# Statistics and Its Interface

## Volume 7 (2014)

### Assessing proportionality assumption in the adjacent category logistic regression model

Pages: 275 – 295

DOI: http://dx.doi.org/10.4310/SII.2014.v7.n2.a12

#### Authors

Anil Dolgun (Department of Biostatistics, Faculty of Medicine, Hacettepe University, Sihhiye, Ankara, Turkey)

Osman Saracbasi (Department of Biostatistics, Faculty of Medicine, Hacettepe University, Sihhiye, Ankara, Turkey)

#### Abstract

Ordinal logistic regression models are classified as either proportional odds models, continuation ratio models or adjacent category models. The common model assumption of these models is that the log odds do not depend on the outcome category. This assumption is also known as the “proportionality” or “parallel logits” assumption. Nonproportional and partial proportional models are proposed for the proportional odds and continuation ratio model. The non-proportional and the partial proportional versions of the adjacent category model are also feasible. Prior to fitting any of the ordinal logistic regression models, it is important to check whether the assumption of proportionality is satisfied by each independent variable. In the proportional odds model, the proportional odds assumption is checked by Brant’s Wald test statistic, and the standard Wald test statistic can be used in the continuation ratio model. However there is no valid approach to test whether the proportionality assumption is satisfied by each independent variable in the adjacent category model. The aim of the study is to determine the variables in the adjacent category model that violate the proportionality assumption. For this purpose, a Wald test is proposed for testing the proportionality assumption in the adjacent category model. The validity of the proposed test is examined under $H_0$ with a Monte Carlo simulation study. Moreover, the proposed method is compared with the likelihood ratio test in terms of type I error rate and power under different scenarios.

#### Keywords

ordinal logistic regression, proportionality assumption, adjacent category model, odds ratio, Wald test, likelihood ratio test

#### 2010 Mathematics Subject Classification

Primary 62F05, 62J12. Secondary 62P10, 62P25.

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