Abstract
Latent class regression models relate covariates and latent constructs such as psychiatric disorders. Though full maximum likelihood estimation is available, estimation is often in three steps: (i) a latent class model is fitted without covariates; (ii) latent class scores are predicted; and (iii) the scores are regressed on covariates. We propose a new method for predicting class scores that, in contrast to posterior probability-based methods, yields consistent estimators of the parameters in the third step. Additionally, in simulation studies the new methodology exhibited only a minor loss of efficiency. Finally, the new and the posterior probability-based methods are compared in an analysis of mobility/exercise.
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Acknowledgements
The authors wish to thank Dr. Sheila West for kindly making the Salisbury Eye Evaluation data available, and the Johns Hopkins Older Americans Independence Center for funding, NIA: P30AG021334.
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Appendix
Appendix
SAS program to perform Step 3. This program performs maximum likelihood estimation in the Step 3 regression.
In the line starting with “th0”, one have to give some starting values for the parameters. These have to be given in following order: IS 1,…,IS M−1, x 1 S 1,…,x 1 S M−1, x 2 S 1,…,x P S M−1, var(S 1), cov(S 1,S 2), var(S 2), cov(S 1,S 3), cov(S 2,S 3), var(S 3),…, var(S M−1), where IS m is the intercept for class m and x p S m is the parameter estimate of covariate p on class m. We recommend that one tries serval different sets of starting values, as local maxima can be reached. As starting values for the covariance matrix for the LSC scores, we suggest the empirical covariance matrix for the LSC predictions.
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Petersen, J., Bandeen-Roche, K., Budtz-Jørgensen, E. et al. Predicting Latent Class Scores for Subsequent Analysis. Psychometrika 77, 244–262 (2012). https://doi.org/10.1007/s11336-012-9248-6
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DOI: https://doi.org/10.1007/s11336-012-9248-6