Showing papers on "Ordinal regression published in 1994"

A random-effects ordinal regression model for multilevel analysis.

Abstract: A random-effects ordinal regression model is proposed for analysis of clustered or longitudinal ordinal response data. This model is developed for both the probit and logistic response functions. The threshold concept is used, in which it is assumed that the observed ordered category is determined by the value of a latent unobservable continuous response that follows a linear regression model incorporating random effects. A maximum marginal likelihood (MML) solution is described using Gauss-Hermite quadrature to numerically integrate over the distribution of random effects. An analysis of a dataset where students are clustered or nested within classrooms is used to illustrate features of random-effects analysis of clustered ordinal data, while an analysis of a longitudinal dataset where psychiatric patients are repeatedly rated as to their severity is used to illustrate features of the random-effects approach for longitudinal ordinal data.

Alternative models for ordinal logistic regression

Abstract: Armstrong and Sloan have reviewed two types of ordinal logistic models for epidemiologic data: the cumulative-odds model and the continuation-ratio model. I review here certain aspects of these models not emphasized previously, and describe a third type, the stereotype model, which in certain situations offers greater flexibility coupled with interpretational advantages. I illustrate the models in an analysis of pneumoconiosis among coal miners.

ROC Curve Regression Analysis: The Use of Ordinal Regression Models for Diagnostic Test Assessment

Abstract: Diagnostic tests commonly are characterized by their true positive (sensitivity) and true negative (specificity) classification rates, which rely on a single decision threshold to classify a test result as positive. A more complete description of test accuracy is given by the receiver operating characteristic (ROC) curve, a graph of the false positive and true positive rates obtained as the decision threshold is varied. A generalized regression methodology, which uses a class of ordinal regression models to estimate smoothed ROC curves has been described. Data from a multi-institutional study comparing the accuracy of magnetic resonance (MR) imaging with computed tomography (CT) in detecting liver metastases, which are ideally suited for ROC regression analysis, are described. The general regression model is introduced and an estimate for the area under the ROC curve and its standard error using parameters of the ordinal regression model is given. An analysis of the liver data that highlights the utility of the methodology in parsimoniously adjusting comparisons for covariates is presented.

Ordinal Log-Linear Models

Abstract: INTRODUCTION Ordinal Measures Log-Linear Models for Nominal Variables A Review ORDINAL LOG-LINEAR MODELS Row Effects Models Column Effects Models Uniform Association Models Assignment of Scores Row and Column Effects Models Odds Ratios for Two-Way Tables Summary Ordinal Log-Linear Models for Higher-Ordered Tables Multidimensional Log-Multiplicative Models Odds Ratios for Three-Way Log-Linear Models Summary Selection for Ordinal Log-Linear Models Advantages of Using Ordinal Log-Linear Models Summary CONCLUSION

Predicting ordinal relations

Abstract: An alternative to multiple regression that is appropriate when the dependent variable is ordinal is suggested. The goal of the system is to predict correctly as many as possible of the binary ordinal relations on the dependent variable. This can be done by treating the problem as one in discriminant analysis by discriminating the pairs of subjects whose ordinal relations are in one direction from those with relations in the other. The bases of prediction can be raw score differences on predictors, their rank differences, or their directions of difference. For each, it is possible to find a system of weights that approximately maximizes discrimination. These turn out to depend on the variables' co-variances, on their rank correlations, and on their tau correlations, respectively. It is also possible to estimate the odds that any given relation is in a particular direction. A solution for the weights that exactly maximizes probability of correct ordinal prediction is available in the case of predicting from directions of difference. An example is given.

