Testing Procedure for Item Response Probabilities of 2Class Latent Model

Abstract

This paper presents Hotelling T² as a procedure for the testing of significance difference between the item response probabilities (ω_ij^′s) of classes in a Latent Class Model (LCM). Parametric bootstrap technique is used in order to generate samples for ω_ij^′s. These samples are based on the estimated parameters of 2-class latent model. The estimation of parameters in either situation is done using  the Expectation Maximization (EM) algorithm through Maximum likelihood method. The hypothesis under consideration is whether the response probabilities (ω_ij^′s)  are equal against each item in both the classes. { H₀ : ω_{i1 =} ω_i2.   against H₁ : =ω_i1 ≠ ω_i2}. If the test exhibits significant difference between response probabilities in both classes, it will be a clear indication of a presence of latent variable. We consider both training and testing data sets to develop the test. In order to apply Hotelling T2 test the basic assumptions of normality and homogeneity of variance are also checked. Chi-square goodness of fit test is used for assessing normal distribution to be good fitted on the hypothesized (bootstrap samples) based on 2-class latent model parameters for each data and Bartlett test to check heterogeneity of variances in ω_ij^′s. Moreover, our procedure produces a minimum standard error of estimates as compared to those obtained through the package in R.Gui environment