The Analysis Factor

Statistical Consulting, Resources, and Statistics Workshops for Researchers

Poisson and Negative Binomial Regression Models

What Are Nested Models?

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Pretty much all of the common statistical models we use, with the exception of OLS Linear Models, use Maximum Likelihood estimation.

This includes favorites like:

That’s a lot of models.

If you’ve ever learned any of these, you’ve heard that some of the statistics that compare model fit in competing models require [Read more…] about What Are Nested Models?

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

Two-Way Tables and Count Models: Expected and Predicted Counts

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by Jeff Meyer

In a previous article, we discussed how incidence rate ratios calculated in a Poisson regression can be determined from a two-way table of categorical variables.

Statistical software can also calculate the expected (aka predicted) count for each group. Below is the actual and expected count of the number of boys and girls participating and not participating in organized sports.

cm-twowaytables-1

 

 

 

 

 

 

 

The value in the top of each cell is the actual count (40 boys do not play organized sports) and the bottom value is the expected/predicted count (36 boys are predicted to not play organized sports).

The Poisson model that we ran in the previous article generated the following table: [Read more…] about Two-Way Tables and Count Models: Expected and Predicted Counts

Understanding Incidence Rate Ratios through the Eyes of a Two-Way Table

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by Jeff Meyer

The coefficients of count model regression tables are shown in either logged form or as incidence rate ratios. Trying to explain the coefficients in logged form can be a difficult process.

Incidence rate ratios are much easier to explain. You probably didn’t realize you’ve seen incidence rate ratios before, expressed differently.

Let’s look at an example.

A school district was interested in how many children in their sixth grade classes played on organized sports teams. So they did a count and also noted the gender of the child. The results were put into a table: [Read more…] about Understanding Incidence Rate Ratios through the Eyes of a Two-Way Table

Differences Between the Normal and Poisson Distributions

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The normal distribution is so ubiquitous in statistics that those of us who use a lot of statistics tend to forget it’s not always so common in actual data.

And since the normal distribution is continuous, many people describe all numerical variables as continuous. I get it: I’m guilty of using those terms interchangeably, too, but they’re not exactly the same.

Numerical variables can be either continuous or discrete.

The difference? Continuous variables can take any number within a range. Discrete variables can only be whole numbers.

So 3.04873658 is a possible value of a continuous variable, but not discrete.

Count variables, as the name implies, are frequencies of some event or state. Number of arrests, fish [Read more…] about Differences Between the Normal and Poisson Distributions

Overdispersion in Count Models: Fit the Model to the Data, Don’t Fit the Data to the Model

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by Jeff Meyer

If you have count data you use a Poisson model for the analysis, right?

The key criterion for using a Poisson model is after accounting for the effect of predictors, the mean must equal the variance. If the mean doesn’t equal the variance then all we have to do is transform the data or tweak the model, correct?

Let’s see how we can do this with some real data. A survey was done in Australia during the peak of the flu season. The outcome variable is the total number of times people asked for medical advice from any source over a two-week period.

We are trying to determine what influences people with flu symptoms to seek medical advice. The mean number of times was 0.516 times and the variance 1.79.

The mean does not equal the variance even after accounting for the model’s predictors.

Here are the results for this model: [Read more…] about Overdispersion in Count Models: Fit the Model to the Data, Don’t Fit the Data to the Model