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Fitting Cumulative Logit Models for Ordinal Response Variables in Retail Trends and Predictions

Sarada Ghosh, G. P. Samanta

Abstract



The polytomous logit model is the most important for estimating odds ratio. A polytomous logit model for estimating cumulative odds ratio is useful when the response variables are ordinal. The multinomial and sequential logit models can be applied as well, but they make no explicit use of the fact that the categories are ordered. The models considered here are specifically designed for ordered data. In this paper, the estimates for the intercepts (which are sometimes called cut-points) indicate where the latent variables are cut to make the groups that we observe in our data. The cumulative odds ratios were estimated based on separate fitting of the model at each of the cut-points level as compared to less than equal to that level. The purpose of this paper is to illustrate the cumulative logit model and apply it to estimate the effects of income and distance for retails purpose or trending and prediction. Our analytical findings are explained through estimation and testing procedure which show the reliability of our logit model from the statistical point of view.

Keywords


Logit model; Odds ratio; Ordinal response variable; Ordinal logistic regression; Cumulative logit model; Proportional odds model.

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