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OptinMon 03 - Poisson and Negative Binomial Regression Models

Why Generalized Linear Models Have No Error Term

by Karen Grace-Martin  1 Comment

Even if you’ve never heard the term Generalized Linear Model, you may have run one. It’s a term for a family of models that includes logistic and Poisson regression, among others.

It’s a small leap to generalized linear models, if you already understand linear models. Many, many concepts are the same in both types of models.

But one thing that’s perplexing to many is why generalized linear models have no error term, like linear models do. [Read more…] about Why Generalized Linear Models Have No Error Term

Tagged With: error term, generalized linear model, generalized linear models, logistic regression, Poisson Regression

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

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

Count Models: Understanding the Log Link Function

by Jeff Meyer  2 Comments

When we run a statistical model, we are in a sense creating a mathematical equation. The simplest regression model looks like this:

Yi = β0 + β1X+ εi

The left side of the equation is the sum of two parts on the right: the fixed component, β0 + β1X, and the random component, εi.

You’ll also sometimes see the equation written [Read more…] about Count Models: Understanding the Log Link Function

Tagged With: count model, generalized linear models, linear regression, link function, log link, log transformation, Negative Binomial Regression, Poisson Regression

Related Posts

  • The Importance of Including an Exposure Variable in Count Models
  • The Difference Between Link Functions and Data Transformations
  • Getting Accurate Predicted Counts When There Are No Zeros in the Data
  • The Problem with Linear Regression for Count Data

Count vs. Continuous Variables: Differences Under the Hood

by Jeff Meyer  Leave a Comment

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.

[Read more…] about Count vs. Continuous Variables: Differences Under the Hood

Tagged With: normal distribution, pmf, Poisson distribution, probability mass function

Related Posts

  • Differences Between the Normal and Poisson Distributions
  • When Can Count Data be Considered Continuous?
  • The Exposure Variable in Poisson Regression Models
  • The Importance of Including an Exposure Variable in Count Models

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

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

Tagged With: conditional mean, Count data, incidence rate ratio, linear regression, Negative Binomial Regression, predicted count, truncated negative binomial model, Zero Truncated

Related Posts

  • The Importance of Including an Exposure Variable in Count Models
  • Count Models: Understanding the Log Link Function
  • The Problem with Linear Regression for Count Data
  • A Few Resources on Zero-Inflated Poisson Models

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