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Abstract:
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Latent trait models have an abroad application in education, health science, 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. The models are applied to an infant morbidity study to develop 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 as a measure of propensity for infant morbidity needs to be further investigated in future research.
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