Multi-way interaction: easy way to get numerical coefficient estimates?

问题

Let's say there's a 4-way interaction, with a 2x2x2 factorial design plus a continuous variable. Factors have the default contrast coding (contr.treatment). Here's an example:

set.seed(1)

cat1 <- as.factor(sample(letters[1:2], 1000, replace = TRUE))
cat2 <- as.factor(sample(letters[3:4], 1000, replace = TRUE))
cat3 <- as.factor(sample(letters[5:6], 1000, replace = TRUE))
cont1 <- rnorm(1000)
resp <- rnorm(1000)
df <- data.frame(cat1, cat2, cat3, cont1, resp)

mod <- lm(resp ~ cont1 * cat1 * cat2 * cat3, data = df)

Looking at the output of coef(mod), we get something like:

        (Intercept)                   cont1                   cat1b 
        0.019822407             0.011990238             0.207604677 
              cat2d                   cat3f             cont1:cat1b 
       -0.010132897             0.105397591            -0.001153867 
        cont1:cat2d             cat1b:cat2d             cont1:cat3f 
        0.023358901            -0.194991402             0.060960695 
        cat1b:cat3f             cat2d:cat3f       cont1:cat1b:cat2d 
       -0.240624582            -0.117278931            -0.069880751 
  cont1:cat1b:cat3f       cont1:cat2d:cat3f       cat1b:cat2d:cat3f 
       -0.120446848            -0.141688864             0.136945262 
cont1:cat1b:cat2d:cat3f 
        0.201792298

And to get the estimated intercept for cat1b (for example), we would add our implicit (Intercept) term and cat1b, i.e. coef(mod)[1] + coef(mod)[3]. To get the change in slope for the same category, we would use coef(mod)[2] + coef(mod)[6], a la this r-bloggers post. It gets pretty tedious to write all of them out, and methods(class="lm") doesn't look like it has any functions that do this right out of the gate.

Is there some obvious way to get numerical estimates for the intercept and slope for each combination of factors?

回答1:

You're looking for the lsmeans package. Check it out:

lstrends(mod, specs = c('cat1', 'cat2', 'cat3'), var = 'cont1')

cat1 cat2 cat3 cont1.trend         SE  df    lower.CL  upper.CL
 a    c    e     0.01199024 0.08441129 984 -0.15365660 0.1776371
 b    c    e     0.01083637 0.08374605 984 -0.15350502 0.1751778
 a    d    e     0.03534914 0.09077290 984 -0.14278157 0.2134799
 b    d    e    -0.03568548 0.09644117 984 -0.22493948 0.1535685
 a    c    f     0.07295093 0.08405090 984 -0.09198868 0.2378905
 b    c    f    -0.04864978 0.09458902 984 -0.23426916 0.1369696
 a    d    f    -0.04537903 0.09363128 984 -0.22911897 0.1383609
 b    d    f    -0.03506820 0.08905581 984 -0.20982934 0.1396929

来源：https://stackoverflow.com/questions/28350573/multi-way-interaction-easy-way-to-get-numerical-coefficient-estimates

标签

glm