ANOVA and ANCOVA of pre- and post-test, ordinal data

Abstract: With random assignment to treatments and standard assumptions, either a one-way ANOVA of post-test scores or a two-way, repeated measures ANOVA of pre- and post-test scores provides a legitimate test of the equal treatment effect null hypothesis for latent variable Θ. In an ANCOVA for pre- and post-test variablesX andY which are ordinal measures ofη and Θ, respectively, random assignment and standard assumptions ensure the legitimacy of inferences about the equality of treatment effects on latent variable Θ. Sample estimates of adjustedY treatment means are ordinal estimators of adjusted post-test means on latent variable Θ.

A robust goodness‐of‐fit test statistic with application to ordinal regression models

Abstract: We propose a goodness-of-fit test statistic for linear regression with heterogeneous variance, which is asymptotically chi-square if the given model is correct. The test statistic is computed as a quadratic form of observed minus predicted responses. We apply the method to a linear regression for an ordinal categorical response, the wheezing status of a child (no wheeze, wheeze with cold, wheeze apart from cold) as a function of maternal smoking and city of residence.

An ordinal coefficient of relational agreement for multiple judges

Abstract: In a recent article, Fagot proposed a generalized family of coefficients of relational agreement for multiple judges, focusing on the concept of empirically meaningful relationships In this paper an ordinal coefficient of relational agreement, based on ranking data, is presented as a special case of the generalized family It is shown that the proposed ordinal coefficient encompasses other ordinal coefficients, such as the Kendall coefficient of concordance, the average Spearman rank-order coefficient, and intraclass correlation based on ranks It is also shown that the Kendall coefficient of concordance, corrected for chance agreement, is equivalent to the ordinal coefficient proposed in this paper

Regression based causal induction with latent variable models

Abstract: Scientists largely explain observations by inferring causal relationships among measured variables. Many algorithms with various theoretical foundations have been developed for causal induction e.g., (Spirtes, Glymour, & Scheines 1993; Pearl & Verma 1991), but it is widely believed that regression is ill-suited to the task of causal induction. Multiple regression techniques attempt to estimate the influence that regressors have on a dependent variable using the standardized regression coefficient, p. Assuming the relationship among variables is linear, pyx measures the expected change in Y produced by a unit change in X with all other predictor variables held constant. Arguments against using regression methods for causal induction rest on the fact that the error in estimating pyx can be large, particularly when unmeasured or latent variables account for the relationship between X and Y, or when X is a common cause of Y and another predictor (Mosteller & Tukey 1977; Spirtes, Glymour, & Scheines 1993). In fact, p may suggest X has a strong influence on Y when it has little or none. We have developed a regressionbased causal induction algorithm called FBD (Cohen et ol. 1994) which performs well in these situations. The heuristic that is primarily responsible for making FBD less sensitive to the above problems is the w score. Let rx y be the correlation between X and Y, and w = (ryx @yx)/ryx. w measures the proportion of ryx not due to the direct effect of X on Y. If wyx exceeds a threshold, X is pruned from the set of candidate predictors. This threshold is set arbitrarily by the user, but we are exploring the use of clustering algorithms to set it by partitioning the w values of the predictor variables. Spirtes et al. describe four causal models (1993, p. 240) for which their studies showed regression methods performed poorly by always choosing predictors whose relationship to the dependent variable is mediated by latent variables or common causes. One model is reproduced in Figure 1. The difficulty with this model is that the error in the estimate for px, y may be large due to X2’s relationship to X3 via the latent variable 2’1. To determine the susceptibility of FBD to latent variable effects, we tested the performance of FBD’ on latent variable models, and ran stepwise regressions as a control. Twelve sets of coefficients for the structural equations for

Partial residuals in cumulative regression models for ordinal data

Abstract: We are concerned with cumulative regression models for an ordered categorical response variable Y. We propose two methods to build partial residuals from regression on a subset Z1 of covariates Z., which take into regard the ordinal character of the response. The first method makes use of a multivariate GLM-representation of the model and produces residual measures for diagnostic purposes. The second uses a latent continuous variable model and yields new (adjusted) ordinal data Y*. Both methods are illustrated by a data set from forestry.