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negative binomial

The Importance of Including an Exposure Variable in Count Models

by Jeff Meyer 11 Comments

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.

[Read more…] about The Importance of Including an Exposure Variable in Count Models

Tagged With: Count data, count model, exposure variable, incidence rate ratio, linear regression, negative binomial, offset variable, Poisson Regression

Related Posts

  • The Problem with Linear Regression for Count Data
  • The Exposure Variable in Poisson Regression Models
  • Count Models: Understanding the Log Link Function
  • Getting Accurate Predicted Counts When There Are No Zeros in the Data

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

Tagged With: count model, dispersion statistic, Model Fit, negative binomial, overdispersion, poisson, predicted count, residual plot

Related Posts

  • Overdispersion in Count Models: Fit the Model to the Data, Don’t Fit the Data to the Model
  • The Problem with Linear Regression for Count Data
  • The Importance of Including an Exposure Variable in Count Models
  • Analyzing Zero-Truncated Count Data: Length of Stay in the ICU for Flu Victims

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.

[Read more…] about The Problem with Linear Regression for Count Data

Tagged With: Count data, count model, linear regression, negative binomial, Poisson Regression, predicted count, Truncated

Related Posts

  • The Importance of Including an Exposure Variable in Count Models
  • Analyzing Zero-Truncated Count Data: Length of Stay in the ICU for Flu Victims
  • Count Models: Understanding the Log Link Function
  • Poisson or Negative Binomial? Using Count Model Diagnostics to Select a Model

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.

[Read more…] about Member Training: Making Sense of Statistical Distributions

Tagged With: Bernoulli, beta, binomial, distributions, gamma, Multinomial, negative binomial, poisson, statistical distributions

Related Posts

  • Member Training: Logistic Regression for Count and Proportion Data
  • Poisson or Negative Binomial? Using Count Model Diagnostics to Select a Model
  • Analyzing Zero-Truncated Count Data: Length of Stay in the ICU for Flu Victims
  • Overdispersion in Count Models: Fit the Model to the Data, Don’t Fit the Data to the Model

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

by Jeff Meyer 3 Comments

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

Tagged With: Count data, linear regression, negative binomial, poisson, predictors, Truncated

Related Posts

  • The Problem with Linear Regression for Count Data
  • The Importance of Including an Exposure Variable in Count Models
  • Poisson or Negative Binomial? Using Count Model Diagnostics to Select a Model
  • Getting Accurate Predicted Counts When There Are No Zeros in the Data

Differences Between the Normal and Poisson Distributions

by Karen Grace-Martin 4 Comments

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

Tagged With: continuous variable, discrete, negative binomial, normal distribution, normality, numeric variable, Poisson Regression

Related Posts

  • The Importance of Including an Exposure Variable in Count Models
  • Count Models: Understanding the Log Link Function
  • Count vs. Continuous Variables: Differences Under the Hood
  • The Problem with Linear Regression for Count Data

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Poisson and Negative Binomial Regression Models for Count Data

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