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Exponential family non-linear models for categorical data with errors of observation
Authors:Juni Palmgren  Anders Ekholm
Abstract:We present a general framework for treating categorical data with errors of observation. We show how both latent class models and models for doubly sampled data can be treated as exponential family nonlinear models. These are extended generalized linear models with the link function substituted by an observationwise defined non-linear function of the model parameters. The models are formulated in terms of structural probabilities and conditional error probabilities, thus allowing natural constraints when modelling errors of observation. We use an iteratively reweighted least squares procedure for obtaining maximum likelihood estimates. This is faster than the traditionally used EM algorithm and the computations can be made in GLIM.1 As examples we analyse three sets of categorical data with errors of observation which have been analysed before by Ashford and Sowden,2 Goodman3 and Chen,4 respectively.
Keywords:Categorical data  Double sampling  Errors of observation  Extended generalized linear model  Fisher scoring  Iteratively reweighted least squares  Latent class models
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