# Poisson and Negative Binomial Regression Models

### Count Models: Understanding the Log Link Function

November 12th, 2020 by

When we run a statistical model, we are in a sense creating a mathematical equation. The simplest regression model looks like this:

Yi = β0 + β1X+ εi

The left side of the equation is the sum of two parts on the right: the fixed component, β0 + β1X, and the random component, εi.

You’ll also sometimes see the equation written (more…)

### Count vs. Continuous Variables: Differences Under the Hood

October 15th, 2018 by

by Jeff Meyer, MBA, MPA

One of the most important concepts in data analysis is that the analysis needs to be appropriate for the scale of measurement of the variable. The focus of these decisions about scale tends to focus on levels of measurement: nominal, ordinal, interval, ratio.

These levels of measurement tell you about the amount of information in the variable. But there are other ways of distinguishing the scales that are also important and often overlooked.

### What is the Purpose of a Generalized Linear Mixed Model?

September 10th, 2018 by

If you are new to using generalized linear mixed effects models, or if you have heard of them but never used them, you might be wondering about the purpose of a GLMM.

Mixed effects models are useful when we have data with more than one source of random variability. For example, an outcome may be measured more than once on the same person (repeated measures taken over time).

When we do that we have to account for both within-person and across-person variability. A single measure of residual variance can’t account for both.

### When to Use Logistic Regression for Percentages and Counts

April 30th, 2018 by

One important yet difficult skill in statistics is choosing a type model for different data situations. One key consideration is the dependent variable.

For linear models, the dependent variable doesn’t have to be normally distributed, but it does have to be continuous, unbounded, and measured on an interval or ratio scale.

Percentages don’t fit these criteria. Yes, they’re continuous and ratio scale. The issue is the (more…)

### Poisson or Negative Binomial? Using Count Model Diagnostics to Select a Model

March 19th, 2018 by

How do you choose between Poisson and negative binomial models for discrete count outcomes?

One key criterion is the relative value of the variance to the mean after accounting for the effect of the predictors. A previous article discussed the concept of a variance that is larger than the model assumes: overdispersion.

(Underdispersion is also possible, but much less common).

There are two ways to check for overdispersion: (more…)

### Getting Accurate Predicted Counts When There Are No Zeros in the Data

March 12th, 2018 by

We previously examined why a linear regression and negative binomial regression were not viable models for predicting the expected length of stay in the hospital for people with the flu.  A linear regression model was not appropriate because our outcome variable, length of stay, was discrete and not continuous.

A negative binomial model wasn’t the proper choice because the minimum length of stay is not zero. The minimum length of stay is one day. Negative binomial and Poisson models can only be used on data where the observations’ outcome have the possibility of having a zero count.

We need to use a truncated negative binomial model to analyze the expected length of stay of people admitted to the hospital who have the flu. Calculating the expected length of stay is an easy task once we create our model. (more…)