Unimodal Ordinal Logit: A Logit Model with a Utility-Correction Term Capturing Correlations from Ordinal Responses

Discrete variables that show a natural ordering across response levels are commonly analyzed based on data collected in surveys and in field observations. These variables follow a natural unimodal probability distribution, as the levels that are closer to the actual chosen level are more likely to have a higher correlation than the levels that are further away. However, conventional Ordered Logit (OL) models do not capture this mechanism and might result in a probability distribution that does not align with this natural ordering. This study develops an Unimodal Ordered Logit (UOL) model to account for the unimodal probability mass distribution of ordered responses.  A correction term is included into the utility function of a logit model to impose an unimodal constraint and capture the monotonically decreasing order of the responses. The UOL model is applied to predict the likelihood that respondents will participate in different COVID-19 measures based on a survey dataset.  The estimated models are compared based on the final log likelihood and three accuracy metrics that account for probability variance and ordinal distances. The results showed that the UOL models improves goodness of fit and predictive accuracy on the validation samples compared to the OL model when the underlying prior is unimodal.