Abstract
Our aim is to develop models for ordered categorical data that are as general as for continuous data and allow for similar inferential procedures. The basic model is the common threshold or grouped continuous model, assuming a underlying continuous variable z which is observed imperfectly. Any family of continuous distributions is a candidate for approximating the distribution of z and a generalised linear mixed model may be specified for its parameters. The choice of distribution induces the link function that links the mean of the observed frequencies to one of the parameters of the distribution of z, usually the location. The remaining parameters of the distribution of z are parameters of this link function. The link parameters are estimated by local linearisation of the link function, which extends the model to an approximate generalised linear mixed model including linear contributions of the link parameters. All parameters of the model are estimated simultaneously by iterative reweighted REML. It is feasible to analyse fairly general models for the parameters of the distribution of z, in particular its location and scale parameter.
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Keen, A., Engel, B. (1995). IRREML, a tool for fitting a versatile class of mixed models for ordinal data. In: Seeber, G.U.H., Francis, B.J., Hatzinger, R., Steckel-Berger, G. (eds) Statistical Modelling. Lecture Notes in Statistics, vol 104. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0789-4_18
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DOI: https://doi.org/10.1007/978-1-4612-0789-4_18
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