Modelling Tabular Data with an Ordered Outcome

(1996) - Vernon Gayle

Journal: Sociological Research Online
Link:: http://journals.sagepub.com/doi/10.5153/sro.22
DOI:: 10.5153/sro.22
Links::
Tags:: #paper #Methods #OrdinalLogit
Cite Key:: [@gayleModellingTabularData1996]

Abstract

A large amount of data that is considered within sociological studies consists of categorical variables that lend themselves to tabular analysis. In the sociological analysis of data regarding social class and educational attainment, for example, the variables of interest can often plausibly be considered as having a substantively interesting order. Standard log-linear models do not take ordinality into account, thereby potentially they may disregard useful information.

Notes

“In the sociological analysis of data regarding social class and educational attainment, for example, the variables of interest can often plausibly be considered as having a substantively interesting order” (Gayle, 1996, p. 1)

“the dependent or outcome variables can often plausibly be considered as having a substantively interesting order. In these circumstances we wish to understand the effect of one or more explanatory variables upon an ordered categorical dependent variable.” (Gayle, 1996, p. 1)

“This is a reasonable solution to the problem of modelling tables with ordered categorical responses but standard log-linear models would not take ordinality into account, thereby disregarding potentially useful information (Berridge, 1992).” (Gayle, 1996, p. 1)

“The motivation for the proportional odds model is provided by an appeal to the existence of an underlying continuous and perhaps unobservable random variable. The continuation ratio model is a useful alternative to the proportional odds model. The continuation ratio model is particularly suited to cases where the categories of the response variable really are discrete.” (Gayle, 1996, p. 1)

“The continuation ratio model was posited by Fienberg and Mason (1979) and discussed by Fienberg (1980) and by McCullagh and Nelder (1983). The continuation ratio model is appropriate when the response variable is constructed as a series of ordered categories.” (Gayle, 1996, p. 3)

“The continuation ratio model can be considered as a series of comparative logistic regression models (a technical definition of the model is provided in Berridge, 1992).” (Gayle, 1996, p. 3)

“Model criticism is an important aspect of the statistical modelling process (Everitt and Dunn, 1983; Dale and Davies, 1994). There is a problem with regards to using residuals such as Pearson’s residuals for an ordinal response which has been modelled using the continuation ratio model.” (Gayle, 1996, p. 7)