I am very new to statistical analysis, so I apologize in advance if this question is too naïve.
I would like to know whether participants be columns in data frames for PCA, but I first want to offer some context.
I have data from 100+ participants rating 40+ stimuli using a 7-point scale. We had reasons to believe that participants differ from each other in terms of the stimuli attributes that most influenced their ratings. I will refer here to these differences as “response strategies” although participants were not necessarily conscious of those response patterns. One of my co-authors suggested we do a PCA of the ratings to help us detect different response patterns.
For each varimax-rotated component we did two things:
a. We extracted the ‘scores’ of that component for that dataset. This is a vector of length equal to the number of participants. It tells us how much each participant responses used that response strategy. Correlational analysis showed us the extent to which various participant variables were associated to that that response strategy.
b. We extracted the ‘loadings’ of that component for that dataset. This is a vector equal to the number of stimuli. It tells us how much that response strategy favours given stimuli. Correlational analysis showed us the extent to which various stimuli features were associated with that response strategy.
The patterns we found make sense. However, the variance explained and clarity of the components greatly increased if instead of arranging our original data set with participants as rows and stimuli as columns, we arranged the data set with participants as columns and stimuli as row. In that alternative arrangement, scores represent stimuli and loadings represent participants.
Every example of PCA analyzing behavioral data from participants arranges the data set with participants as rows and stimuli as columns. So, I imagine that there may be something fundamentally wrong about creating the data matrix with participants as columns. However, I have not been able to find any specific explanation about why participants should be rows and not columns.
To restate my main question: Can participants be columns in data frames for PCA? and if possible, I would also like why.
