# Poisson and Negative Binomial Regression Models

### Differences Between the Normal and Poisson Distributions

December 23rd, 2016 by

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 (more…)

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

December 21st, 2016 by

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: (more…)

### Member Training: Zero Inflated Models

June 1st, 2016 by
A common situation with count outcome variables is there are a lot of zero values.  The Poisson distribution used for modeling count variables takes into account that zeros are often the most common value, but sometimes there are even more zeros than the Poisson distribution can account for.

This can happen in continuous variables as well–most of the distribution follows a beautiful normal distribution, except for the big stack of zeros.

This webinar will explore two ways of modeling zero-inflated data: the Zero Inflated model and the Hurdle model. Both assume there are two different processes: one that affects the probability of a zero and one that affects the actual values, and both allow different sets of predictors for each process.

We’ll explore these models as well as some related models, like Zero-One Inflated Beta models for proportion data.

Note: This training is an exclusive benefit to members of the Statistically Speaking Membership Program and part of the Stat’s Amore Trainings Series. Each Stat’s Amore Training is approximately 90 minutes long.

### Issues with Truncated Data

May 12th, 2016 by

In a previous post we explored bounded variables and the difference between truncated and censored. Can we ignore the fact that a variable is bounded and just run our analysis as if the data wasn’t bounded? (more…)

### When to Check Model Assumptions

March 7th, 2016 by

Like the chicken and the egg, there’s a question about which comes first: run a model or test assumptions? Unlike the chickens’, the model’s question has an easy answer.

There are two types of assumptions in a statistical model.  Some are distributional assumptions about the residuals.  Examples include independence, normality, and constant variance in a linear model.

Others are about the form of the model.  They include linearity and (more…)

### Generalized Linear Models in R, Part 7: Checking for Overdispersion in Count Regression

August 27th, 2015 by

In my last blog post we fitted a generalized linear model to count data using a Poisson error structure.

We found, however, that there was over-dispersion in the data – the variance was larger than the mean in our dependent variable.