Analyzing similarity scores between subjects

Hi all,

I have a modeling problem involving similarity scores between subjects.
During 4 time points in my experiment, I sampled eye movements of my
subjects. At each time point, subjects had either one of two different
states, Y or N. I have no control of the state, it is purely observational.
My data produces 4 similarity matrices - for each sampling, every subject
was compared to every other subject on some similarity measure of eye
movements (self-comparisons excluded). Each matrix contains three types of
comparison: N-N, N-Y, and Y-Y. My hypothesis is that the eye movements of
those in state N were more similar to each other, compared to N-Y, or Y-Y.
So N-N > N-Y or Y-Y.

I came up with a model like this:

lmer(dist ~ type + (1|sub_i) + (1|sub_i:type) + (1|segment) +
(1|segment:type) + (1|sub_i: segment) + (1|sub_i: segment:type), data,
REML=F)

where dist is the similarity score, type is a 3-level factor (n-n, n-y,
y-y), sub_i is subject ID, segment is sample ID. I was
trying to build a model with a "maximal" random structure.

Have I correctly specified my model? I have two concerns:
(1) because any given data point in the matrix belongs to two subjects, i
and j, should I include random effects for both subject i and subject j?

(2) Becuase each matrix is symmetrical, I am duplicating my data in the
above model. Should I use only the unique pairwise comparisons and do
something like this:

lmer(dist ~ type + (1|segment) + (1|segment:type), half_data, REML=F)

Thanks!

Han Zhang
Graduate Student
Combined Program in Education and Psychology
University of Michigan, Ann Arbor
Email: hanzh at umich.edu
Phone: 1-734-680-6031

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