Resumo:
In this work we develop a longitudinal IRT model considering skewed latent trait
distributions, based on the work of Pourahmadi (1999). In our case we consider the
Cholesky decomposition of the matrix of variance and covariance (dependence) related to
the latent traits. A multivariate skew-normal distribution for the latent traits is introduced by
an antedependence model with univariate centered skew-normal errors. We focus on
dichotomous responses and a single group of individuals followed over several evaluation
conditions (time-points). In each of these evaluation conditions the subjects are submitted
to a (possibly different along these time-points) measuring instruments which have some
common items structure. Using an appropriate augmented data framework, a longitudinal
IRT model is developed through the Pourahmadi's approach. Parameter estimation, model
fit assessment tools and model comparison statistics are implemented through a hybrid
MCMC approach, such that when the full conditionals are not known, the Metropolis-
Hastings algorithm is used. Our approach showed to be very useful to handle different
latent trait distributions, unbalanced data (dropouts and/or inclusion of subjects), different
covariance structures among other advantages. Simulation studies indicate that the
parameters are well recovered. Finally, a longitudinal study in education, conducted by the
Brazilian federal government, is analyzed to illustrate the methodology developed.

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