Multinomial logistic regression is a statistical method used to model the relationship between one or more independent variables and a categorical dependent variable with more than two unordered categories. It is an extension of binary logistic regression to situations where the outcome variable has multiple categories that are not ordered.

In multinomial logistic regression, the dependent variable is categorical and nominal, meaning the categories have no natural ordering. Examples of such variables include types of diseases (e.g., cancer types), political affiliations, or educational levels.

The model estimates the probability of an observation belonging to each category of the outcome variable, given the values of the independent variables. Instead of estimating the odds of being in one category versus another (as in binary logistic regression), multinomial logistic regression estimates the odds of being in each category relative to a reference category.

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

Assumptions of multinomial logistic regression include:

1. Independence of observations: Each observation should be independent of the others.
2. Absence of multicollinearity: Independent variables should not be highly correlated with each other.
3. No perfect separation: There should be variability in the outcome variable across the levels 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 belonging to each category of the outcome variable, relative to the reference category.

Multinomial logistic regression is commonly used in biostatistics and other fields for analyzing data with categorical outcome variables with more than two unordered categories, providing insights into the relationships between predictors and multiple outcome categories.