I am using the `statsmodel.ols` module to compute an omnibus (ANOVA) F-test for three within-subjects factors; 2\*3\*2 levels design. The Cond. No. of the omnibus test (26.2) suggests multicollinearity. My understanding is that this means the model parameters are correlated, is that a correct statement? And a follow-up, what is the appropriate remedy in this case? E.g., Non-parametric alternative or some sort of adjustment.

**Edit:** The question here concerns electrophysiological time series data for repeated measurements. I have 3 independent categorical variables (*x1, x2, x3*) with *3x2x2* levels respectively. Briefly, I have specific hypotheses about whether auditory stimulation (3 distinct types) and socioeconomic status level (low vs. high) modulate neural activity recorded at the scalp from sensor arrays over the two hemispheres (left vs. right) in the brain. 

The initial omnibus ANOVA indicated a significant interaction between factors (stimulus*ses*hemisphere), and also multicollinearity on the basis of the **Cond. No.** metric in `statsmodel.ols`. Prior to this question I was unaware of VIF, thus this question does overlap with [Multicollinearity when individual regressions are significant, but VIFs are low](https://stats.stackexchange.com/questions/24464/multicollinearity-when-individual-regressions-are-significant-but-vifs-are-low), though I am unsure about the VIFs in this case.