Largely I agree with him, and at times I suspected some such. E.g., just testing some software, I generated some 'random' symmetric, positive definite matrices, found the eigenvalues, and noticed that there was a big one and the sizes went down quickly. So, in linear equations, a few variables constructed from the eigenvectors of the largest few eigenvalues, can make a good approximation to all of many variables. So, factor analysis makes a good data compression technique. Can't find fault with that.
That just a few of the largest eigenvalues/vectors can explain all the data well is curious. So really he might have just used R and some Monte Carlo to show us how variance explained increases with number of factors used. I'm surprised he didn't do this.
Much or all of this has long been clear.
But what I didn't like was his drifting off into old goals of the psychologists. I couldn't figure out if he was a psychologist with an ax to grind or what. Instead, he's a statistical physicist. Curious.
The psychologists looking for 'causality' have a goal that is from tough down to impossible. We should have been concluding that. That he got off into arguing about 'causality' seemed a bit silly. I don't know all what silly stuff the psychos are trying to believe, but arguing with silly psychos is a bit silly.
But it remains: Give a test with some mental puzzle problems, and in just a linear way can explain a lot of the data with just one factor. Curious. Maybe somewhat useful. 'Causality'? Likely not if only because we know that there is a biological and neurological basis and have made no connection with that.
Then I didn't like his use of 'factors': He has some factors correlated. No: The usual approach is that, like all the eigenvectors are orthogonal, the factors are all uncorrelated. Maybe the psychos look for some uncorrelated 'factors' trying to get at some of their guesses about causality, but in this case he should have been more clear.
Finally, he wants Gaussian to justify being interested in means, variances, and covariances. Well, in the Gaussian case, sample mean and variance are 'sufficient' statistics. But even without Gaussian, means and covariances remain important, e.g., for the inner products in the Hilbert space of L^2 real random variables.
That just a few of the largest eigenvalues/vectors can explain all the data well is curious. So really he might have just used R and some Monte Carlo to show us how variance explained increases with number of factors used. I'm surprised he didn't do this.
Much or all of this has long been clear.
But what I didn't like was his drifting off into old goals of the psychologists. I couldn't figure out if he was a psychologist with an ax to grind or what. Instead, he's a statistical physicist. Curious.
The psychologists looking for 'causality' have a goal that is from tough down to impossible. We should have been concluding that. That he got off into arguing about 'causality' seemed a bit silly. I don't know all what silly stuff the psychos are trying to believe, but arguing with silly psychos is a bit silly.
But it remains: Give a test with some mental puzzle problems, and in just a linear way can explain a lot of the data with just one factor. Curious. Maybe somewhat useful. 'Causality'? Likely not if only because we know that there is a biological and neurological basis and have made no connection with that.
Then I didn't like his use of 'factors': He has some factors correlated. No: The usual approach is that, like all the eigenvectors are orthogonal, the factors are all uncorrelated. Maybe the psychos look for some uncorrelated 'factors' trying to get at some of their guesses about causality, but in this case he should have been more clear.
Finally, he wants Gaussian to justify being interested in means, variances, and covariances. Well, in the Gaussian case, sample mean and variance are 'sufficient' statistics. But even without Gaussian, means and covariances remain important, e.g., for the inner products in the Hilbert space of L^2 real random variables.