Poisson Regression

A Poisson regression is another type of GLM. This requires integers or count data (i.e., 0, 1, 2, 3, …). For some situations, a Poisson regression can be more powerful (e.g., detecting statistically significantly trends) than a linear model or "Gaussian" regression.

During this exercise, we're going to build a linear regression using the lm() function and a Poisson regression using glm().

The objects x and y are loaded into R for you.

This exercise is part of the course

Hierarchical and Mixed Effects Models in R

Exercise instructions

Build an lm() where y is predicted by x and then print the summary.
Build a glm() where y is predicted by x with a "poisson" distribution function and then print the summary to the terminal.
Examine the coefficient estimates for each and notice how only the glm() produces statistically significant estimates for x.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Fit the linear model
summary(lm(___))

# Fit the generalized linear model
summary(glm(___, family = "___"))

Edit and Run Code

This exercise is part of the course

Hierarchical and Mixed Effects Models in R

AdvancedSkill Level

4.7+

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The first chapter provides an example of when to use a mixed-effect and also describes the parts of a regression. The chapter also examines a student test-score dataset with a nested structure to demonstrate mixed-effects.

Exercise 1: What is a hierarchical model?Exercise 2: Examples of hierarchical datasets Exercise 3: Multi-level student data Exercise 4: Exploring multiple-levels: Classrooms and schools Exercise 5: Parts of a regression Exercise 6: Intercepts Exercise 7: Slopes and multiple regression Exercise 8: Random-effects in regressions with school data Exercise 9: Random-effect intercepts Exercise 10: Random-effect slopes Exercise 11: Building the school model Exercise 12: Interpreting the school model

This chapter providers an introduction to linear mixed-effects models. It covers different types of random-effects, describes how to understand the results for linear mixed-effects models, and goes over different methods for statistical inference with mixed-effects models using crime data from Maryland.

Exercise 1: Linear mixed effect model- Birth rates data Exercise 2: Building a lmer model with random effects Exercise 3: Including a fixed effect Exercise 4: Random-effect slopes Exercise 5: Uncorrelated random-effect slope Exercise 6: Fixed- and random-effect predictor Exercise 7: Understanding and reporting the outputs of a lmer Exercise 8: Comparing print and summary output Exercise 9: Extracting coefficients Exercise 10: Displaying the results from a lmer model Exercise 11: Statistical inference with Maryland crime data Exercise 12: Visualizing Maryland crime data Exercise 13: Rescaling slopes Exercise 14: Null hypothesis testing Exercise 15: Controversies around P-values Exercise 16: Model comparison with ANOVA

This chapter extends linear mixed-effects models to include non-normal error terms using generalized linear mixed-effects models. By altering the model to include a non-normal error term, you are able to model more kinds of data with non-linear responses. After reviewing generalized linear models, the chapter examines binomial data and count data in the context of mixed-effects models.

Exercise 1: Crash course on GLMs Exercise 2: Logistic regression Exercise 3: Poisson Regression

Current Exercise

Exercise 4: Plotting GLMs Exercise 5: Binomial data Exercise 6: Toxicology data Exercise 7: Marketing example Exercise 8: Calculating odds-ratios Exercise 9: Count data Exercise 10: Internet click-throughs Exercise 11: Chlamydia by age-group and county Exercise 12: Displaying chlamydia results

This chapter shows how repeated-measures analysis is a special case of mixed-effect modeling. The chapter begins by reviewing paired t-tests and repeated measures ANOVA. Next, the chapter uses a linear mixed-effect model to examine sleep study data. Lastly, the chapter uses a generalized linear mixed-effect model to examine hate crime data from New York state through time.

Exercise 1: An introduction to repeated measures Exercise 2: Paired t-test Exercise 3: Repeated measures ANOVA Exercise 4: Sleep study Exercise 5: Exploring the data Exercise 6: Building models Exercise 7: Comparing regressions and ANOVAs Exercise 8: Plotting results Exercise 9: Hate in NY state?Exercise 10: Exploring NY hate data Exercise 11: Building the model Exercise 12: Interpreting model results Exercise 13: Displaying the results Exercise 14: Hierarchical models in R review Exercise 15: Conclusion