Ordinal logistic regression is a statistical method used to model the relationship between one or more independent variables and an ordinal dependent variable. It is an extension of binary logistic regression to situations where the outcome variable has more than two ordered categories but maintains the ordinal nature of the categories.

In ordinal logistic regression, the dependent variable is categorical and ordinal, meaning it has a natural ordering but the intervals between categories may not be equal. For example, Likert scale responses (e.g., strongly disagree, disagree, neutral, agree, strongly agree) or medical severity scales (e.g., mild, moderate, severe) are often analyzed using ordinal logistic regression.

The model estimates the cumulative probabilities of an observation falling into or below each category of the ordinal outcome variable, given the values of the independent variables. Unlike linear regression, which assumes a continuous outcome, ordinal logistic regression estimates the odds of being at or below a certain category versus being in a higher category.

The assumptions of ordinal logistic regression include:

1. Proportional odds assumption: This assumes that the odds ratios comparing any two categories are constant across different levels of the independent variables.
2. Independence of observations: Each observation should be independent of the others.
3. Linearity of the logit: The relationship between the independent variables and the log odds of the outcome should be linear.

The model parameters are estimated using maximum likelihood estimation, and hypothesis tests are conducted to assess the significance of the independent variables.

Interpretation of the results involves examining the coefficients associated with the independent variables to understand their impact on the odds of being in a lower category versus a higher category of the ordinal outcome variable.

Ordinal logistic regression is a valuable tool in biostatistics for analyzing data with ordinal outcome variables, providing insights into the relationship between predictors and ordered categorical outcomes while accommodating the ordinal nature of the data.