Showing papers on "Ordinal regression published in 1990"

Assessing proportionality in the proportional odds model for ordinal logistic regression.

Abstract: The proportional odds model for ordinal logistic regression provides a useful extension of the binary logistic model to situations where the response variable takes on values in a set of ordered categories. The model may be represented by a series of logistic regressions for dependent binary variables, with common regression parameters reflecting the proportional odds assumption. Key to the valid application of the model is the assessment of the proportionality assumption. An approach is described arising from comparisons of the separate (correlated) fits to the binary logistic models underlying the overall model. Based on asymptotic distributional results, formal goodness-of-fit measures are constructed to supplement informal comparisons of the different fits. A number of proposals, including application of bootstrap simulation, are discussed and illustrated with a data example.

On the Statistical Analysis of Ordinal Data When Extravariation is Present

Abstract: Threshold models can be useful for analysing ordered categorical data, like ratings Such models provide a link between the ordinal scale of measurement and a linear scale on which treatments are supposed to act In this paper a simple agricultural plot experiment is considered with two sources of variation, namely between-plot variation and within-plot variation It is shown that for a threshold model with two sources of variation maximum likelihood estimates can be obtained by iterative weighted least squares

Parametric statistics and levels of measurement : factorial designs and multiple regression

Abstract: Let Y be a continuous, ordinal measure of a latent variable θ. In general, for factorial designs, an analysis of variance of the observed variable Y cannot be used to draw inferences about main effects and interactions on the latent variable θ even when the standard normality and equality of variance assumptions hold.

Smoothed categorical regression based on direct kernel estimates

Abstract: A nonparametric method is considered which yields smoothed estimates of the response probabilities when the response variable is categorical. The method is based on Lauder's (1983) direct kernel estimates which are extended to allow for ordinal kernels. Thus one can make use of the ordinal scale of the response variable. A class of predictive loss functions is introduced on which the cross-validatory choice of smoothing parameters is based. Plots of the smoothed response probabilities may be used to uncover the form of covariate effects

Two-Step Estimation of Linear Models With Ordinal Unobserved Variables: The Case of

Abstract: This article proposes a two-step method for estimating the impact of bond indenture provisions and other financial variables on the risk and yields of investment-grade and speculative corporate bonds. In the first step, the default risk of bonds is estimated as a function of indenture provisions and the characteristics of bonds and the issuing firms by an ordered probit. In the second step, the effects of default risk and bond characteristics on yields are estimated after a measure of bond default risk is obtained by a conditional-mean method.

Inducing relations on incomplete ordinal data

Abstract: Let X denote a set of n elements or stimuli which have an underlying linear ranking L based on some attribute of comparison. Incomplete ordinal data is known about L, in the form of a partial order P on X. This study considers methods which attempt to induce, or reconstruct, L based only on the ordinal information in P. Two basic methods for approaching this problem are the cardinal and sequel construction methods. Exact values are computed for the expected error of weak order approximations of L from the cardinal and sequel construction methods. Results involving interval orders and semiorders for P are also considered. Previous simulation comparisons for cardinal and sequel construction methods on interval orders were found to depend on the specific model that was used to generate random interval orders, and were not found to hold for interval orders in general. Finally, we consider the likelihood that any particular linear extension of P is the underlying L.

Ordinal uncertainty models

Abstract: Uncertainty models can be classified as ordinal, interval, radio and absolute based on the scale strength of the data and information requirements of a model. The ordinal uncertainty models require the weakest set of assumptions known as the weak order properties. Such models are very cost effective since data test requirements are minimal. But the fuzzy approximate reasoning models based on the ordinal uncertainty provide sound inference techniques for use in knowledge based systems design and development. >