The Outlier Detection for Ordinal Data Using Scalling Technique of Regression Coefficients

Abstract

ABSTRACT. The aims of this study is to detect the outliers by using coefficients of Ordinal Logistic Regression (OLR) for the case of k category responses where the score from 1 (the best) to 8 (the worst). We detect them by using the sum of moduli of the ordinal regression coefficients calculated by jackknife technique. This technique is improved by scalling the regression coefficients to their means. R language has been used on a set of ordinal data from reference distribution. Furthermore, we compare this approach by using studentised residual plots of jackknife technique for ANOVA (Analysis of Variance) and OLR. This study shows that the jackknifing technique along with the proper scaling may lead us to reveal outliers in ordinal regression reasonably well. IntroductionOn the category scale, the panellists are asked to give a score, for an example 1, 2, …, 8 on his opinion about the taste of a certain food. This scale is a discrete number and arranged as an ordinal scale which usually ranges from 1 (the best) to 8 (the worst), or from 'extremely tender' to 'extremely tough' for tenderness of meat, for example. Joo et al. [8] reviewed the definition of fresh meat quality, meat quality traits and variations of meat quality. They also presented the recent knowledge underlying the relationship between fresh meat quality traits and muscle fiber characteristics. In the research, they proposed several potential factors including breed, genotype, sex, hormone, growth performance, diet, muscle location, exercise and ambient temperature that can be used to manipulate muscle fiber characteristics and subsequently meat quality in animals.This problem is a very popular topic on sensory evaluation. A comprehensive review of sensory and consumer science has been conducted by Naes et al. [10]. They also used a 8-category scale for scoring quality attributes. Some researchers omit a central, neutral category to produce a more even distribution of responses. A line or an unstructured scale is a judge response on a solid line from 'little' to 'much' or from 'none' to extremely'.One of the common used response models for ordinal data analysis is the proportional odds model. This model is an extension of logistic model for binary data where their responses are more than two categories [3]. He discussed loglinear models for ordinal variables which have some advantages compared to the model treating all variable as nominal. Whenever the relationship between response and explanatory variables needs to be distinguished then we use the 'logit'model. The model is based on the success probability on response variables, hence, the procedure has to ensure that fitted probabilities are in the range (0,1). Logit model can be found using logit transformation based on logistic function.