Showing papers on "Ordinal regression published in 1975"
TL;DR: In this article, an extension of the dichotomous probit model for ordinal dependent variables is presented. But the model assumes that the ordinal nature of the observed dependent variable is due to methodological limitations in collecting the data, which force the researcher to lump together and identify various portions of an interval level variable.
Abstract: This paper develops a model, with assumptions similar to those of the linear model, for use when the observed dependent variable is ordinal. This model is an extension of the dichotomous probit model, and assumes that the ordinal nature of the observed dependent variable is due to methodological limitations in collecting the data, which force the researcher to lump together and identify various portions of an (otherwise) interval level variable. The model assumes a linear eflect of each independent variable as well as a series of break points between categories for the dependent variable. Maximum likelihood estimators are found for these parameters, along with their asymptotic sampling distributions, and an analogue of R 2 (the coefficient of determination in regression analysis) is defined to measure goodness of fit. The use of the model is illustrated with an analysis of Congressional voting on the 1965 Medicare Bill.
2,520 citations
Abstract: This article examines the assumptions underlying two multivariate strategies commonly used in analyzing ordinal data Both strategies employ as a descriptive tool the ordinary multiple regression algorithms; the crucial difference between the two is that the first, ordinal strategy, uses the matrix of Kendall's 's as the building block of multivariate analysis, while the second, parametric strategy, uses the matrix of Pearson's 's These two strategies are evaluated and constrasted in terms of their usefulness in answering basic research questions that arise in multivariate analysis One overriding conclusion is that, contrary to the claims of its proponents, the ordinal strategy is no better than the parametric strategy at meeting some of the basic requirements of multivariate analysis It is argued that parametric strategy, when accompanied by careful evaluation of the validity of the implict quantification of ordinal variables, is more amenable to one of the goals of scientific research: successive app
194 citations
TL;DR: It is shown that the two most commonly used methods (Guttman's rank-image principle and Kruskal's least-square monotonic transformation) are the boundary conditions of a newly proposed single parameter family of methods.
26 citations
TL;DR: Evidence is presented showing that selected tests of significance and the correlation coefficient are chosen so that they are essentially unaffected by nonlinear, order-preserving transformations of the data.
Abstract: This paper has been prompted by two recent additions (Labovitz, 1967, 1970a) to the continuing controversy over levels of measurement and permissible statistics. In these articles Labovitz urges us to treat ordinal and \"quasi-interval\" data (data scaled between the ordinal and interval level) as though they were scaled at the interval evel. The justification for this position is the pragmatic argument hat little error is introduced into the analysis by doing this, since empirical analyses have shown a number of statistics to be essentially unaffected by nonlinear, order-preserving transformations of the data. To this end he presents evidence showing that selected tests of significance (1967) and the correlation coefficient (1970a) are
14 citations