Poisson and Negative Binomial Regression Models

The Importance of Including an Exposure Variable in Count Models

When our outcome variable is the frequency of occurrence of an event, we will typically use a count model to analyze the results. There are numerous count models. A few examples are: Poisson, negative binomial, zero-inflated Poisson and truncated negative binomial.

There are specific requirements for which count model to use. The models are not interchangeable. But regardless of the model we use, there is a very important prerequisite that they all share.

Count vs. Continuous Variables: Differences Under the Hood

by Jeff Meyer Leave a Comment

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?

by Kim Love 1 Comment

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

by Karen Grace-Martin 1 Comment

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 [Read more…] about When to Use Logistic Regression for Percentages and Counts

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

by Jeff Meyer 7 Comments

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: [Read more…] about Poisson or Negative Binomial? Using Count Model Diagnostics to Select a Model

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

by Jeff Meyer Leave a Comment

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. [Read more…] about Getting Accurate Predicted Counts When There Are No Zeros in the Data