# Multiple regression with an unbalanced grouping factor

I have a question regarding multiple regression with an unbalanced grouping factor. Essentially what I am doing is an ANCOVA, but the interaction term ends up significant (which is interesting!) so I've chosen not to call it a true ANCOVA.

# The Data

The dataset is comprised of 72 individuals who responded to many different measures for the purposes of conducting a cluster analysis to uncover relatively heterogenous subgroups within the dataset. Three clusters resulted form this analysis, where the resulting cluster sizes were n=30, n=32, and n=10. These clusters were interpreted for the purpose of a descriptive analysis.

An independent dataset describes these same 72 individuals on two separate continuous measures: score, and dv. The hope for my current project is to asses the effect of group (cluster membership, unbalanced) and score (and the interaction) on the dv.

# The Data (Example)

g1    <-rep(1,30)
g2    <-rep(2,32)
g3    <-rep(3,10)
group <-as.factor(c(g1,g2,g3))
score <-as.numeric(sample(1:10,72,replace=T))
dv    <-as.numeric(sample(1:7,72,replace=T))
data  <-data.frame(cbind(group, score, dv))

group     score       dv
1     1          9          5
2     1          3          6
3     1         10          6
4     1         10          6
5     1         10          6
6     1          4          5


# My Question

1) Can I run an analysis despite my groups being so unbalanced? If I understand correctly, by using type III SS, all groups will be weighted equally but I'm not sure if this solves my issue so simply.

For example:

lm<-lm(dv~1+score*group,data=data)
library(car)
Anova(lm,type="III)


2) If not, am I unable to proceed in some other way?

I am looking for any suggestions / guidance as I try to sort this out.

Thanks!

• Does the discussion on this Cross Validated page and the pages linked from the answer to that question help? – EdM Jun 30 '15 at 14:56