I'm moving into speculative mode here....
With only 9 subjects and random (i.e., unplanned) treatment sequences, I doubt that you will be able to address carryover in this study. But you certainly could plan for carryover in future experiments, while keeping in mind one of my favorite quotes from SAS-L by Ronald Crosier: "No one should ever do an experiment without analyzing it first." Crossover designs are complex, and of course we are always dealing with logistical constraints (like number of subjects). I would seek help from someone at your institution with experimental design expertise (someone on the Stat or Biostat or medical school faculty who teaches experimental design, for example).
I can think of many different models, none of which is perfect and none of which I can vouch for. Here's one example that might address something vaguely like "pseudo-carryover" (as distinct from carryover as defined for crossover designs), based on comparing the effect of a given treatment applied the first time to its effect applied the second time. The problem of course is that there are multiple possible explanations if the order effect is signficant (true carryover and/or learning and/or acclimation, etc.). (Did I say I won't vouch for this model? Yes, I did. Caveat emptor.)
proc glimmix data=new;
class trial_day trial_type order;
model log_ratio = trial_type order trial_type*order / ddfm=kr2;
random trial_day / subject=male type=<whatever> residual;
lsmeans trial_type / pdiff adjust=<something>;
lsmeans order;
lsmeans trial_type*order / plot=meanplot(join cl sliceby=trial_type);
run;
where the new dataset has 90 observations (9 males x 10 trial_days), log_ratio computed as log(post/pre) for each trial_day within each male; and order with two levels (first application of treatment, second application of treatment). <whatever> might be cs or ar(1), etc. <something> might be tukey or simulate, etc. The response log_ratio invokes a "change from baseline" approach and allows a simpler model (we get rid of lights as a factor); there are multiple ways to quantify change in the literature and log_ratio might not be your best choice. Note that trial_type x order has 10 combinations, and so it is confounded with trial_day; the model uses trial_day in the RANDOM statement to index the repeated measures in time but not as a fixed effects factor that determines the mean of the response; in this sense, this model is not like a typical crossover model because it does not have "period" explicitly as a fixed effect (which does serve to highlight that a period effect is confounded with effects due to trial_type and/or order effects).
Good luck!
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