Linear Regression Module III: Deep Dive
[Pages:26]Linear Regression Module III: Deep Dive
Dr. Mark Williamson DaCCoTA
University of North Dakota
Introduction
? Previously:
? Covered a broad overview ? Looked at more detail ? Ran through examples
? This time: looked at more advanced linear regression methods
? Generalized Linear Mixed Model ? Longitudinal Analysis ? Structural Equation Modeling
Reviewing the Basics
? Linear regression: modeling the relationship between a response variable and one or more predictor variables
? Structure->simple, multiple, multivariate ? Predictor variables->polynomial, fixed/random, nested ? Response variables->Gaussian, Logistic, Poisson, etc. ? Other considerations
? Process of ordinary least squares ? Need to consider assumptions and model fit ? Lots of ways to run a regression
Topics Covered
? Generalized Linear Mixed Model
? Software: SAS Studio
? Longitudinal Analysis
? Software: R
? Structural Equation Modeling
? Software: STATA
Generalized Linear Mixed Models
Descriptions
4
? A Generalized Linear Mixed Model is combination of a Generalized Linear Model and a Linear Mixed Model
? Generalized -> accommodates non-normal distributions
? Mixed -> allows for random effects
2
0
-2
-4
-4
-2
0
2
4
identity link
? Key differences in generalized linear mixed model and linear model:
? Method of estimation: Ordinary Least Squares vs. Maximum Likelihood (iteratively maximize likelihood of parameters given data)
? Distributions: Normal distribution vs. Others ? Model scale: GLMMs link expected values to
model scale with link
? Random Intercepts/ Random Slopes:
150
125
100
75
50
25
0
-4
-2
0
2
4
log-link
Measurement Count
Proportion
1.0
0.8
0.6
0.4
0.2
0.0
-4
-2
0
2
4
logit-link
Generalized Linear Mixed Models
Formats
Basic (Random Intercepts): PROC GLIMMIX data=dataset;
class TREATMENT RANDOM; model RESPONSE= TREATMENT; random intercept /subject=RANDOM; PROC GLIMMIX data=dataset; class RANDOM; model RESPONSE= TREATMENT; random intercept /subject=RANDOM; PROC GLIMMIX data=dataset; class RANDOM; model RESPONSE= TREATMENT; random RANDOM;
Nested: PROC GLIMMIX data=dataset;
class TEACHINGSTYLE STATE SCHOOL; model RESPONSE = TEACHINGSTYLE; random STATE SCHOOL(STATE);
Random Effects Only; PROC GLIMMIX data=dataset;
class TREE BRANCH LEAF; model RESPONSE = ; random TREE BRANCH(TREE) LEAF(BRANCH TREE);
Random Slopes: PROC GLIMMIX data=dataset;
class RANDOM; model RESPONSE = TREATMENT; random intercept TREATMENT/subject=RANDOM;
Generalized Linear Mixed Models
Examples
Multicenter1 NPK RC2 Wings
1 edings/sugi30/196-30.pdf 2
Generalized Linear Mixed Models
Examples
Multicenter1 NPK RC2 Wings
1 edings/sugi30/196-30.pdf 2
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