Resumen

TOVAR, ROGER JESÚS  y  SALAZAR, JUAN CARLOS. A Linear Mixed Model Adapted to a Markov Chain with Ordinal State Space. Application to Data about Grade Point Average (GPA). Rev.Colomb.Estad. [online]. 2009, vol.32, n.2, pp.213-230. ISSN 0120-1751.

In this paper we study methodology to estimate the effects of covariates using a linear mixed model with random intercept and polytomous ordinal categorical response, under different distributional specifications of this random intercept. This methodology represents an extension of the one proposed in Salazar et al. (2007), where it is presented results obtained using a model where the response is treated in a nominal scale. Specifically, it is considered a Markov chain with k+2 states with two absorbing and k transient states. The likelihood function for the data is derived. Under this model and using a simulation study we assess the effects on the estimates under different distributional specifications for the random intercept. The likelihood function is maximized using the Gauss quadrature method in conjunction with the Newton-Raphson algorithm. Finally, we ilustrated the methodology using data about the Grade Point Average (GPA) from students of the Universidad Nacional de Colombia, at Medellín, collected from 2005 to 2007.

Palabras clave : Longitudinal data; Markov chains; Logistic regression; Gaussian quadrature.

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