Nested ANOVA: Correct use for colinearity problem? We have neuronal data, that we want to analyse for effects of two factors that are hierarchically structured.
The data:
We have recorded neuronal data from a neuron, where the organism received visual stimulation from 10 different spatial positions (arranged in a circle, five positions on the left and five on the right side). We have 100 stimulations for each position.
The two questions that we want to answer are:

*

*Is the neuron increasing its firing rate for stimulations from left or right (e.g. higher firing rate for left side stimulation vs. right side stimulation)

*Is the neuron increasing its firing rate for stimulations for individual positions (e.g. higher firing rate for one single position or multiple adjacent positions vs. the rest). For this question we want to test each position independently.

The problem:
The factors side (left and right side) and position (10 positions) are hierarchically structured. A individual position is only found on one side.
What we did:
We performed a nested ANOVA (Matlab anovan with 'nested'), where we defined the position (10 positions) as a factor of the factor side (left and right side).
From what I understand both factors are "fixed effects".
The question:
We are not sure, if the nested ANOVA is accounting for the colinearity of the two factors. Is this a valid use of the nested ANOVA or do we have a problem of colinearity?
I hope this question has not been answered before, I was not able to find a similar question.
I am very grateful for any answer or comment!
 A: If there are no paired correspondences among the  stimulus locations on the left and right and you are treating the locations as independent, then you could simply do your fixed-effects ANOVA on all 10 locations, then get the left-right difference by testing the difference between the 5 on the left and the 5 on the right as a contrast. ANOVA will give you a pooled estimate of within-location variance to use, along with the number of observations, to perform that test. It's possible that is how MATLAB is processing your hierarchical model, but I'm not familiar with its statistics functions.
A potential problem is your treating all 10 locations as completely separate fixed effects. With 10 locations there are 45 pairwise comparisons to perform, leading to a substantial multiple comparisons problem. Furthermore, you are omitting the information you have about systematic changes in firing rates with the locations along the circle.
Consider modeling the firing rates as a continuous function of the angles of the locations along the circle. (If the locations go fully around the circumference of the circle you could use circular statistics to deal with the wrap-around problem at an angle of 0/360 degrees.) A flexible modeling approach like regression with restricted cubic splines could allow you to estimate a smooth continuous function that describes the data.
A continuous modeling approach could give your analysis more power to demonstrate differences among the responses to the locations. It would also provide a simple way to summarize your 1000 observations per neuron in a plot of the smooth estimated function with confidence intervals.
