I am investigating whether particular factor models are identified. To this end, I create a population covariance matrix in R, which I subsequently analyze in Mplus.
When I specify the model that I used to generate the covariance matrix with, this (of course) results in a perfect fit. Also, the factor loadings have exactly the same value as I used when generating the matrix.
However, the factor variances and the residual variances are slightly smaller than what I used in creating the matrix (e.g., 1.996 instead of 2). When I make the sample size very large (note this is just the number in the Mplus input file; there is no actual sample, as I am analyzing the population covariance matrix), this discrepancy disappears, so I believe it has something to do with the n/(n-1) factor, but I cannot quite figure it out. Do you have any thoughts on this?