lmPerm :: LMP（Y〜X * F，中心= TRUE）對LM（Y〜X * F）：非常不同的係數

Question

雖然

lmp(y~x, center=TRUE,perm="Prob") 
lm(y~x) 

給出x和y是定量變量類似的結果，

lmp(y~x*f, center=TRUE,perm="Prob") 
lm(y~x*f) 

不同，其中f是一個因素變量。

require(lmPerm) 
## Test data 
x <- 1:1000 
set.seed(1000) 
y1 <- x*2+runif(1000,-100,100) 
y1 <- y1+min(y1) 
y2 <- 0.75*y1 + abs(rnorm(1000,50,10)) 
datos <- data.frame(x =c(x,x),y=c(y1,y2),tipo=factor(c(rep("A",1000),rep("B",1000)))) 

然後如預期，

coefficients(lmp(y~x,perm="Prob",data=datos,center=FALSE)) 
# [1] "Settings: unique SS " 
# (Intercept)   x 
# -37.69542  1.74498 

coefficients(lm(y~x,data=datos)) 
# (Intercept)   x 
# -37.69542  1.74498 

但

fit.lmp <- lmp(y~x*tipo,perm="Prob",data=datos,center=FALSE) 
fit.lm <- lm(y~x*tipo, data=datos) 

coefficients(fit.lm) 
# (Intercept)   x  tipoB  x:tipoB 
# -71.1696395 1.9933827 66.9484438 -0.4968049 

coefficients(fit.lmp) 
# (Intercept)   x  tipo1  x:tipo1 
# -37.6954176 1.7449803 -33.4742219 0.2484024 

我明白係數從lm()：

coefficients(fit.lm)[1:2] # coefficients for Level A 
# (Intercept)   x 
# -71.169640 1.993383 

coefficients(fit.lm)[1:2] + coefficients(fit.lm)[3:4] # coefficients for Level B 
# (Intercept)   x 
# -4.221196 1.496578 

相當於

contrasts(datos$tipo) 
# B 
#A 0 
#B 1 
#attributes(fit.lm$qr$qr)$contrasts 
#$tipo 
#[1] "contr.treatment" 

而不是那些爲lmp()：

coefficients(fit.lmp)[1:2] + coefficients(fit.lmp)[3:4] # coefficients for Level A 
# (Intercept)   x 
# -71.169640 1.993383 

coefficients(fit.lmp)[1:2] - coefficients(fit.lmp)[3:4] # coefficients for Level B 
# (Intercept)   x 
# -4.221196 1.496578 

爲什麼？

Answer 1

lmp應用contr.sum而不是contr.treatment。您可以通過以下方式獲得相同的lm結果：

lm(y~x*tipo, data=datos, contrasts = list(tipo = "contr.sum")) 
#Coefficients: 
#(Intercept)   x  tipo1  x:tipo1 
# -37.6954  1.7450  -33.4742  0.2484