The above process yielded a baseline and response measure for each of the 22 phenotypes in each session (placebo, 10 mg, and 20 mg). Next we sought to combine information across sessions and phenotypes to yield a small number of phenotypes that efficiently captured the primary patterns in the whole data; this process is commonly referred to as dimension reduction. Combining data across correlated measurements reduces environmental noise and measurement error. We chose to perform dimension reduction using sparse factor analysis (SFA) [31], which is a variant of factor analysis that attempts to improve interpretability of factors (summary measures) by encouraging each factor to be a summary of a small subset of all data points. Because SFA is based on a normal model, we transformed each baseline and response measure to follow the standard normal distribution (using a quantile-quantile transformation) and applied SFA to these transformed data. After experimenting with different numbers of factors we chose eleven factors as providing the most reproducible and interpretable results, yielding an 11 by 381 matrix of measurements. Of the 11 factors identified, one
