Details on the CIs for interaction ef...
Message/Author
 Fabricio Vasselai posted on Tuesday, February 25, 2014 - 4:58 pm
Dears Drs Muthen and Muthen,

I am using TECH3 to calculate moderated effects of an interaction between observed variables. My model is non-recursive, with two equations. Interaction appears only in eq.1:

Y1 = ALPHA + GAMMA*Y2 + BETA1*X1 + BETA2*X2 + BETA3*X1*X2 + e

I am aware of how to calculate by hand both the conditional effect of X2 on Y1, for each value of X1, and its variance(e.g. Dr Muthen's reply from Oct-25th-2008, at: http://www.statmodel.com/discussion/messages/11/385.html?1390255311).

My problem is how to get the proper CIs in a way that is consistent with the symmetric frequentist CIs calculated by Mplus. For instance, in single equation models one can usually use the SE and a t-distribution with the degrees of freedom of the model. But here, I don't know if Mplus uses a t or z table, and which is the DF used, i.e. the overall DF for the system of equations or the "DF" of the equation being considered.

If I -/+ the SE from/to the estimated parameter, I get CIs too small, too optimistic, compared to the ones Mplus gives for the interaction coefficient. If I use the overall DF and a t-distribution, I get much larger CIs.

Please, could you give me some ideas on how to get the CIs from the SE, in the same way Mplus does for the rest of the model? Thanks!
 Fabricio Vasselai posted on Tuesday, February 25, 2014 - 8:51 pm
PS: I forgot an important information. My model is clustered (type=complex; estimator=MLR).
 Linda K. Muthen posted on Wednesday, February 26, 2014 - 6:51 am
Symmetric confidence intervals are computed using z-scores. The 95 percent confidence interval is the parameter estimate +/- 1.96 times the standard error. If you get numbers that differ from that, please send the output and your license number to support@statmodel.com.
 Fabricio Vasselai posted on Wednesday, February 26, 2014 - 1:10 pm
Nice. I guess the crux of my question was, in fact, whether Mplus does calculate the CIs with z-scores even for small samples, instead of t-distribution with a given DF. Since the z-scores are always used, this solves the issue. Many thanks for your quick response.