L1 random effects: zero variance; non-zero covariance

[fletch1729]

I have a three level model with random affects for two dichotomous L1 variables (plus the L1 constant). I find the estimates of L1 variances / covariances puzzling. MLWin estimates the L1 variances of the two dichotomous variables as zero but gives large estimates of the L1 covariance terms. The problem does not arise at L2 and L3.
My dichotomous variables define nested subsets of the L1 individuals, so there may be insufficient information to estimate six terms in the L1 variance-covariance matrix. However, that does not help me interpret the estimates MLWin produces. Is it explained in a manual?

[ChrisCharlton]

Professor Kelvyn Jones has asked me to pass on the following response:

The issue is that categorical predictors are being allowed to vary at the same level at which they are measured. Consequently you do not have sufficient information to estimate a full quadratic variance function at level 1 You can model the level 1 variance indirectly as you have done and then get the variance of the base category directly and the variance of the contrasted category indirectly as the variance of the base plus 2 * the covariance. The variance of the contrasted category will automatically go to zero as has happened correctly in your case. The variance function window will give you the correct answer for each category. For a short guide on this see Chapter 7 of the User Manual, more discussion is given in Chapter 7 of

https://www.researchgate.net/publicatio ... o_on_RGate

which also covers the use of separate coding (two dummies and no constant for 2 categories) to get the level 1 variance for each category directly.