Poisson and Negative Binomial Regression Models

What is the Purpose of a Generalized Linear Mixed Model?

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 4 Comments

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 10 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

The Problem with Linear Regression for Count Data

by Jeff Meyer Leave a Comment

Imagine this scenario:

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.

Member Training: Making Sense of Statistical Distributions

by guest contributer Leave a Comment

Many who work with statistics are already functionally familiar with the normal distribution, and maybe even the binomial distribution.

These common distributions are helpful in many applications, but what happens when they just don’t work?

This webinar will cover a number of statistical distributions, including the:

Poisson and negative binomial distributions (especially useful for count data)
Multinomial distribution (for responses with more than two categories)
Beta distribution (for continuous percentages)
Gamma distribution (for right-skewed continuous data)
Bernoulli and binomial distributions (for probabilities and proportions)
And more!

We’ll also explore the relationships among statistical distributions, including those you may already use, like the normal, t, chi-squared, and F distributions.

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.