Find online courses made by experts from around the world.
Take your courses with you and learn anywhere, anytime.
Learn and practice realworld skills and achieve your goals.
Linear Regression, GLMs and GAMs with R demonstrates how to use R to extend the basic assumptions and constraints of linear regression to specify, model, and interpret the results of generalized linear (GLMs) and generalized additive (GAMs) models. The course demonstrates the estimation of GLMs and GAMs by working through a series of practical examples from the book Generalized Additive Models: An Introduction with R by Simon N. Wood (Chapman & Hall/CRC Texts in Statistical Science, 2006). Linear statistical models have a univariate response modeled as a linear function of predictor variables and a zero mean random error term. The assumption of linearity is a critical (and limiting) characteristic. Generalized linear models (GLMs) relax this assumption of linearity. They permit the expected value of the response variable to be a smoothed (e.g. nonlinear) monotonic function of the linear predictors. GLMs also relax the assumption that the response variable is normally distributed by allowing for many distributions (e.g. normal, poisson, binomial, loglinear, etc.). Generalized additive models (GAMs) are extensions of GLMs. GAMs allow for the estimation of regression coefficients that take the form of nonparametric smoothers. Nonparametric smoothers like lowess (locally weighted scatterplot smoothing) fit a smooth curve to data using localized subsets of the data. This course provides an overview of modeling GLMs and GAMs using R. GLMs, and especially GAMs, have evolved into standard statistical methodologies of considerable flexibility. The course addresses recent approaches to modeling, estimating and interpreting GAMs. The focus of the course is on modeling and interpreting GLMs and especially GAMs with R. Use of the freely available R software illustrates the practicalities of linear, generalized linear, and generalized additive models.
Not for you? No problem.
30 day money back guarantee.
Forever yours.
Lifetime access.
Learn on the go.
Desktop, iOS and Android.
Get rewarded.
Certificate of completion.
Section 1: Introduction to Course and to Linear Modeling  

Lecture 1 
Introduction to Course
Preview

01:51  
Lecture 2 
Preliminaries: Installing R, RStudio, R Commander, Course Materials and Exercise
Preview

05:16  
Lecture 3 
Beginning Agenda (slides)
Preview

08:18  
Lecture 4  05:11  
The term "linear" refers to the fact that we are fitting a line. The term model refers to the equation that summarizes the line that we fit. The term "linear model" is often taken as synonymous with linear regression model. 

Lecture 5  06:08  
Assumptions of Linear Models (regression):


Lecture 6 
Desirable Properties of Betahat (slides, part 3)

07:19  
Lecture 7 
Example: Estimate Age of Universe (slides)

04:39  
Lecture 8 
Example: Estimate Age of Universe Live in R (part 1)

07:44  
Lecture 9 
Example: Estimate Age of Universe Live in R (part 2)
Preview

09:22  
Lecture 10 
Example: Estimating Age of the Universe (part 3)

08:50  
Lecture 11 
Finish Example and More Notes on Linear Modeling

08:31  
Lecture 12 
Linear Modeling Exercises

01:48  
Section 2: Generalized Linear Models (GLMs) Part 1  
Lecture 13  06:58  
In statistics, the generalized linear model (GLM) is a flexible generalization of ordinary linear regression that allows for response variables that have error distribution models other than a normal distribution. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. 

Lecture 14 
Introduction to GLMs (slides, part 2)

07:29  
Lecture 15 
Introduction to GLMs (slides, part 3)

07:50  
Lecture 16 
Introduction to GLMs (slides, part 4)

06:44  
Lecture 17  07:50  
Proportion data has values that fall between zero and one. Naturally, it would be nice to have the predicted values also fall between zero and one. One way to accomplish this is to use a generalized linear model (glm) with a logit link and the binomial family. 

Lecture 18 
Example: Binomial (Proportion) Model with Heart Disease (part 2)

07:26  
Lecture 19 
Example: Binomial (Proportion) Model with Heart Disease (part 3)

08:16  
Lecture 20 
Example: Binomial (Proportion) Model with Heart Disease (part 4)
Preview

06:22  
Lecture 21 
GLM Exercises

01:05  
Section 3: Generalized Linear Models Part 2  
Lecture 22 
Current Agenda

01:46  
Lecture 23 
Linear Regression Exercise Solutions (part 1)

07:31  
Lecture 24 
Linear Regression Exercise Solutions (part 2)

07:29  
Lecture 25 
GLM Exercise Solutions (part 3)

09:30  
Lecture 26  08:15  
In statistics, Poisson regression is a form of regression analysis used to model count data and contingency tables. Poisson regression assumes the response variable Y has a Poisson distribution, and assumes the logarithm of its expected value can be modeled by a linear combination of unknown parameters. A Poisson regression model is sometimes known as a loglinear model, especially when used to model contingency tables. Poisson regression models are generalized linear models with the logarithm as the (canonical) link function, and the Poisson distribution function as the assumed probability distribution of the response. 

