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Poisson Regression

The Importance of Including an Exposure Variable in Count Models

by Jeff Meyer 5 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 Leave a Comment

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

The Difference Between Link Functions and Data Transformations

by Kim Love 1 Comment

Generalized linear models—and generalized linear mixed models—are called generalized linear because they connect a model’s outcome to its predictors in a linear way. The function used to make this connection is called a link function. Link functions sounds like an exotic term, but they’re actually much simpler than they sound.

For example, Poisson regression (commonly used for outcomes that are counts) makes use of a natural log link function as follows:

[Read more…] about The Difference Between Link Functions and Data Transformations

Tagged With: generalized linear models, linear model, link function, log link, log transformation, Poisson Regression

Related Posts

  • Count Models: Understanding the Log Link Function
  • Member Training: Generalized Linear Models
  • The Difference Between Logistic and Probit Regression
  • Generalized Linear Models in R, Part 7: Checking for Overdispersion in Count Regression

Member Training: Generalized Linear Models

by guest Leave a Comment

In this webinar, we will provide an overview of generalized linear models. You may already be using them (perhaps without knowing it!).
For example, logistic regression is a type of generalized linear model that many people are already familiar with. Alternatively, maybe you’re not using them yet and you are just beginning to understand when they might be useful to you.
[Read more…] about Member Training: Generalized Linear Models

Tagged With: bayesian, distribution, error distribution, generalized linear models, GLM, linear model, linear regression, link function, logistic regression, maximum likelihood, mixed model, Poisson Regression

Related Posts

  • Member Training: Types of Regression Models and When to Use Them
  • Count Models: Understanding the Log Link Function
  • Member Training: A Predictive Modeling Primer: Regression and Beyond
  • The Difference Between Link Functions and Data Transformations

When to Use Logistic Regression for Percentages and Counts

by Karen Grace-Martin 1 Comment

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

Tagged With: binomial, Count data, count model, dependent variable, events, logistic regression, Negative Binomial Regression, percentage data, Poisson Regression, trials

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  • Member Training: Count Models
  • When Dependent Variables Are Not Fit for Linear Models, Now What?
  • Proportions as Dependent Variable in Regression–Which Type of Model?
  • Poisson Regression Analysis for Count 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.

[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

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