Generalized linear model as non-parametric ANCOVA vs. modern robust methods and non-parametric equivalant of ANCOVA

I am a medical student and I'm a rookie in the field of statistics but I was searching and digging for a long time to do a simple (for most of people involved in the field) analysis all by myself, and I'm exhausted so please help me on this. I have a data of subcortical structure volumes for three different groups, the goal is to compare between these three groups while controlling for intracranial volume and age, but several of these subcortical structures exhibit non normality or heteroscedastic variances across the three groups (significant Levene's test at 0.02). Moreover, my data is unbalanced in terms of group size (n1=35, n2=30, n3=24).

Since all of the resources I've looked say that violation of assumptions is negligible where groups are not unbalanced, I started to transform the data which did nothing. Then I looked for a non-parametric ANCOVA (e.g., the one in Wilcox 2005, or Quade 1967, Rank analysis of covariance). However, I'm not familiar with R and in SPSS I have to use R plug-in to be able to use a robust ANCOVA, and unfortunately I'm short of time to learn R. I know that GZLM is a semi-parametric test and it is available in SPSS.

Now I have 2 questions:

1. Am I being too conservative and should I just ignore violation of model assumptions because imbalance is not substantial?
2. Is it ok to run a GZLM to overcome these violations, or should I use robust methods described by Wilcox and others?
• I'm missing the relevance of unequal group sizes. As to your question, the proportional odds model is a semiparametric rank-based regression model that generalizes Wilcoxon-Mann-Whitney-Kruskal-Wallis. I'd recommend this model for your situation, based on what you wrote. – Frank Harrell Dec 29 '12 at 0:41
• @FrankHarrell: thank you for your suggestion, I should probably study this model too. About the unequal group sizes, I have seen, in all the resources that I've studied, that ANCOVA is robust to violation of the assumptions when group sizes are equal. but Later on I have found that If the Assumption of Homogeneity of Variance had not be met(found significant)–this is not a major problem if the cell sizes are equal (i.e., the largest group size is not more than 1½ times greater than the smallest group size)(Leech, Barrett, & Morgan, 2005). this solves my current problem. – Sadjjad Riyahi Feb 11 '13 at 10:09
• I didn't realize that. The prop. odds model has fewer assumptions though. – Frank Harrell Feb 11 '13 at 14:54