Showing papers on "Ordinal regression published in 1986"

Ordinal scale and statistics in medical research.

Abstract: A survey of the 1982 editions of 12 medical journals showed that in at least 70% of 175 papers employing ordinal measurement scales, statistical methods were used, which do, in fact, assume a more refined measurement scale. Non-parametric methods suited for analysis of ordinal data are listed.

The Use Of Rank Transformation And Multiple Regression Analysis In Estimating Residential Property Values With A Small Sample

Abstract: Conventional multiple regression analysis which has been used in estimating residential property values typically relies upon cardinal data. This paper argues that appraisal theory requires the appraiser to rank the comparables from best to worst and use a regression technique which can be applied to ordinal data. The rank regression procedure illustrated here was successfully used on small sample sizes, and did not violate the critical assumptions underlying conventional multiple regression. The results indicate that the rank regression technique illustrated here is more theoretically correct than conventional multiple regression and produces a better model with more accurate price estimates.

Tests of significance using regression models for ordered categorical data

Abstract: Regression models of the type proposed by McCullagh (1980, Journal of the Royal Statistical Society, Series B 42, 109-142) are a general and powerful method of analyzing ordered categorical responses, assuming categorization of an (unknown) continuous response of a specified distribution type. Tests of significance with these models are generally based on likelihood-ratio statistics that have asymptotic chi 2 distributions; therefore, investigators with small data sets may be concerned with the small-sample behavior of these tests. In a Monte Carlo sampling study, significance tests based on the ordinal model are found to be powerful, but a modified test procedure (using an F distribution with a finite number of degrees of freedom for the denominator) is suggested such that the empirical significance level agrees more closely with the nominal significance level in small-sample situations. We also discuss the parallels between an ordinal regression model assuming underlying normality and conventional multiple regression. We illustrate the model with two data sets: one from a study investigating the relationship between phosphorus in soil and plant-available phosphorus in corn grown in that soil, and the other from a clinical trial comparing analgesic drugs.

Assessing the correspondence of one or more vectors to a symmetric matrix using ordinal regression

Abstract: A statistical model for interpreting psychological scaling research, based on the heuristic work of Reynolds (1983), is developed. This new approach has certain advantages over the standard property fitting approach (Chang and Carroll, 1969) currently used to interpret multidimensional scaling spaces (Shepard, 1962; Torgerson, 1965). These advantages are (a) the ability to directly assess the correspondence of a descriptor vector(s) to a symmetric matrix, and (b) to provide a method in which only ordinal properties of such descriptors are required: thus standard rating, ranking, or sorting data collection methods can be used as the basis to interpret the multidimensional space resulting from the distance data.

Bayesian and Maximum Likelihood Approaches to Order-Restricted Inference for Models for Ordinal Categorical Data

Abstract: A class of association models for contingency tables has parameters that are sometimes interpreted as category scores. For classifications having ordered categories, it is often reasonable to assume that the score parameters have a corresponding ordering. This article proposes order-restricted estimates of score parameters in these models. For these estimates, the local log odds ratios have uniform sign. For the Bayesian approach proposed here, prior distributions can induce the order restriction, and prior beliefs reflecting strong association have the effect of moving the estimates away from the boundary of the restricted parameter space. The orderrestricted maximum likelihood solution is obtained in the limit as the prior standard deviation for the strength of association parameter grows unboundedly.

Ordinal Pattern Analysis

Abstract: Our task in writing this chapter is to outline a strategy for analyzing data that we believe to be better suited to most psychological research than the most widely used statistical techniques (e.g., t, F, and chi square tests, product moment correlation, regression, covariance, discriminant, and factor analyses). We call the strategy Ordinal Pattern Analysis (OPA), and derive it from a small set of first principles that deviate somewhat from those on which most classical statistical models are based. First, we assume that the goal of statistical practice is to aid in detecting and analyzing patterns in data rather than to aid in making decisions about populations given samples of data. Second, we assume that a statistic must be useful in analyzing data generated by individual subjects as well as data based on aggregations of subjects. Third, we assume that most predictions and observations in psychological research possess no more than ordinal scale properties, and that statistics employed to assess the fit between predictions and observations must be derived on the basis of this constraint.

A new model for ordinal pain data from a pharmaceutical study

Abstract: For the pain data analysed previously by Cox and Chuang. This paper proposes a new model that assumes monotone scores for ordered response categories. This proposed model possesses several attractive features and allows a stochastic ordering of the drugs under comparison. Such a model also provides insight regarding the ordinal scale used to classify response. Estimation of the parameters in the model is obtained by use of BMDP3R.

A new algorithm for analysis of ordinal data based on a general linear model

Abstract: An algorithm to analyze ordinal data based on a general linear model is presented, which is applicable to many scaling problems, such as ordinal multiple regression, external analysis of preference data, and general Fechnerian scaling. Especially, external analysis of preference data is discussed in detail, and the efficacy of the algorithm is examined by analyzing a preference data.

A general form of ordinal association

Abstract: A general form of ordinal association is defined in a prediction analysis framework. This definition provides a useful way of identifying and selecting prediction rules a priori. Various classes of association are considered and a general approach is provided for the selection and significance testing of optimal prediction rules (ex post). This methodology is also extended to the degree‐k, k ≥ 2, and multivariate cases. Nearly all of the common measures of ordinal association are special cases of the general type of association considered here.