1. Do exercises 46 and 47 in the notes.

  2. The data matrix in the file mixAudio.rds consists of \(p=8\) recordings of a mixture of less than or equal to \(p\) sound sources (you can play these using the audio package in R - the sampling rate is 8000 Hz and the bitrate is 16). Do a factor analysis of these data and try to recover the latent factors:

    1. For what values of \(q\) does the Gaussian factor model have dimension less than or equal to that of the unrestricted variance model?
    2. Fit a Gaussian factor model for each value of \(q\) up to and including the maximum value in a. Use BIC to select a likely value of \(q\).
    3. Use a VARIMAX rotation to select an estimate of the latent factors.
    • Play the recovered factors. Do you think you recovered the actual factors, or some rotation?