

Eta_t, given random innovations 

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Dan Berry posted on Friday, October 13, 2017  12:25 pm



Hello. I was hoping that someone might be able to help me with the substantive interpretation of the estimated mean of the covariance between to random innovations in a DSEM. (e.g., the mean of eta_t on slide 48 of Hopkins Day 1). Specifically, I’m trying to figure out the analog of the WP residual covariance in a multilevel vector AR (per slide 27), but when the innovations are allowed to vary randomly between individuals (per slide 48). For instance, if I’ve constrained the loadings for eta_t to be positive 1 (based on theory), would this be the antilog of the mean for eta_t? If I wanted the standardized version of the mean covariance, would I antilog the (across cluster) standardized mean for et_t? Thanks in advance for any thoughts. Best, db 


1. There are two correlations residual and not residual. The full correlation average across cluster is available with the residual(cluster) output command option RESIDUAL OUTPUT ESTIMATED MODEL AVERAGE CLUSTER ESTIMATES Correlations DAYPA DAYNA DAYPA&1 DAYNA&1 ________ ________ ________ ________ DAYPA 1.000 DAYNA 0.280 1.000 2. The residual correlation has to be computed for each cluster separately and then averaged across cluster. Probably the easiest way to get it is using the stand(cluster) output option and look at the STD results for each cluster. For example STD Standardization Posterior OneTailed 95% C.I. Estimate S.D. PValue Lower 2.5% Upper 2.5% Significance COV BY DAYPA 0.070 0.169 0.000 0.045 0.775 * DAYNA 0.070 0.169 0.000 0.775 0.045 * LOGCOV  COV 1.000 0.000 0.000 1.000 1.000 LOGVARPA  DAYPA 0.049 0.165 0.000 0.035 0.729 * LOGVARNA  DAYNA 0.004 0.137 0.000 0.002 0.459 * resid correl = 0.070*0.070/(sqrt(0.004+0.070*0.070)*sqrt(0.049+0.070*0.070)) =0.22 3. While the above computation is generally ok, it is still a shortcut. The most accurate computation for the residual correlation involves saving the plausible values for each LOGVARPA, LOGVARNA and LOGCOV for each cluster. Then the residual correlation estimate would be (for each cluster computed separately) the average across plausible values of exp(LOGCOV)/ (sqrt( exp(LOGVARPA)+exp(LOGCOV))*sqrt( exp(LOGVARNA )+exp(LOGCOV))) Then this has to be further averaged across clusters. 

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