Introduction the General Linear Model (GLM) l 2 quantitative variables l 3a main effects model with no interaction l 3b interaction model l 2 categorical variables l 4a main effects model with no interaction l 4b interaction model
Common kinds of GLModels #3a 2 centered quant vars y’ = b 0 + b 1 x 1 + b 2 x 2 “X 1 ” is a centered quantitative variable X 1 X 1 – X 1mean “X 2 ” is a centered quantitative variable X 1 X 1 – X 1mean
Common kinds of GLModels #3a 2 centered quant vars y’ = b 0 + b 1 x 1 + b 2 x 2 b 0 mean of those in Cz with X=0 (mean) b 1 slope of Y-X 1 regression - slope same for all values of X 2 no interaction b 2 slope of Y-X 2 regression - slope same for all values of X 1 no interaction
y’ = b 0 + b 1 X 1 + b 2 X 2 X 2 =0 +1 std X 2 -1 std X X b 0 = ht of X 2mean line b 1 = slope of X 2mean line b 2 = htdifs among X 2 -lines X 2 -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’ = b 0 + b 1 x 1 + b 2 x 2 + b 3 xz “X 1 ” is a centered quantitative variable X 1 X 1 – X 1mean “X 2 ” is a centered quantitative variable X 1 X 1 – X 1mean “XZ” represents the interaction of “X 1 ” and”X 2 ”
Common kinds of GLModels #3a 2 centered quant vars y’ = b 0 + b 1 x 1 + b 2 x 2 + b 3 xz b 0 mean of those in Cz with X=0 (mean) b 1 slope of Y-X 1 regression - slope same for all values of X 2 no interaction b 2 slope of Y-X 2 regression - slope same for all values of X 1 no interaction b 3 how slope of Y-X 1 reg lines change with X 2 value how slope of Y-X 2 reg lines change with X 1 value
y’ = b 0 + b 1 X cen + b 2 Z cen + b 3 XZ b0b0 b1b1 -b 2 Z=0 +1 std Z -1 std Z b2b2 Z cen = Z – X mean 3b 2 quantitative predictors w/ interaction (both are standardized std = 1) X cen a = ht of Z mean line b 1 = slope of Z mean line b 2 = htdifs among Z-lines X cen = X – X mean ZX = X cen * Z cen b3b3 b3b3 b 3 = slpdifs among Z-lines