Abstract
The present chapter applies an entropy-based method of path analysis to multiple-indicator, multiple-cause models and the latent Markov chain model. First, a multiple-indicator, multiple-cause model is considered in a path analysis framework. Second, the entropy-based path analysis method is reviewed, and the effects of variables are calculated in some examples. Third, a numerical illustration is provided to demonstrate path analysis in the multiple-indicator, multiple-cause model. Fourth, path analysis is discussed in the latent Markov chain model, and a numerical example demonstrates the approach. Finally, discussions and a further perspective of path analysis in latent class models are provided.
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References
Albert, J. M., & Nelson, S. (2011). Generalized causal mediation analysis. Biometrics, 1028–1038.
Bentler, P. M., & Weeks, D. B. (1980). Linear structural equations with latent variables. Psychometrika, 45, 289–308.
Christoferson, A. (1975). Factor analysis of dichotomous variables. Psychometrika, 40, 5–31.
Eshima, N., & Tabata, M. (1999). Effect analysis in loglinear model approach to path analysis of categorical variables. Behaviormetrika, 26, 221–233.
Eshima, N., & Tabata, M. (2007). Entropy correlation coefficient for measuring predictive power of generalized linear models. Statistics and Probability Letters, 77, 588–593.
Eshima, N., & Tabata, M. (2010). Entropy coefficient of determination for generalized linear models. Computational Statistics and Data Analysis, 54, 1381–1389.
Eshima, N., Asano, C., & Obana, E. (1990). A latent class model for assessing learning structures. Behaviormetrika, 28, 23–35.
Eshima, N., Tabata, M., & Geng, Z. (2001). Path analysis with logistic regression models: Effect analysis of fully recursive causal systems of categorical variables. Journal of the Japan Statistical Society, 31, 1–14.
Eshima, N., Tabata, M., Borroni, C. G., & Kano, Y. (2015). An entropy-based approach to path analysis of structural generalized linear models: A basic idea. Entropy, 17, 5117–5132.
Fienberg, S. E. (1991). The analysis of cross-classified categorical data (2nd ed.). Cambridge, England: The MIT Press.
Goodman, L. A. (1973b). The analysis of multidimensional contingency tables when some variables are posterior to others: A modified path analysis approach. Biometrika, 60, 179–192.
Goodman, L. A. (1973a). Causal analysis of data from panel studies and other kinds of surveys. American Journal of Sociology, 78, 1135–1191.
Goodman, L. A. (1974). The analysis of systems of qualitative variables when some of the variables are unidentifiable: Part I. A modified latent structure approach. American Journal of Sociology, 79, 1179–1259.
Hagenaars, J. A. (1998). Categorical causal modeling: Latent class analysis and directed loglinear models with latent variables. Sociological Methods & Research, 26, 436–489.
Jöreskog, K.G., & Sörbom, D. (1996). LISREL8: user’s reference guide (2nd ed.). Chicago: Scientific Software International.
Kuha, J., & Goldthorpe, J. H. (2010). Path analysis for discrete variables: The role of education in social mobility. Journal of Royal Statistical Society, A, 173, 351–369.
Lazarsfeld, P. F. (1948). The use of panels in social research. Proceedings of the American Philosophical Society, 92, 405–410.
Macready, G. B. (1982). The use of latent class models for assessing prerequisite relations and transference among traits, Psychometrika, 47, 477-488.
McCullagh, P., & Nelder, J. A. (1989). Generalized linear models (2nd ed.). London: Chapman and Hall.
Muthen, B. (1978). Contribution of factor analysis of dichotomous variables. Psychometrika, 43, 551–560.
Muthen, B. (1984). A general structural equation model with dichotomous ordered categorical and continuous latent variable indicators. Psychometrika, 49, 114–132.
Nelder, J. A., & Wedderburn, R. W. M. (1972). Generalized linear model. Journal of the Royal Statistical Society A, 135, 370–384.
Owston, R. D. (1979). A maximum likelihood approach to the “test of inclusion.” Psychometrika, 44, 421–425.
White, R. T., & Clark, R. M. (1973). A test of inclusion which allows for errors of measurement. Psychometrika, 38, 77–86.
Wright, S. (1934). The method of path coefficients. The Annals of Mathematical Statistics, 5, 161–215.
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Eshima, N. (2022). Path Analysis in Latent Class Models. In: An Introduction to Latent Class Analysis. Behaviormetrics: Quantitative Approaches to Human Behavior, vol 14. Springer, Singapore. https://doi.org/10.1007/978-981-19-0972-6_7
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DOI: https://doi.org/10.1007/978-981-19-0972-6_7
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