问题
I have measurements obtained from 2 groups where each group has the same 3 levels.
Here's my example data.frame:
df <- data.frame(measurement = c(rnorm(10,1,1),rnorm(10,0.75,1),rnorm(10,1.25,1),
rnorm(10,0.5,1),rnorm(10,1.75,1),rnorm(10,0.25,1)),
group = as.factor(c(rep("a",30),rep("b",30))),
level = as.factor(rep(c(rep("x",10),rep("y",10),rep("z",10)),2)))
I'm interested in quantifying how measurement in each level is affected by group.
I guess a linear model (lm) is the appropriate approach for this, where the group:level interaction terms capture the effects I'm interested in.
Is there a way to specify an lm that will only compute these interaction terms: groupb:levelx, groupb:levely, and groupb:levelz? I believe this tells me how each level is affected by group "b" (relative to group "a"), which I think is what I'm interested in.
The closest I got is:
lm(measurement ~ 0 + group * level - group, data = df)
But that still computes the effects of levelx, levely, and levelz, which I'm not interested in.
回答1:
As @Lyzander mentioned above you should clarify a bit more what you want. Based on what you said "how measurement is affected by group "b" (relative to group "a") for each level", I guess there are 3 simple ways to do that.
df <- data.frame(measurement = c(rnorm(10,1,1),rnorm(10,0.75,1),rnorm(10,1.25,1),
rnorm(10,0.5,1),rnorm(10,1.75,1),rnorm(10,0.25,1)),
group = as.factor(c(rep("a",30),rep("b",30))),
level = as.factor(rep(c(rep("x",10),rep("y",10),rep("z",10)),2)))
library(dplyr)
#### calculate stats (mean values) ---------------------------------------------
df %>% group_by(level, group) %>% summarise(MeanMeasurement = mean(measurement))
# level group MeanMeasurement
# (fctr) (fctr) (dbl)
# 1 x a 1.6708659
# 2 x b 0.8487751
# 3 y a 0.7977769
# 4 y b 1.4209206
# 5 z a 1.5484668
# 6 z b -0.3244225
#### build a model for each level ---------------------------------------------
summary(lm(measurement ~ group , data = df[df$level=="x",]))
# Coefficients:
# Estimate Std. Error t value Pr(>|t|)
# (Intercept) 1.6709 0.3174 5.264 5.27e-05 ***
# groupb -0.8221 0.4489 -1.831 0.0837 .
summary(lm(measurement ~ group , data = df[df$level=="y",]))
# Coefficients:
# Estimate Std. Error t value Pr(>|t|)
# (Intercept) 0.7978 0.2565 3.111 0.00604 **
# groupb 0.6231 0.3627 1.718 0.10295
summary(lm(measurement ~ group , data = df[df$level=="z",]))
# Coefficients:
# Estimate Std. Error t value Pr(>|t|)
# (Intercept) 1.5485 0.3549 4.363 0.000375 ***
# groupb -1.8729 0.5019 -3.731 0.001528 **
## build a model only with interactions ------------------------------------------
summary(lm(measurement ~ group : level , data = df))
# Coefficients: (1 not defined because of singularities)
# Estimate Std. Error t value Pr(>|t|)
# (Intercept) -0.3244 0.3123 -1.039 0.303452
# groupa:levelx 1.9953 0.4416 4.518 3.43e-05 ***
# groupb:levelx 1.1732 0.4416 2.657 0.010354 *
# groupa:levely 1.1222 0.4416 2.541 0.013951 *
# groupb:levely 1.7453 0.4416 3.952 0.000227 ***
# groupa:levelz 1.8729 0.4416 4.241 8.76e-05 ***
# groupb:levelz NA NA NA NA
If you check the stats (1st approach) and the models' coefficients you'll see that all those 3 approaches agree with each other.
I'd go with the 2nd approach as it is the only one that gives you info about whether a difference of group (a vs b) within a level is statistically significant or not. 1st approach just reports means. 3rd approach includes p values but they correspond to comparisons with a baseline interaction value and not to comparisons between groups a and b.
You mentioned "ONLY compute these interaction terms: groupb:levelx, groupb:levely, and groupb:levelz" which means that you won't get the other 3 interactions of a and x,y,z. In other words you force your model to include those 3 interactions.
You can do that manually like this
df <- data.frame(measurement = c(rnorm(10,1,1),rnorm(10,0.75,1),rnorm(10,1.25,1),
rnorm(10,0.5,1),rnorm(10,1.75,1),rnorm(10,0.25,1)),
group = as.factor(c(rep("a",30),rep("b",30))),
level = as.factor(rep(c(rep("x",10),rep("y",10),rep("z",10)),2)))
library(dplyr)
df %>%
mutate(interactions = paste0(group,":",level),
interactions = ifelse(group=="a","a",interactions)) -> df2
summary(lm(measurement ~ interactions, data = df2))
# Coefficients:
# Estimate Std. Error t value Pr(>|t|)
# (Intercept) 0.9318 0.1831 5.089 4.36e-06 ***
# interactionsb:x -0.7803 0.3662 -2.131 0.03752 *
# interactionsb:y 0.2747 0.3662 0.750 0.45638
# interactionsb:z -1.1367 0.3662 -3.104 0.00299 **
but now the other 3 interactions are combined and every time you compare each one of your 3 interactions (b:x, b:y, b:z) with the general group a. You don't compare a vs. b within x,y and z but you compare x vs. y vs. z within group b.
回答2:
Based on this sentence: "Is there a way to specify an lm that will only compute these interaction terms: groupb:levelx, groupb:levely, and groupb:levelz?", I think you just want:
lm( measurement ~ level +0, subset = group=="b", data = df)
来源：https://stackoverflow.com/questions/33527089/how-to-specify-lm-model-matrix