Lecture 27 
Example: Poisson Model with Count Data (part 2)

09:29  
Lecture 28 
Example: Binary Response Variable (part 1)
Preview

04:43  
Lecture 29 
Example: Binary Response Variable (part 2)
Preview

06:12  
Lecture 30 
Exercise: GLM to GAM

01:40  
Lecture 31  05:55  
Loglinear analysis is a technique used in statistics to examine the relationship between more than two categorical variables. 

Lecture 32 
More on Deviance and Overdispersion (slides)

03:11  
Section 4: Generalized Additive Models Explained  
Lecture 33  07:41  
In statistics, a generalized additive model (GAM) is a generalized linear model in which the linear predictor depends linearly on unknown smooth functions of some predictor variables, and interest focuses on inference about these smooth functions. GAMs were originally developed by Trevor Hastie and Robert Tibshirani to blend properties of generalized linear models with additive models. 

Lecture 34 
What are GAMs? (Crawley, slides, part 2)

06:02  
Lecture 35 
Demonstrate GAM Ozone Data (part 1)

09:40  
Lecture 36 
Demonstrate GAM Ozone Data (part 2)

09:42  
Lecture 37 
General Approaches for Fitting GAMs (slides)
Preview

02:44  
Lecture 38 
What are GAMs? (Wood, slides, part 1)

11:34  
Lecture 39 
Univariate Polynomial GAMs (Wood, slides, part 2)

07:27  
Lecture 40 
Univariate Polynomial GAMs (Wood, slides, part 3)

05:52  
Lecture 41 
GAMs as 4th Order Polynomials (slides, part 1)

06:21  
Lecture 42 
GAMs as 4th Order Polynomials (slides, part 2)

04:29  
Lecture 43 
GAMs as Regression Splines (slides)

03:38  
Lecture 44 
Cubic Splines (slides, part 1)

08:45  
Lecture 45 
Cubic Splines (slides, part 2)

04:21  
Lecture 46 
Function to Establish Basis for Spline (slides)

07:33  
Lecture 47 
BuildaGAM (slides, part 1)

07:46  
Lecture 48 
BuildaGAM (slides, part 2)

10:16  
Lecture 49 
BuildaGAM (slides, part 3)

06:17  
Lecture 50 
BuildaGAM Demonstration in R Script
Preview

11:34  
Lecture 51 
BuildaGAM Cross Validation

08:13  
Lecture 52 
Bivariate GAMs with 2 Explanatory Independent Variables (slides, part 1)

09:17  
Lecture 53 
Bivariate GAMs with 2 Explanatory Independent Variables (slides, part 2)

07:31  
Lecture 54 
Exercises

01:33  
Section 5: Detailed GAM Examples  
Lecture 55 
Current Agenda (slides)

05:23  
Lecture 56 
Cherry Trees and Finer Control (slides, part 1)

08:10  
Lecture 57 
Finer Control of GAM (slides, part 2)

10:52  
Lecture 58 
Using Smoothers with More than One Predictor (slides)

07:04  
Lecture 59 
More on Alternative Smoothing Bases (slides)

08:06  
Lecture 60 
Parametric Model Terms (slides)

08:29  
Lecture 61 
Example: Brain Imaging (part 1)
Preview

07:51  
Lecture 62 
Example: Brain Imaging (part 2)

08:09  
Lecture 63 
Example: Brain Imaging (part 3)

07:38  
Lecture 64 
Example: Brain Imaging (part 4)

07:03  
Lecture 65 
Example: Brain Imaging (part 5)

07:41  
Lecture 66 
Example: Air Pollution in Chicago (part 1)

09:33  
Lecture 67 
Example: Air Pollution in Chicago (part 2)

09:17  
Lecture 68 
Air Pollution in Chicago (part 3)

04:40  
Lecture 69 
More Exercises

05:41 
Dr. Geoffrey Hubona held fulltime tenuretrack, and tenured, assistant and associate professor faculty positions at 3 major state universities in the Eastern United States from 19932010. In these positions, he taught dozens of various statistics, business information systems, and computer science courses to undergraduate, master's and Ph.D. students. He earned a Ph.D. in Business Administration (Information Systems and Computer Science) from the University of South Florida (USF) in Tampa, FL (1993); an MA in Economics (1990), also from USF; an MBA in Finance (1979) from George Mason University in Fairfax, VA; and a BA in Psychology (1972) from the University of Virginia in Charlottesville, VA. He was a fulltime assistant professor at the University of Maryland Baltimore County (19931996) in Catonsville, MD; a tenured associate professor in the department of Information Systems in the Business College at Virginia Commonwealth University (19962001) in Richmond, VA; and an associate professor in the CIS department of the Robinson College of Business at Georgia State University (20012010). He is the founder of the Georgia R School (20102014) and of RCourseware (2014Present), online educational organizations that teach research methods and quantitative analysis techniques. These research methods techniques include linear and nonlinear modeling, multivariate methods, data mining, programming and simulation, and structural equation modeling and partial least squares (PLS) path modeling. Dr. Hubona is an expert of the analytical, opensource R software suite and of various PLS path modeling software packages, including SmartPLS. He has published dozens of research articles that explain and use these techniques for the analysis of data, and, with software codevelopment partner Dean Lim, has created a popular cloudbased PLS software application, PLSGUI.