Effects of covariance misspecification in a latent variable model for multiple outcomes

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Journal Article
Statistica Sinica, 2002, 12 (4), pp. 1207 - 1222
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Sammel and Ryan (1996) developed a latent variable model that allows for covariate effects on multiple continuous outcomes. While the approach provides an effective tool for data reduction and global test for covariate effects, it makes strong assumptions about the covariance among the outcomes. In addition, some parameters are common to both the mean and variance suggesting that robustness could be a problem. This manuscript evaluates model misspecification on tests of exposure effects derived from the latent variable model. We develop a robust score test which is valid under misspecified variance assumptions and compare it to one based on Generalized Estimating Equations (GEE) (Liang and Zeger (1986)), under varying assumptions on the true model. Both models have similar loss in power under variance misspecification while the estimated global effect of the covariate is more biased towards the null for the GEE model than the LV model. As the variance/scale of the outcomes increases, the performance of the LV model improves. As for asymptotic comparisons, test performance depends upon the amount of variability and correlation among the outcomes. The LV model test is superior when the data are highly correlated, ρ > 0.3, and with large variance. When uncorrelated outcomes are incorporated, the GEE model is superior, except when only the correlated outcomes are impacted by the exposure.
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