Get p-value for group mean difference without refitting linear model with a new reference level

Question

When we have a linear model with a factor variable X (with levels A, B, and C)

y ~ factor(X) + Var2 + Var3 
<         


        

Answer 1

glht (general linear hypothesis testing) from multcomp package makes this sort of multiple hypothesis test easy without re-running a bunch of separate models. It is essentially crafting a customized contrast matrix based on your defined comparisons of interest.

Using your example comparisons and building on the data @ZheyuanLi provided:

x <- gl(3,100,labels = LETTERS[1:3])
set.seed(0)
y <- c(rnorm(100, 0), rnorm(100, 1), rnorm(100, 2)) + 0.1

fit <- lm(y ~ x)

library(multcomp)
my_ht <- glht(fit, linfct = mcp(x = c("B-A = 0",
                             "C-A = 0",
                             "C-B = 0")))

summary(my_ht) will give you the adjusted p-values for the comparisons of interest.

#Linear Hypotheses:
#           Estimate Std. Error t value Pr(>|t|)    
#B - A == 0   0.9318     0.1371   6.798 1.11e-10 ***
#C - A == 0   2.0446     0.1371  14.916  < 1e-10 ***
#C - B == 0   1.1128     0.1371   8.118  < 1e-10 ***