Let's say I have a dataset with 1000 observations in 10 variables, "A" through "J." I have 1000 responses/measures for each of the first 8 variables, through "H," but only the first 500 observations for "I" are not missing, and only the last 500 observations for "J" are not missing -- there are no observations for which I have measures of both of the last two variables, I and J.
Thus, if I calculate (pairwise) correlations, I have a full correlation matrix, with only the correlation between I and J missing. Let's say I want to run Principal Component Analysis, or some other such scaling procedure on this correlation matrix.
What I think I would like to do is:
- Randomly generate (perhaps from some distribution on [-1, 1], or perhaps via sampling from existing values in the rest of the correlation matrix) an "invented" correlation between I and J.
- Put that in the correlation matrix.
- Run PCA on the correlation matrix with this invented value.
- Repeat steps 1 - 3 some large number of times.
- Assess the collective results of this large number of PCAs, looking at the mean and variance of the loadings, scores, eigenvalues, etc., based on the "pseudo-bootstrapped" iterations.
- Is there a better way to handle (a) missing value(s) in the correlation matrix?
- Is there any precedent for replacing such (a) missing value(s) with random invented values? If so, what is it called?
- Is this related to the bootstrap?
Thanks a lot, in advance.
Edit: Question 4. Is this a defensible approach to imputation?