双向方差分析-在r中重复测量，缺少预期效果

Question

I am trying to do a two way mixed factorial ANOVA with repeated measures. From:

aov(Estimate ~ Dose*Visit, data = AUClast) 

I get 3 sums of squares: two main effects (Visit and Dose) and their interaction (Dose:Visit) which I figured out by hand are correct.

Both Dose and Visit are explanatory variables with Dose being a between subject variable with 4 levels, 3, 10, 30, 100 and Visit being a within subjects variable (repeated measure) of 2 levels, 1 and 28. Also, the subjectID variable is 'Animal'

I want to include one more effect into the result but do not know how. The desired effect is variance between Animal within Dose, or how SAS puts it Animal(Dose). The SS is calculated by:

sum((mean(Animal(ik))-mean(Dose(i))^2)

Where k is the animal of a dose i (averaging the Estimates of the observation in Visit 1 and Visit 28 for each Animal and subtracting the mean Estimate of animals in that Dose quantity squared for all Animals in this study).

Does anyone know how to adjust the formula accordingly to include the Animal(Dose) effect?

Thanks in advance for the help and sorry if all of this is too unspecific.

Answer 1

If I understand you correctly, I have a suggestion. First, a sample data set

#sample data
set.seed(15)
AUClast<-data.frame(
    expand.grid(
    Animal=1:3,
    Dose=c(3,10,30,100),
    Visit=c(1,28)
    ), Estimate=runif(24)
)

Now we calculate the interaction term as requested. First, we split the data into dosage groups, then for each does, we subtract the overall mean from the mean for each animal. Then we sum the squared of those differences. Finally, we expand them back out to does group using unsplit .

animaldose<-unsplit(lapply(split(AUClast, AUClast$Dose), function(x) {
    rep(
        sum((tapply(x$Estimate, x$Animal, mean) - mean(x$Estimate))^2)
    , nrow(x))
}), AUClast$Dose)

And we can see what that looks like next to the original data.frame

cbind(AUClast, animaldose)

Which gives the result

   Animal Dose Visit   Estimate animaldose
1       1    3     1 0.60211404  0.1181935
2       2    3     1 0.19504393  0.1181935
3       3    3     1 0.96645873  0.1181935
4       1   10     1 0.65090553  0.1641363
5       2   10     1 0.36707189  0.1641363
6       3   10     1 0.98885921  0.1641363
7       1   30     1 0.81519341  0.0419291
8       2   30     1 0.25396837  0.0419291
9       3   30     1 0.68723085  0.0419291
10      1  100     1 0.83142902  0.1881314
11      2  100     1 0.10466936  0.1881314
12      3  100     1 0.64615091  0.1881314
13      1    3    28 0.50909039  0.1181935
14      2    3    28 0.70662857  0.1181935
15      3    3    28 0.86231366  0.1181935
16      1   10    28 0.84178515  0.1641363
17      2   10    28 0.44744372  0.1641363
18      3   10    28 0.96466695  0.1641363
19      1   30    28 0.14118707  0.0419291
20      2   30    28 0.77671251  0.0419291
21      3   30    28 0.80372740  0.0419291
22      1  100    28 0.79334595  0.1881314
23      2  100    28 0.35756312  0.1881314
24      3  100    28 0.05800106  0.1881314

So you can see each does group has it's own adjustment.