Generalized latent trait models for multiple correlated health endpoints

Latent trait models have an abroad application in health education, psychology and other areas. There are two common assumptions in latent trait models: local independence of manifest outcomes and normal distribution of latent traits. In practice, these assumptions may not be satisfied, especially for the normality of latent traits. In this study, a class of generalized latent trait models and modified Gauss–Newton algorithms for multiple outcomes are proposed. Instead of assuming latent traits to be normal, we specify a skew normal distribution for latent traits of which a normal distribution is a special case, and then model the conditional probability of each outcome as a nonlinear quadratic function of latent traits, which has properties similar to the logistic function. The estimated generalized nonlinear least-square method is used to solve equations for parameters of interest. Bayesian information criteria are developed to compare the new latent trait models with standard ones. The models are applied to an infant morbidity study to identify the effects of pregnancy risk factors on infant morbidity. A new single variable, called infant morbidity index (IMI) that functions as a summary of four infant morbidity outcomes and represents propensity for infant morbidity, is developed. The validity of this index is then assessed in detail. It is shown that the IMI is correlated with each of the individual outcomes, with infant mortality and with a face-valid index of morbidity outcomes, and can be used in future research as a measure of propensity for infant morbidity.