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Semi-parametric bivariate polychotomous ordinal regression. (English) Zbl 1505.62127

Summary: A pair of polychotomous random variables \((Y_1,Y_2)^\top =:{\mathbf{Y}}\), where each \(Y_j\) has a totally ordered support, is studied within a penalized generalized linear model framework. We deal with a triangular generating process for \({\mathbf{Y}}\), a structure that has been employed in the literature to control for the presence of residual confounding. Differently from previous works, however, the proposed model allows for a semi-parametric estimation of the covariate-response relationships. In this way, the risk of model mis-specification stemming from the imposition of fixed-order polynomial functional forms is also reduced. The proposed estimation methods and related inferential results are finally applied to study the effect of education on alcohol consumption among young adults in the UK.

MSC:

62-08 Computational methods for problems pertaining to statistics
62G08 Nonparametric regression and quantile regression
62J12 Generalized linear models (logistic models)
62J05 Linear regression; mixed models
62P25 Applications of statistics to social sciences

Software:

trust; SemiPar; Stata; gamair
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Full Text: DOI Link

References:

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