Count data models are statistical tools used to analyze data that represent counts of events or occurrences, such as the number of times a person visits a doctor or the number of accidents at an intersection. These models are particularly useful when the data are non-negative integers, often following a Poisson distribution, which assumes that events occur independently and at a constant rate. Common types of count data models include the Poisson regression and the Negative Binomial regression. The Poisson regression is suitable for data with a mean equal to the variance, while the Negative Binomial regression is used when the variance exceeds the mean, accommodating overdispersion in the data.