## Question1: How to define IV with interaction alone, without main effects? ## Question2: Should Type III ANOVA in package car be independent of the factor level order?
## data from http://www.otago.ac.nz/sas/stat/chap30/sect52.htm drug <- c(t(t(rep(1,3)))%*%t(1:4)); disease <- c(t(t(1:3)) %*% t(rep(1,4))); y <- t(matrix(c( 42 ,44 ,36 ,13 ,19 ,22 ,33 ,NA ,26 ,NA ,33 ,21 ,31 ,-3 ,NA ,25 ,25 ,24 ,28 ,NA ,23 ,34 ,42 ,13 ,NA ,34 ,33 ,31 ,NA ,36 ,3 ,26 ,28 ,32 ,4 ,16 ,NA ,NA ,1 ,29 ,NA ,19 ,NA ,11 ,9 ,7 ,1 ,-6 ,21 ,1 ,NA ,9 ,3 ,NA ,24 ,NA ,9 ,22 ,-2 ,15 ,27 ,12 ,12 ,-5 ,16 ,15 ,22 ,7 ,25 ,5 ,12 ,NA ),nrow=6)); ## verify data with http://www.otago.ac.nz/sas/stat/chap30/sect52.htm (cbind(drug,disease,y)); ## make a big table drug <- as.factor(rep(drug,6)); disease <- as.factor(rep(disease,6)); y <- c(y); ## verify data through type I ANOVA to http://www.otago.ac.nz/sas/stat/chap30/sect52.htm anova(lm(y~drug*disease)); require(car); ## Type III ANOVA in package car is not Type III ANOVA in SAS Anova(lm(y~drug*disease),type='III'); ## Type III ANOVA in package car equates to wishful ## "anova(lm(y~INTERACTION +disease),lm(y~drug*disease))" ## However in R, df of lm(y~drug:disease) is automatically df of lm(y~drug*disease) ## How to define IV with interaction alone, without main effects? ## Verify type III of package car to be (INTERACTION + disease) vs. (disease*drug) ## However at the 3rd row, replace the maximun levels(drug==4, disease=3) with the minimum levels (==1). rbind(Anova(lm(y~drug*disease),type='III')$'Sum Sq'[2:4] , c( anova( lm(y~ 1 + ( I((drug==2)&(disease==2)) + I((drug==3)&(disease==2)) + I((drug==4)&(disease==2)) + I((drug==2)&(disease==3)) + I((drug==3)&(disease==3)) + I((drug==4)&(disease==3)) ) + ( I(disease==2) + I(disease==3))) ,lm(y~drug*disease))$'Sum of Sq'[2] , anova( lm(y~ 1 + ( I((drug==2)&(disease==2)) + I((drug==3)&(disease==2)) + I((drug==4)&(disease==2)) + I((drug==2)&(disease==3)) + I((drug==3)&(disease==3)) + I((drug==4)&(disease==3)) ) + ( I(drug==2) + I(drug==3) + I(drug==4))) ,lm(y~drug*disease))$'Sum of Sq'[2] , anova(lm(y~drug+disease),lm(y~drug*disease))$'Sum of Sq'[2] ) , c( anova( lm(y~ 1 + ( I((drug==2)&(disease==2)) + I((drug==3)&(disease==2)) + I((drug==1)&(disease==2)) + I((drug==2)&(disease==1)) + I((drug==3)&(disease==1)) + I((drug==1)&(disease==1)) ) + ( I(disease==2) + I(disease==1))) ,lm(y~drug*disease))$'Sum of Sq'[2] , anova( lm(y~ 1 + ( I((drug==2)&(disease==2)) + I((drug==3)&(disease==2)) + I((drug==1)&(disease==2)) + I((drug==2)&(disease==1)) + I((drug==3)&(disease==1)) + I((drug==1)&(disease==1)) ) + ( I(drug==2) + I(drug==3) + I(drug==1))) ,lm(y~drug*disease))$'Sum of Sq'[2] , anova(lm(y~drug+disease),lm(y~drug*disease))$'Sum of Sq'[2] ) ) ## I don't know whether the problem is in anova(lm1,lm2) or lm, or Anova ## while type II is independent of level order -- rbind(Anova(lm(y~drug*disease),type='II')$'Sum Sq'[1:3] , c( anova( lm(y~ 1+disease) ,lm(y~ 1 + ( I(drug==2) + I(drug==3) + I(drug==4) ) + ( I(disease==2) + I(disease==3))) ,lm(y~drug*disease))$'Sum of Sq'[2] , anova( lm(y~ 1+drug) ,lm(y~ 1 + ( I(drug==2) + I(drug==3) + I(drug==4) ) + ( I(disease==2) + I(disease==3))) ,lm(y~drug*disease))$'Sum of Sq'[2] , anova(lm(y~drug+disease),lm(y~drug*disease))$'Sum of Sq'[2] ) , c( anova( lm(y~ 1+disease) ,lm(y~ 1 + ( I(drug==2) + I(drug==3) + I(drug==1) ) + ( I(disease==2) + I(disease==1))) ,lm(y~drug*disease))$'Sum of Sq'[2] , anova( lm(y~ 1+drug) ,lm(y~ 1 + ( I(drug==2) + I(drug==3) + I(drug==1) ) + ( I(disease==2) + I(disease==1))) ,lm(y~drug*disease))$'Sum of Sq'[2] , anova(lm(y~drug+disease),lm(y~drug*disease))$'Sum of Sq'[2] ) ) ## LI, Xiaoxu ## School of Humanities & Social Sciences, Shenzhen Graduate School of Peking Univ. ## http://lixiaoxu.lxxm.com/ ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
