Showing papers on "Ordinal regression published in 1998"

Ordinal invariant measures for individual and group changes in ordered categorical data

Abstract: Subjective judgements of complex variables are commonly recorded as ordered categorical data. The rank-invariant properties of such data are well known, and there are various statistical approaches to the analysis and modelling of ordinal data. This paper focuses on the non-additive property of ordered categorical data in the analysis of change. A rank-invariant non-parametric method of analysis is presented that is valid regardless of the number of response categories. The unique feature of this method is the augmented ranking approach that is related to the joint distribution of paired observations. This approach makes it possible to measure separately the individual order-preserved categorical changes, which are attributable to the group change, and the individual categorical changes that are not consistent with the pattern of group change. The method is applied to analysis of change in a three-point scale and in a visual analogue scale of continuous ordinal responses.

Development of a clinical prediction model for an ordinal outcome: the World Health Organization Multicentre Study of Clinical Signs and Etiological Agents of Pneumonia, Sepsis and Meningitis in Young Infants

Abstract: This paper describes the methodologies used to develop a prediction model to assist health workers in developing countries in facing one of the most difficult health problems in all parts of the world: the presentation of an acutely ill young infant. Statistical approaches for developing the clinical prediction model faced at least two major difficulties. First, the number of predictor variables, especially clinical signs and symptoms, is very large, necessitating the use of data reduction techniques that are blinded to the outcome. Second, there is no uniquely accepted continuous outcome measure or final binary diagnostic criterion. For example, the diagnosis of neonatal sepsis is ill-defined. Clinical decision makers must identify infants likely to have positive cultures as well as to grade the severity of illness. In the WHO/ARI Young Infant Multicentre Study we have found an ordinal outcome scale made up of a mixture of laboratory and diagnostic markers to have several clinical advantages as well as to increase the power of tests for risk factors. Such a mixed ordinal scale does present statistical challenges because it may violate constant slope assumptions of ordinal regression models. In this paper we develop and validate an ordinal predictive model after choosing a data reduction technique. We show how ordinality of the outcome is checked against each predictor. We describe new but simple techniques for graphically examining residuals from ordinal logistic models to detect problems with variable transformations as well as to detect non-proportional odds and other lack of fit. We examine an alternative type of ordinal logistic model, the continuation ratio model, to determine if it provides a better fit. We find that it does not but that this model is easily modified to allow the regression coefficients to vary with cut-offs of the response variable. Complex terms in this extended model are penalized to allow only as much complexity as the data will support. We approximate the extended continuation ratio model with a model with fewer terms to allow us to draw a nomogram for obtaining various predictions. The model is validated for calibration and discrimination using the bootstrap. We apply much of the modelling strategy described in Harrell, Lee and Mark (Statist. Med. 15, 361-387 (1998)) for survival analysis, adapting it to ordinal logistic regression and further emphasizing penalized maximum likelihood estimation and data reduction.

Measuring Customer Satisfaction Using a Collective PreferenceDisaggregation Model

Abstract: A new model to assess customer satisfaction is developed through this paper. The proposed model is based on the principles of multicriteria analysis, using ordinal regression techniques. The procedure uses survey‘s data on customer satisfaction criteria and disaggregates simultaneously all the global satisfaction judgments via a linear programming disaggregation formulation. The model provides collective global and partial satisfaction functions as well as average satisfaction indices. These results sufficiently describe customer behavior and they can be used in the strategic planning of an organization. The implementation of the model in three real world applications is used for illustration and for testing the model‘s reliability. Finally, several extensions and future research in the area of customer satisfaction analysis are discussed.

Estimating consumer satisfaction: ols versus ordered probability models

Abstract: This paper reviews the use of logit and probit models in marketing and focuses on demonstrating the use of ordered probability models. This type of model is appropriate for many applications in marketing and business where the dependent variable of interest is ordinal (e.g., likert scales). A comparison between the properties of the ordinary least squares (OLS) model and ordered logit and probit models is made using consumer satisfaction data on automobiles. This comparison between the two models shows that the use of OLS for ordered categorical data gives misleading results and produces biased estimates, leading to inaccurate hypothesis testing. The paper concludes that ordered probability models, such as the ones illustrated, should be employed in marketing and business research where the dependent variable is ordinal.

A Bayesian approach to a general regression model for ROC curves.

Abstract: A fully Bayesian approach to a general nonlinear ordinal regression model for ROC-curve analysis is presented. Samples from the marginal posterior distributions of the model parameters are obtained by a Markov-chain Monte Carlo (MCMC) technique--Gibbs sampling. These samples facilitate the calculation of point estimates and credible regions as well as inferences for the associated areas under the ROC curves. The analysis of an example using freely available software shows that the use of noninformative vague prior distributions for all model parameters yields posterior summary statistics very similar to the conventional maximum-likelihood estimates. Clinically important advantages of this Bayesian approach are: the possible inclusion of prior knowledge and beliefs into the ROC analysis (via the prior distributions), the possible calculation of the posterior predictive distribution of a future patient outcome, and the potential to address questions such as: "What is the probability that a certain diagnostic test is better in one setting than in another?"

