A Multidimensional Finite Mixture Structural Equation Model for Nonignorable Missing Responses to Test Items |
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| Authors: | Silvia Bacci Francesco Bartolucci |
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| Institution: | 1. University of Perugia, Perugia, Italysilvia.bacci@stat.unipg.it;3. University of Perugia, Perugia, Italy |
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| Abstract: | We propose a structural equation model, which reduces to a multidimensional latent class item response theory model, for the analysis of binary item responses with nonignorable missingness. The missingness mechanism is driven by 2 sets of latent variables: one describing the propensity to respond and the other referred to the abilities measured by the test items. These latent variables are assumed to have a discrete distribution, so as to reduce the number of parametric assumptions regarding the latent structure of the model. Individual covariates can also be included through a multinomial logistic parameterization for the distribution of the latent variables. Given the discrete nature of this distribution, the proposed model is efficiently estimated by the expectation–maximization algorithm. A simulation study is performed to evaluate the finite-sample properties of the parameter estimates. Moreover, an application is illustrated with data coming from a student entry test for the admission to some university courses. |
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| Keywords: | EM algorithm finite mixture models item response theory semiparametric inference student entry test |
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