OptinMon 03 - 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

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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.

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

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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

The Problem with Linear Regression for Count Data: Predicting Length of Stay in Hospital

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This year’s flu strain is very vigorous. The number of people checking in at hospitals is rapidly increasing. Hospitals are desperate to know if they have enough beds to handle those who need their help.

You have been asked to analyze a previous year’s hospitalization length of stay by people with the flu who had been admitted to the hospital. The predictors in your data set are age group, gender and race of those admitted. You also have an indicator that signifies whether the hospital was privately or publicly run.

Analyzing Zero-Truncated Count Data: Length of Stay in the ICU for Flu Victims

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by Jeff Meyer

It’s that time of year: flu season.

Let’s imagine you have been asked to determine the factors that will help a hospital determine the length of stay in the intensive care unit (ICU) once a patient is admitted.

The hospital tells you that once the patient is admitted to the ICU, he or she has a day count of one. As soon as they spend 24 hours plus 1 minute, they have stayed an additional day.

Clearly this is count data. There are no fractions, only whole numbers.

To help us explore this analysis, let’s look at real data from the State of Illinois. We know the patients’ ages, gender, race and type of hospital (state vs. private).

A partial frequency distribution looks like this: [Read more…] about Analyzing Zero-Truncated Count Data: Length of Stay in the ICU for Flu Victims