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Introduction the General Linear Model (GLM)
2 quantitative variables 3a main effects model with no interaction 3b interaction model
2 categorical variables 4a main effects model with no interaction 4b interaction model
Common kinds of GLModels
#3a 2 centered quant vars
y’ = b0 + b1x1 + b2x2
“X1” is a centered quantitative variable
X1 X1 – X1mean
“X2” is a centered quantitative variable
X1 X1 – X1mean
Common kinds of GLModels
#3a 2 centered quant vars
y’ = b0 + b1x1 + b2x2
b0 mean of those in Cz with X=0 (mean)
b1 slope of Y-X1 regression
- slope same for all values of X2 no interaction
b2 slope of Y-X2 regression
- slope same for all values of X1 no interaction
0 1
0
20
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4
0
50
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y’ = b0 + b1X1 + b2X2
X2=0
+1std X2
-1std X2
-2 -1 0 1 2 X
b0 = ht of X2mean line
b1 = slope of X2mean line
b2 = htdifs among X2-lines
X2-lines all have same slp(no interaction)
3a Xs are centered quant variables (both are standardized std = 1)
Common kinds of GLModels #3b 2 centered quant var & their product term/interaction
y’ = b0 + b1x1 + b2x2 + b3xz
“X1” is a centered quantitative variable
X1 X1 – X1mean
“X2” is a centered quantitative variable
X1 X1 – X1mean
“XZ” represents the interaction of “X1” and”X2”
Common kinds of GLModels
#3a 2 centered quant vars
y’ = b0 + b1x1 + b2x2 + b3xz
b0 mean of those in Cz with X=0 (mean)
b1 slope of Y-X1 regression
- slope same for all values of X2 no interaction
b2 slope of Y-X2 regression
- slope same for all values of X1 no interaction
b3 how slope of Y-X1 reg lines change with X2 value
how slope of Y-X2 reg lines change with X1 value
0 1
0
20
30
4
0
50
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y’ = b0 + b1Xcen + b2Zcen + b3XZ
b0
b1
-b2Z=0+1std Z
-1std Z
b2
Zcen = Z – Xmean
3b 2 quantitative predictors w/ interaction (both are standardized std = 1)
-2 -1 0 1 2 Xcen
a = ht of Zmean line
b1 = slope of Zmean line
b2 = htdifs among Z-lines
Xcen = X – Xmean ZX = Xcen * Zcen
b3
b3 b3 = slpdifs among Z-lines
