Let’s imagine a relatively simple model where this might be useful. We have five responses which are measures of 2 latent traits we are interested in. For half of our sample we administer an intervention with the hopes that it will increase our latent traits. We administer a pretest measuring the 5 observables before the treatment and a posttest after measuring the 5 observables after.
set obs 4000 gen id = _n gen eta1 = rnormal() gen eta2 = rnormal() * Generate 5 irrelevant factors that might affect each of the * different responses on the pretest gen f1 = rnormal() gen f2 = rnormal() gen f3 = rnormal() gen f4 = rnormal() gen f5 = rnormal() * Now let's apply the treatment expand 2, gen(t) // double our data gen treat=0 replace treat=1 if ((id<=_N/4)&(t==1)) * Now let's generate our changes in etas replace eta1 = eta1 + treat*1 + t*.5 replace eta2 = eta2 + treat*.5 + t*1 * Finally we generate out pre and post test responses gen v1 = f1*.8 + eta1*1 + eta2*.4 // eta1 has more loading on gen v2 = f2*1.5 + eta1*1 + eta2*.3 // the first few questions gen v3 = f3*2 + eta1*1 + eta2*1 gen v4 = f4*1 + eta1*.2 + eta2*1 // eta2 has more loading on gen v5 = f5*1 + eta2*1 // the last few questions * END Simulation * Begin Estimation sem (L1 -> v1 v2 v3 v4 v5) (L2 -> v1 v2 v3 v4 v5) if t==0 predict L1 L2, latent sem (L1 -> v1 v2 v3 v4 v5) (L2 -> v1 v2 v3 v4 v5) if t==1 predict L12 L22, latent replace L1 = L12 if t==1 replace L2 = L22 if t==1 * Now let's see if our latent predicted factors are correlated with our true factors. corr eta1 eta2 L1 L2 * We can see already that we are having problems. * I am no expert on SEM so I don't really know what is going wrong except * that eta1 is reasonably highly correlated with L1 and L2 and * eta2 is less highly correlated with L1 and L2 equally each * individually, which is not what we want. * Well too late to stop now. Let's do our diff in diff estimation. * In this case we can easily accomplish it by generating one more variable. * Let's do a seemingly unrelated regression form to make a single joint estimator. sureg (L1 t id treat) (L2 t id treat) * Now we have estimated the effect of the treatment given a control for the * time effect and individual differences. Can we be sure of our results? * Not quite. We are treating L1 and L2 like observed varaibles rather than * random variables we estimated. We need to adjust out standard errors to * take this into account. The easiest way though computationally intensive is * to use a bootstrap routine. * This is how it is done. Same as above but we will use temporary variables. cap program drop SEMdnd program define SEMdnd tempvar L1 L2 L12 L22 sem (L1 -> v1 v2 v3 v4 v5) (L2 -> v1 v2 v3 v4 v5) if t==0 predict `L1' `L2', latent sem (L1 -> v1 v2 v3 v4 v5) (L2 -> v1 v2 v3 v4 v5) if t==1 predict `L12' `L22', latent replace `L1' = `L12' if t==1 replace `L2' = `L22' if t==1 sureg (`L1' t id treat) (`L2' t id treat) drop `L1' `L2' `L12' `L22' end SEMdnd // Looking good * This should do it though I don't hae the machine time available to wait * for it to finish. bs , rep(200) cluster(id): SEMdnd Formatted By EconometricsbySimulation.com