# Generalized Linear Models

This course will explain the theory of generalized linear models (GLM), outline the algorithms used for GLM estimation, and explain how to determine which algorithm to use for a given data analysis.

## Overview

Generalized linear models (GLMs) are used to model responses (dependent variables) that are derived in the form of counts, proportions, dichotomies (1/0), positive continuous values, and values that follow the normal Gaussian distribution. This course explains the theory of generalized linear models, outlines the algorithms used for GLM estimation, and explains how to determine which algorithm to use for a given data analysis.

• 4 Weeks
• Expert Instructor
• Tuiton-Back Guarantee
• 100% Online
• TA Support

## Learning Outcomes

Upon completing this course students will have a general overview of how to derive GLM functions and apply continuous response models, discrete response models, and panel models.

• Explain the derivation of the GLM
• Explain the statistics used to assess model fit
• Fit continuous response models like the Gaussian, log-normal and Gamma
• Fit binomial models like logit and probit
• Fit count models like Poisson and negative binomial
• Deal with overdispersion in the data

## Who Should Take This Course

Analysts in any field who need to move beyond standard multiple linear regression models for modeling their data.

If you understand GLMs, you understand linear regression, logistic regression, Poisson regression, negative binomial regression, gamma regression, multinomial regression and so many other models that are either directly included in GLMs or are simple extensions. Random effects models and generalized estimating equation (GEE) models are built on top of GLMs, so understanding GLMs is a great introduction to these advanced subjects

## Course Syllabus

### Week 1

General Overview of GLM

• Derivation of GLM functions
• GLM algorithms: OIM, EIM
• Fit and residual statistics

### Week 2

Continuous Response Models

• Gaussian
• Log-normal
• Gamma
• Log-gamma models for survival analysis
• Inverse Gaussian

### Week 3

Discrete Response Models

• Binomial models: logit, probit, cloglog, loglog, others
• Count models: Poisson, negative binomial, geometric

### Week 4

Problems with Overdispersion

• Overview of ordered and unordered logit and probit regression
• Overview of panel models

## Class Dates

### 2024

06/14/2024 to
Instructors: Dr. James Hardin

### 2025

06/13/2025 to 07/11/2025
Instructors: Dr. James Hardin

## Prerequisites

The first week of the course presents theory to support the applications covered in weeks 2-4. If you are interested only in the applications, you can skim over the material in week 1. If you wish to follow along with week 1’s development of theory, the following additional prerequisites apply:

• Calculus
• Matrix Algebra

### Private: Logistic Regression

This course will teach you logistic regression ordinary least squares (OLS) methods to model data with binary outcomes rather than directly estimating the value of the outcome, logistic regression allows you to estimate the probability of a success or failure.
• Credit Options: CEU

### Private: Matrix Algebra

This course will teach you the basics of vector and matrix algebra and operations necessary to understand multivariate statistical methods, including the notions of the matrix inverse, generalized inverse and eigenvalues and eigenvectors.
• Credit Options: CEU

## Register For This Course

Analysis of Survey Data from Complex Sample Designs

#### Homework

Homework in this course consists of short answer questions to test concepts, guided data analysis problems using software, guided data modeling problems using software, and end of course data modeling project.

In addition to assigned readings, this course also has supplemental readings available online, example software codes, and an end of course data modeling project.

#### Course Text

Generalized Linear Models and Extensions, fourth edition by James Hardin and Joseph Hilbe. When you order your copy, be sure to put ‘GLM course at Statistics.com’ in the Company/University field of the order form.

#### Software

In some lessons, you will benefit from being able to implement models in a software program that is able to do GLM (for example, Stata, SAS, S-PLUS, R). For information on obtaining a free (or nominal cost) copy of various software packages for use during the course, please read our knowledge base article “What software is used in courses?

Stata: The instructor is familiar with Stata. If you are undecided about which software to use, Stata, which is relatively easy to learn and use, is a safe choice.

R: If you want to use R with this course, you should have some prior experience and facility with it (tutorial help from the instructor or TA will be available but limited.) If you wish to use R, but no have current expertise in it, you should consider taking one of our introductory R courses before taking this one.

SAS: The TA can offer limited assistance with SAS in this course. If you want to use SAS with this course, you should have some prior experience and facility with it. If you wish to use SAS, but no have current expertise in it, you should consider taking an introductory course or courses from SAS Institute or elsewhere.

SPSS: The instructor and TA are not familiar with SPSS. If you want to use SPSS with this course, you should have some prior experience and facility with it. If you wish to use SPSS, but no have current expertise in it, you should consider taking an introductory course or courses from SPSS.

#### Literacy, Accessibility, and Dyslexia

At Statistics.com, we aim to provide a learning environment suitable for everyone. To help you get the most out of your learning experience, we have researched and tested several assistance tools. For students with dyslexia, colorblindness, or reading difficulties, we recommend the following web browser add-ons and extensions:

Chrome

Firefox

Safari

• Navidys (for colorblindness, dyslexia, and reading difficulties)
• HelperBird for Safari (for colorblindness, dyslexia, and reading difficulties)

#### Miscellaneous

The Institute gratefully acknowledges the contributions of Prof. Joseph Hilbe to the development of this course.

## Register For This Course

Analysis of Survey Data from Complex Sample Designs