Show your boss the following :
set.seed(100)
x1 <- runif(100,0,1)
x2 <- as.factor(sample(letters[1:3],100,replace=T))
y <- x1+x1*(x2=="a")+2*(x2=="b")+rnorm(100)
summary(lm(y~x1*x2))
Which gives :
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.1525 0.3066 -0.498 0.61995
x1 1.8693 0.6045 3.092 0.00261 **
x2b 2.5149 0.4334 5.802 8.77e-08 ***
x2c 0.3089 0.4475 0.690 0.49180
x1:x2b -1.1239 0.8022 -1.401 0.16451
x1:x2c -1.0497 0.7873 -1.333 0.18566
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Now, based on the p-values you would exclude which one? x2 is most significant and most non-significant at the same time.
Edit : To clarify : This exaxmple is not the best, as indicated in the comments. The procedure in Stata and SPSS is AFAIK also not based on the p-values of the T-test on the coefficients, but on the F-test after removal of one of the variables.
I have a function that does exactly that. This is a selection on "the p-value", but not of the T-test on the coefficients or on the anova results. Well, feel free to use it if it looks useful to you.
#####################################
# Automated model selection
# Author : Joris Meys
# version : 0.2
# date : 12/01/09
#####################################
#CHANGE LOG
# 0.2 : check for empty scopevar vector
#####################################
# Function has.interaction checks whether x is part of a term in terms
# terms is a vector with names of terms from a model
has.interaction <- function(x,terms){
out <- sapply(terms,function(i){
sum(1-(strsplit(x,":")[[1]] %in% strsplit(i,":")[[1]]))==0
})
return(sum(out)>0)
}
# Function Model.select
# model is the lm object of the full model
# keep is a list of model terms to keep in the model at all times
# sig gives the significance for removal of a variable. Can be 0.1 too (see SPSS)
# verbose=T gives the F-tests, dropped var and resulting model after
model.select <- function(model,keep,sig=0.05,verbose=F){
counter=1
# check input
if(!is(model,"lm")) stop(paste(deparse(substitute(model)),"is not an lm object
"))
# calculate scope for drop1 function
terms <- attr(model$terms,"term.labels")
if(missing(keep)){ # set scopevars to all terms
scopevars <- terms
} else{ # select the scopevars if keep is used
index <- match(keep,terms)
# check if all is specified correctly
if(sum(is.na(index))>0){
novar <- keep[is.na(index)]
warning(paste(
c(novar,"cannot be found in the model",
"
These terms are ignored in the model selection."),
collapse=" "))
index <- as.vector(na.omit(index))
}
scopevars <- terms[-index]
}
# Backward model selection :
while(T){
# extract the test statistics from drop.
test <- drop1(model, scope=scopevars,test="F")
if(verbose){
cat("-------------STEP ",counter,"-------------
",
"The drop statistics :
")
print(test)
}
pval <- test[,dim(test)[2]]
names(pval) <- rownames(test)
pval <- sort(pval,decreasing=T)
if(sum(is.na(pval))>0) stop(paste("Model",
deparse(substitute(model)),"is invalid. Check if all coefficients are estimated."))
# check if all significant
if(pval[1]<sig) break # stops the loop if all remaining vars are sign.
# select var to drop
i=1
while(T){
dropvar <- names(pval)[i]
check.terms <- terms[-match(dropvar,terms)]
x <- has.interaction(dropvar,check.terms)
if(x){i=i+1;next} else {break}
} # end while(T) drop var
if(pval[i]<sig) break # stops the loop if var to remove is significant
if(verbose){
cat("
--------
Term dropped in step",counter,":",dropvar,"
--------
")
}
#update terms, scopevars and model
scopevars <- scopevars[-match(dropvar,scopevars)]
terms <- terms[-match(dropvar,terms)]
formul <- as.formula(paste(".~.-",dropvar))
model <- update(model,formul)
if(length(scopevars)==0) {
warning("All variables are thrown out of the model.
",
"No model could be specified.")
return()
}
counter=counter+1
} # end while(T) main loop
return(model)
}