生成和编码方案

Question

I have a dataframe which looks like this:

df <- data.frame(id= rep(seq(1:125),3),
  timpoint= c(rep("T1", 125), rep("T2", 125), rep("T3", 125)),
                 treatment=c(rep("A",25),rep("B",25),rep("C",25),rep("D",25),rep("E",25)))
interaction.col <- paste(df$timpoint, df$treatment, sep = "_")  

df <- cbind(df, interaction.col)

I am trying to generate a sum coding scheme for the interaction column which is a combination of the first two columns. According to this paper I should get a matrix of (a−1)×(b−1) columns and n rows(in this case 375)

I have read up on using contrasts:

 contrasts(df$interaction.col) <-  "contr.sum"
     df.c <- contrasts(df$interaction.col)

However, somehow the output is a 15x14 matrix, while it should be a 375 x8. Also, only the very last row is set to -1, which shouldn't be the case. For all the ID's of the last treatment (E) the interaction column should be set to -1 for the corresponding timepoint. The last ID in treatment group E should be -1 for all columns. What am i doing wrong here?

Answer 1

Depending on what effects you are interested in and how you will fit the model, you will end up with different number of effects. For example, in the case whereby you fit the main and interaction effects, you should end up with 8 columns for the interactions ie (a-1) x (b-1). In the case you do not fit the main effects you end up with a*b - 1:

Here is how to create your matrix:

With main effects:

model.matrix(~treatment * timpoint, df, list(treatment = contr.sum, timpoint=contr.sum))

In this case, the last 8 columns are the ones you are interested in

Without main effects:

model.matrix(~treatment:timpoint, df, list(treatment = contr.sum, timpoint=contr.sum))