What is the difference between ordered probit and logit model?

Ordered logit (OL) and ordered probit (OP) models are statistical techniques utilized in various fields to analyze ordinal data, where observations are categorized into ordered categories rather than numerical values.

In practical applications, these models are often employed to study phenomena where there are naturally occurring ordered categories, such as satisfaction levels, performance ratings, or risk assessments.

The OL model assumes that the underlying continuous variable follows a logistic distribution. This implies that the probability of an observation falling into a particular category increases or decreases in a sigmoidal pattern as the value of the continuous variable changes.

Conversely, the OP model postulates that the underlying continuous variable has a normal distribution. In this framework, the probability of categorization is influenced by the distance of the continuous variable from a set of thresholds, with larger values indicating a higher likelihood of belonging to a higher category.

A key feature of both OL and OP models is that they allow for the interpretation of the relationship between the dependent variable and explanatory variables in terms of how they affect the likelihood of an observation falling into a particular ordered category.