so... here's the situation. i'm slowly becoming more and more interested in the problem of missing data because of pervasive it is. there're usually two ways to go around it: Full Information Maximum Likelihood (FIML) and Multiple Imputation (MI). routines for both methods have been automated in Structural Equation Modelling software programs but i was hoping to use them for simpler analyses (ANOVA, regression... the tea-test )

anyway, so i'm trying to help someone who has missing data and wishes to perform a straightforward multiple regression analysis. i thought to myself "no problem. with lavaan/R i can get the EM (expectation-maximization) covariance matrix, operate on it and obtain what i want. there is a problem, though, with the standard errors.

the formula i have for the standard errors is \frac{\beta}{\sqrt{\sigma^{2}C_{jj}}} where \sigma^{2} is the variance of the residuals and C_{jj} is the diagonal element of (X'X)^{-1} associated with that particular variable.

i believe i have heard before that i cannot "naively" estimate the SEs of the regression coefficients because that underestimates the true variability due to missing data. does anyone know how to correct for it?