## Factor Analysis Projections

I'm working with some time series data and I'm trying to determine if using factor analysis as a clustering method will lead me to a different conclusion than PCA.

For my particular research, the way I proceed with PCA is as follows:

- I have a nxm matrix of data, where n >> m. (m being the time points)
- I perform PCA on the data using SVD.
- I take the resulting loadings matrix (which is nxp, where p is the number of pc's) and multiply its transpose by my original data, to obtain a pxm matrix of projections. I then use this projection matrix for further analysis.

I want to do this with factor analysis, but I'm not sure what the corresponding steps would be. I'm using R's factanal command to perform the factor analysis, and then using the varimax command to do the rotation. This gives me an mxf (where f is the number of factors) matrix like:

Time Factor 1 Factor 2 Factor 3
0 0.128 0.205
15 0.191 0.364 0.555
45 0.520 0.698
90 0.715 0.686 0.115
180 0.861 0.415 0.150
300 0.927 0.288
420 0.957 0.236
540 0.963 0.181

At first I thought that what factor analysis is calling its "loadings" is in fact what I want for my projections. However, I'm not so sure. I also don't understand what the missing values indicate, as there were no missing values in the original data.

Any help is appreciated.