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Fitting linear models to ordinal responses
Author(s) -
Stirling W. Douglas
Publication year - 1984
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1984.tb00804.x
Subject(s) - ordinal data , mathematics , statistics , ordinal regression , linear model , variable (mathematics) , generalized linear model , iteratively reweighted least squares , function (biology) , least squares function approximation , econometrics , non linear least squares , estimation theory , mathematical analysis , evolutionary biology , biology , estimator
The distribution of an ordinal response can be modelled as a grouping of an underlying quantitative variable whose mean is a linear function of explanatory variables. Possible distributional assumptions about the underlying quantitative response are compared. An iteratively reweighted least squares algorithm for parameter estimation in these models is described in detail and variances and tests of hypotheses are given. Two data sets are analysed to illustrate the methods.