# Using Factor Analysis prior to repeated measures ANOVA

Please note, stats is NOT my area (hence why I need help!) and I may not be using the correct terminology. I hope I can explain my question clearly enough.

BACKGROUND: I have collected behavioural data from individual mice at 5 different time points. One group of mice (n=25) has been infected with a parasite that potentially changes behaviour. One group was sham infected - no parasite (n=25).

I have collected multiple behavioural measurements from each mouse at each timepoint. Some of the behavioural measures are probably correlated, so I want to use Factor Analysis to find the common factors that describe the data. I then want to get the factor scores for individuals and compare the factors scores for the treatment groups (parasite vs. no parasite) over time. This is to see whether behaviour changes over time, and whether the parasite infection has an effect on behaviour).

QUESTION: Can I pool the data from all time points for the Factor Analysis prior to repeated measures ANOVA using factor scores? The repeated measures from each animal are not independent, but I have a balanced design whereby each mouse is equally represented at each time point. My supervisor has suggested this means the lack of independence isn't a problem.

However, for the hell of it I performed a factor analysis (principal axis method) for each time point individually (n=50 for each time point). For the first two time points I get the same factor structure, however the third time point is different (the measures loading on factor 1 at time point three are the measures that loaded on factor 2 in the first two time points). This makes me think something is different about the structure of the data at this time point, and simply pooling all time points together doesn't make sense.

Can anybody recommend a better way to analyse these data? Basically I want to know whether or not behaviour changes over time, and whether infection with the parasite has an effect on behaviour (over and above the change over time).

• There must be a number of similar questions already. Have you searched factor-analysis repeated measures or PCA repeated measures? – ttnphns Oct 31 '14 at 1:00