Modelling ordinal responses from co‐twin control studies

Abstract: The co-twin control design has been widely used in studying the effects of environmental factors on the development of diseases. For binary outcomes that arise from co-twin control studies, the conditional likelihood method is commonly used. This approach, however, does not readily extend to ordinal response data because the standard conditional likelihood does not exist for cumulative logit or proportional odds models. In this paper, we investigate the applicability of the random-effects and GEE approaches in analysing ordinal response data from co-twin control studies. Using both approaches, we re-analyse data from a co-twin control study of the impact of military services during the Vietnam era on post-traumatic stress disorders (PTSD). The ordinal models have considerably increased power in detecting the effects of exposure when compared to the analyses using a dichotomized response. We discuss the interpretation of the estimates from GEE and random-effects models in the context of the twin data. © 1998 John Wiley & Sons, Ltd.

A study of the effect of dichotomizing ordinal data upon modeling

Abstract: Investigators in health services research often analyze ordinal outcome data as if it were dichotomous by collapsing outcomes into two groups and using standard logistic regression, rather than an alternate discrete model. This paper assesses the degree to which parameters are inaccurately estimated and ower is lost when this is done. Simulations with a five level ordinal outcome variable demonstrated that the loss of precision and power can be very pronounced. Parameter estimates were especially poor in the presence of moderately sparse data, while the loss of power was most evident with balanced data. Polychotomous models are also examined and discussed. An example using length of hospital stay data grouped into discrete outcome levels is given.

Different Nonlinear Regression Models with Incorrectly Observed Covariates

Abstract: We present quasi-likelihood models for different regression problems when one of the explanatory variables is measured with heteroscedastic error. In order to derive models for the observed data the conditional mean and variance functions of the regression models are only expressed through functions of the observable covariates. The latent covariable is treated as a random variable that follows a normal distribution. Furthermore it is assumed that enough additional information is provided to estimate the individual measurement error variances, e.g. through replicated measurements of the fallible predictor variable. The discussion includes the polynomial regression model as well as the probit and logit model for binary data, the Poisson model for count data and ordinal regression models.

Statistical Modelling of Platypus, Ornithorhynchus anatinus, Habitat Preferences Using Generalised Linear Models.

Abstract: Bryant (1993) collected extensive data on the habitat preferences of the platypus (Ornithorhynchus anatinus) measured in 36 pools in the upper Macquarie River system. Platypus presence or absence in these pools was measured on three occasions. Detailed modelling of the factors affecting pool preference was complicated by the scale of response being ordinal due to the inability of the observer to distinguish between repeated sightings of the same animal and several different animals. Initial modelling using logistic regression on a presence/absence index, collapsed from the ordinal response, discounted time of day and seasonal effects. These temporal simplifications allowed a binomial analysis of success rate based on the three visits, which identified an additional habitat factor not identified in the original analysis. Finally, a full ordinal regression of the proportions falling into each ordered category is presented as the ultimate modelling of platypus pooI preferences. The analysis indicated that length and depth of pools and the presence of overhanging vegetation were positively related to the observed presence of platypuses.

A probit model for multivariate random length ordinal data

Abstract: Multivariate random length ordinal data are data such that the ordinal response variable is observed a random number of times for each experimen¬tal unit. For example, depression may occur a random number of times and the severity of each depression episode is measured by an ordinal scale (e.g., l=mildly depressed, 2=moderately depressed, 3=very depressed). There is a need to evaluate how treatment or disease status impacts both the sever¬ity of the ordinal responses and the number of occurrences. In this paper, we propose a probit model which can realistically describe the relationships between the number of events and the ordinal responses of these events. This model also takes into account the correlation among multiple ordinal measurements. We describe estimation issues and the asymptotic efficiency of the maximum likelihood estimators. A simulation study is performed to examine the asymptotic behavior of the maximum likelihood estimators. An example using data from a pediatric longitudinal study is p...

Locally Weighted Least Squares in Categorical Varying-Coefficient Models

Abstract: In varying-coefficient models the number of coefficients that have to be estimated is usually very high. Consequently local likelihood estimates which are based on an iterative procedure are rather time-consuming. In the present paper an alternative local estimation procedure is proposed. It is based on the weighted least squares estimate applied locally for fixed effect modifier but additionally observations in the neighbourhood are used in a weighted form. Asymptotic behaviour of the locally weighted least squares estimator is shown to be equivalent to the local likelihood estimate. The performance of the estimator is illustrated by a small simulation study and an application to ordinal regression.

OCRATIO: Stata modules to fit continuation-ratio models on ordinal response data

Abstract: ocratio fits models based on continuation-ratio probabilities to ordinal responses (using maximum-likelihood). Three models are available using the logit, probit and complementary-log-log (f(x)=log[-log(1-x)]) functions. These models are an alternative to the models based on cumulative probabilities fitted by ologit and oprobit. ocratio also enables the fitting of a "ocloglog" model by using the cumulative option. This is possible because the "ocloglog" model is equivalent to the continuation-ratio complementary-log-log.

Power Indices based on Ordinal Games

Abstract: Shapley (1953) and Banzhaf (1965) solved multiperson cooperative games by assessing a value (power index) to each player of a game. Shapley value can be interpreted as giving each player his average marginal contribution to all coalitions of players. Banzhaf power index related to a player i corresponds to the probability that a coalition wins when the player i joins randomly the coalition. Given a game v : 2N → IR (i.e. a real valued set function on N), where N is a set of players, the Shapley power index related to the player i ∈ N is given by

Dynamic clustering model for ordinal similarity

Abstract: This paper proposes a clustering model for ordinal similarity data. The data is 3-way data, which is observed by similarities of objects for several times. The essential merit of this model is to capture the differences of clusterings while keeping the feature of object ordering. In order to keep this feature, the monotone relation is used for fitting the data and the model. The fitness is calculated based on the monotone regression principle (Kruskal, 1964).