social Sciences, Tilburg University, 5000 LE Tilburg, The Netherlands. e-mail: jacques.a.hagenaars@uvt.nl
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Abstract

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.

Information

Type
Research Article
Information
Political Analysis , Volume 12 , Issue 1 , Winter 2004 , pp. 3 - 27
Copyright
Copyright © Society for Political Methodology 2004 

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References

Anderson, James C., Gerbing, David W. 1992. “Assumptions and Comparative Strengths of the Two-Step Approach.” Sociological Methods & Research 20: 321—333.CrossRefGoogle Scholar
Bartholomew, David J., and Knott, Martin. 1999. Latent Variable Models and Factor Analysis, 2nd ed. London: Arnold.Google Scholar
Bassi, Francesca, Hagenaars, Jacques A., Croon, Marcel A., Vermunt, Jeroen K. 2000. “Estimating True Changes When Categorical Panel Data Are Affected by Uncorrelated and Correlated Classification Errors.” Sociological Methods & Research 29: 230—268.CrossRefGoogle Scholar
Bentler, Peter, Yuan, Ke-Hai. 1996. “Optimal Conditionally Unbiased Equivariant Factor Score Estimators.” In Latent Variable Modeling and Applications to Causality, ed. Berkane, M. New York: Springer, pp. 259–281.Google Scholar
Bolck, Annabel, Croon, Marcel A., and Hagenaars, Jacques A. 1997. “On the Use of Latent Scores in Causal Models for Categorical Variables.” WORC Research Paper, Tilburg University.Google Scholar
Bollen, Kenneth A. 1989. Structural Equations with Latent Variables. New York: Wiley.CrossRefGoogle Scholar
Croon, Marcel. 2002. “Using Predicted Latent Scores in General Latent Structure Models.” In Latent Variable and Latent Structure Models, eds. Marcoulides, G. A. and Moustaki, I. Mahwah, NJ: Erlbaum Associates, pp. 195–223.Google Scholar
Croon, Marcel A., Bolck, Annabel. 1997. “On the Use of Factor Scores in Structural Equations Models.” WORC Research Paper, Tilburg University.Google Scholar
Ferguson, Thomas A. 1996. A Course in Large Sample Theory. London: Chapman and Hall.CrossRefGoogle Scholar
Goodman, Leo A. 1973. “The Analysis of Multidimensional Contingency Tables When Some Variables Are Posterior to the Others.” Biometrika 60: 179—192.CrossRefGoogle Scholar
Goodman, Leo A. 1974a. “The Analysis of Systems of Qualitative Variables When Some of the Variables are Unobservable. Part I: A Modified Latent Structure Approach.” American Journal of Sociology 79: 1179—1259.CrossRefGoogle Scholar
Goodman, Leo A. 1974b. “Exploratory Latent Structure Analysis Using Both Identifiable and Unidentifiable Models.” Biometrika 61: 215—231.CrossRefGoogle Scholar
Haberman, Shelby J. 1979. Analysis of Qualitative Data: New Developments, vol. 2. New York: Academic Press.Google Scholar
Hagenaars, Jacques A. 1990. Categorical Longitudinal Data: Log-Linear Panel, Trend and Cohort Analysis. Newbury Park, CA: Sage.Google Scholar
Hagenaars, Jacques A. 1993. Loglinear Models with Latent Variables. Newbury Park, CA: Sage.CrossRefGoogle Scholar
Hagenaars, Jacques A. 1998. “Categorical Causal Modeling: Latent Class Analysis and Directed Log-Linear Models with Latent Variables.” Sociological Methods & Research 26: 436—487.CrossRefGoogle Scholar
Hagenaars, Jacques A. 2002. “Directed Loglinear Modeling with Latent Variables: Causal Models for Categorical Data with Nonsystematic and Systematic Measurement Errors.” In Applied Latent Class Analysis, eds. Hagenaars, J. A. and McCutcheon, A. L. Cambridge: Cambridge University Press, pp. 234–286.Google Scholar
Hagenaars, Jacques A., McCutcheon, Allan L. 2002. Applied Latent Class Analysis. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Heinen, Ton G. 1996 Latent Class and Discrete Latent Trait Models: Similarities and Differences. Thousand Oaks, CA: Sage.Google Scholar
Lazarsfeld, Paul F. 1950a. “The Interpretation and Mathematical Foundation of Latent Structure Analysis.” In Measurement and Prediction, ed. Stouffer, S. Princeton, NJ: Princeton University Press, pp. 413–472.Google Scholar
Lazarsfeld, Paul F. 1950b. “The Logical and Mathematical Foundation of Latent Structure Analysis.” In Measurement and Prediction, ed. Stouffer, S. Princeton, NJ: Princeton University Press, pp. 362–412.Google Scholar
Lazarsfeld, Paul F., Henry, Neil W. 1968. Latent Structure Analysis. Boston, MA: Houghton Mifflin.Google Scholar
Rubin, Donald B. 1987. Multiple Imputation for Nonresponse in Surveys. New York: Wiley.CrossRefGoogle Scholar
Saris, Willem H., de Pijper, M., Mulder, J. 1978. “Optimal Procedures for Estimation of Factor Scores.” Sociological Methods & Research 7: 85—106.Google Scholar
Skrondal, Anders, Laake, Petter. 2001. “Regression among Factor Scores.” Psychometrika 66: 1—13.CrossRefGoogle Scholar
Steiger, James H. 1979a. “Factor Indeterminacy in the 1930's and the 1970's: Some Interesting Parallels.” Psychometrika 44: 157—167.Google Scholar
Steiger, James H. 1979b. “The Relationship between External Variables and Common Factors.” Psychometrika 44: 93—97.CrossRefGoogle Scholar
Steiger, James H., and Schönemann, Peter H. 1978. “A History of Factor Indeterminacy.” In Theory Construction and Data Analysis in Behavioral Sciences, ed. Shye, S. San Francisco, CA: Jossey-Bass, pp. 136–178.Google Scholar
Van de Pol, Frank, and Langeheine, Rolf, de Jong, Wil. 1996. PANMARK 3 User's Manual. Voorburg: CBS.Google Scholar
Vermunt, Jeroen K. 1997a. Loglinear Models for Event History Analysis. Thousand Oaks, CA: Sage.Google Scholar
Vermunt, Jeroen K. 1997b. ”ℓEM: A General Program for the Analysis of Categorical Data.” WORC Research Paper, Tilburg University.Google Scholar
Vermunt, Jeroen K., and Magidson, Jay. 2000. Latent Gold; User's Guide. Belmont, MA: Statistical Innovations.Google Scholar
Whittaker, Joe. 1990. Graphical Models in Applied Multivariate Statistics. Chichester: Wiley.Google Scholar