Showing papers on "Ordinal regression published in 1993"

Dominance statistics: Ordinal analyses to answer ordinal questions.

Abstract: Much behavioral rescarch involves comparing the central tendencies of different groups, or of the same subjects under different conditions, and the usual analysis is some form of mean comparison. This article suggests that an ordinal statistic, d, is often more appropriate. d compares the number of times a score from one group or condition is higher than one from the other, compared with the reverse. Compared to mean comparisons, d is more robust and equally or more powerful; it is invariant under transformation; and it often conforms more closely to the experimenter's research hypothesis. It is suggested that inferences from d be based on sample estimates of its variance rather than on the more traditional assumption of identical distributions

Sample Size and Power Determination for a Binary Outcome and an Ordinal Exposure when Logistic Regression Analysis Is Planned

Abstract: General methods of sample size determination for logistic regression analyses are now available, but these will often require substantial information for their application. The author presents methods useful in the special case of a binary outcome and a three-level quantitative exposure, which includes application to a three-level ordinal exposure for a specified scaling. The computationally simple methods were developed in planning an investigation of the prognostic value of multidrug resistance gene (mdr1) expression in sarcoma. Because logistic regression was planned for the analysis, calculations were based on the ability to detect a linear trend in the log odds of tumor response to chemotherapy associated with increases in the level of mdr1 expression from negative to low positive to high positive. Closed form expressions were used to assess sensitivity to the ordinal scaling and the distribution of the mdr1 levels, and to the assumption of a linear trend in the log odds versus a linear trend in the proportions.

Some tools for the analysis of ordinal data

Abstract: A scientist sometimes makes measurements on an ordinal scale, for example a sheep may be 'very ill', 'ill', 'recovering' or 'completely recovered'. For convenience while performing the experiment, the scientist often records I, 2, 3 and 4 in the place of these descriptions. Use of the abbreviations A, B, C and D would have been just as convenient but unfortunately the scientist is often misled by the use of numbers as symbols for the classes, with the result that the class labels are manipulated according to the rules of ordinary arithmetic. To understand why this is invalid (Stevens, 1946; 1958) one must appreciate that measurement classes have properties (i.e. they can be meaningfully manipulated in certain ways), as do numbers, but that one does not necessarily use all the properties of the number system when one uses a number as symbol for a measurement class. For example, the numbers I, 2 and 3 are equally spaced; the 'distance' from I to 2 is that from 2 to 3. However, in the example, the distance from 'very ill' to 'ill' is not necessarily the same as that from 'ill' to 'recovering'. This explains why this sort of measurement is described as being on an ordinal scale. The particular property of numbers exploited on this scale is that I < 2 < 3, corresponding with 'very ill' < 'ill' < 'recovering'. If the numbers had also reflected the distance between classes, the scale would have been interval. Until recently, scientists wishing to analyse ordinal data were frustrated by the lack of suitable statistical methods. Consequently, they often proceeded to analyse their data by performing arithmetic directly on the numbers used to symbolize the measurement classes, i.e. by the methods appropriate to interval (or ratio) data. The invention of the concept of a 'generalized linear model' (GLM) by NeIder & Wedderburn (1972), and the subsequent flood of research in this area, should render this incorrect practice unnecessary. A very complete account of the theory concerned is to be found in McCullagh & NeIder (1989) while Dobson (1990) provides a quick introduction to the basic ideas of GLM techniques. The latter has little to say about ordinal data and should be read in conjunction with McCullagh (1980). An alternate school of thought is exemplified by Agresti (1984) and, perhaps most recently, by Lipsitz (1992). The purpose of this paper is to draw attention to some techniques not described by any of the above publications.

Estimating effects in ordinal dummy variable regression

Abstract: This paper discusses the ordinal dummy variable coding system and its use on categorical data. In this method each originally coded interval-scale parent independent variable is represented by a set of ordinal dummy variables of 1's and 0's designating the various levels of that parent variable. The effect of a specified parent independent variable on a dependent variable is shown to be the weighted sum of the net effects of its representative ordinal dummy variables on the dependent variable, where the weights are the simple regression effects of the ordinal variable on its parent dummy variables. The method is illustrated with some data set.

On scaling of ordinal categorical data

Abstract: This paper discusses the analysis of data when responses are in the form of categories in a multiway contingency table. The methodology is based on quantifying or scaling the categories of each attribute and applying the usual multivariate techniques developed for continuous variables. In the case of ordinal categories, the scales are obtained to match the natural order. This enables a meaningful interpretation of results based on estimated scales. Key words and phrases: Correlation ratio; Dual scaling; Ordinal categorical data; Restricted scaling

A Stochastic Programming Model to Analyze Ordinal Preference Data

Abstract: Many marketing situations require analysis of ordinal preference data. Existing analysis methods include OLS, variations of the logit model and methods such as LINMAP. An alternative method is proposed that has the following features: 1) Tie rankings are allowed; 2) all rank order information is incorporated into the estimation — not just first preferences; 3) the procedure is formulated as a L.P. model, which is easily implemented with existing software; 4) statistical inference is supported by the underlying stochastic model; and 5) it supports estimation of individual and group preferences.

A solution to multiple linear regression problems with ordered attributes

Abstract: A class of multiple linear regression techniques is discussed, in which the order of magnitude is constrained among regression coefficients. Each predictor variable is a qualitative variate having some categories which are on an ordinal scale. The criterion variable is quantitative. The problem to be solved is reduced to a quadratic programming problem in which the objective function is the residual sum of the squares in regression, and the constraints are linear ones imposed on the regression coefficients. Under some conditions for the observed data, this problem can be solved numerically. The proposed technique works effectively for some types of regression analysis.

The relation between ordinal problem space sizes and the maximum number of ordinal classification rules

Abstract: A method is presented of establishing bounds on the number of classification rules in such applications as credit worthiness assessment, investment decisions, premium determination, consumer choices, employee selection, and editorial preferences, to name just a few. A function that relates the maximum number of classification rules to the problem space size of such application domains is established. It is shown that in this important class of ordinal classification problems, the maximum possible number of rules is significantly lower than the relative problem space sizes. The approach grants the ability to a priori estimate worst case response time and memory requirements, and to better predict the effectiveness of knowledge acquisition efforts.

Comparing time trends in a two-arm longitudinal study with an ordinal categorical response

Abstract: A within-subject monotonicity index is proposed to summarize the fol-lowup for each subject in a longitudinal study where the response is required to be only ordinal. The individual measures can be weighted to detect different trend behaviors of interest. Asymptotically normal tests for single group alternatives or for comparing the means of two groups are derived and illustrated with clinical data.

Category-specific covariate effects in longitudinal study designs

Abstract: For polytomous ordinal response data, McCullagh (1980) proposed a proportional odds model that describes a regression relationship between the ordinal response and a set of covariates. In a longitudinal setting, Stram et al. (1988) apply a marginal modeling approach to repeated ordinal response data by choosing a proportional odds model at each time point and describe the overall response distribution using the joint asymptotic distribution of the parameter estimates collected across time. However, in clinical and medical research, the underlying proportionality assumption is not always true. This refers to a covariate or a set of covariates that influence each category of a polytomous ordinal response in a differential way leading to non-proportional odds. In this paper, we consider allowing for non-proportional odds arising at each time point from repeated ordinal response data in a longitudinal study context. Following the marginal modeling approach given earlier, we have fitted a category-specific cum...