Count Models

Overview

Count data models are used when the dependent variable is a non-negative integer (0, 1, 2, …), such as the number of doctor visits, accident claims, or defects in a product. While basic Poisson regression is the starting point, real-world data often violates its assumptions (e.g., variance > mean, or too many zeros).

Handling Excess Zeros

In many datasets (like insurance claims or manufacturing defects), there are far more zeros than a standard Poisson or Negative Binomial distributions would predict. Specialized models are needed to handle this “zero inflation”.

  • ZIP_MODEL: Zero-Inflated Poisson. Assumes two processes: one that generates only zeros (e.g., “Non-smokers never buy cigarettes”) and one that generates counts (including some zeros) via a Poisson process.
  • ZINB_MODEL: Zero-Inflated Negative Binomial. Similar to ZIP but uses a Negative Binomial distribution for the count process to handle overdispersion.
  • HURDLE_COUNT_MODEL: Hurdle Model. Also uses two parts: a binary model (Logit/Probit) to cross the “hurdle” of having any count vs zero, and a truncated count model (Poisson/NegBin) for the positive counts. Unlike ZIP, hurdle models treat zeros and non-zeros as completely separate processes.
Figure 1: Zero-Inflation: Standard distributions (dashed) typically underestimate the peak at zero in real-world count data. Zero-inflated models (solid) explicitly model this excess mass.

Native Excel Capabilities

Excel has no native support for advanced count models. - Poisson: POISSON.DIST exists for calculating probabilities, but there is no function to fit a Poisson regression model to data. - Zero-Inflation: Modeling ZIP or Hurdle processes in Excel requires complex custom likelihood formulations and Solver optimization, which is error-prone and computationally slow.

Tools

Tool Description
HURDLE_COUNT_MODEL Fits a Hurdle model for count data with two-stage process (zero vs. positive counts).
ZINB_MODEL Fits a Zero-Inflated Negative Binomial (ZINB) model for overdispersed count data with excess zeros.
ZIP_MODEL Fits a Zero-Inflated Poisson (ZIP) model for count data with excess zeros.