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 Paul Silvia posted on Wednesday, April 28, 2010 - 5:50 am

Congrats on a rich and mature update. I was wondering what books you might recommend for those of us new to the Bayesian/MCMC approach to SEM estimation.

All the best,

 Bengt O. Muthen posted on Wednesday, April 28, 2010 - 7:28 am
Thanks from the whole Mplus team.

Funny you should ask about Bayes books - I have a about a dozen sitting on the floor. Many are good. Two stand out so far:

Gelman, Carlin, Stern & Rubin (2004). Bayesian data analysis. - My favorite among "advanced" texts.

Lynch (2010). Introduction to applied Bayesian statistics and estimation for social scientists. - A somewhat more applied book

Lots of good articles as well. I will reference some of them in my writing "A brief introdution to using Bayes in Mplus", which will be posted before too long.
 davide morselli posted on Monday, December 09, 2013 - 7:24 am
I was wondering whether it makes sense to interpret p-values in BSEM the same way than in frequentist approach (rejection over a certain threshold).
Similarly, standardized coefficients in BSEM are interpreted in the same way than in ML?

thank you

 Linda K. Muthen posted on Monday, December 09, 2013 - 10:58 am
No, the p-values are not interpreted in the same way as in the frequentist approach. With Bayes, you should interpret the credibility intervals.
 davide morselli posted on Monday, December 09, 2013 - 1:32 pm
Thanks for your reply,
I still have a doubt: can i make an interpretation about the proporion of cases on each side of the zero (that is the lower bound of th CI divided by the full range)? Or the credibility intervals give only range of the estimate, like confidence intervals?
In other words, do the credibility intervals refer to number of observations or the possible values that the parameter can assume?
 Bengt O. Muthen posted on Monday, December 09, 2013 - 2:02 pm
Credibility intervals are just like confidence intervals.
 Scott R. Colwell posted on Wednesday, August 06, 2014 - 7:23 am
For an multiple group analysis of an ALT Model where the estimator = bayes, I understand that we must use TYPE=MIXTURE and the KNOWNCLASS option.

If I have 2 groups (say gender with 0 and 1) and I do not want to explore classes within gender (only looking at gender differences) then do I set it as follows?

CLASSES = cgender (2) c (1);
KNOWNCLASS = cgender (gender = 0 gender = 1);

Thank you,
 Linda K. Muthen posted on Wednesday, August 06, 2014 - 7:55 am
You can use only a KNOWNCLASS variable:

CLASSES = cgender (2);
KNOWNCLASS = cgender (gender = 0 gender = 1);
 Annibale Cois posted on Tuesday, March 03, 2015 - 1:23 am
Dear Mplus team
I am fitting an endogenous treatment model. All variables continuous, T binary. Sample size=6500

Define: ONE=1;
L1 BY s1@1 s2@1;L2 BY d1@1 d2@1;
[L1 L2](m n); [s1 s2 d1 d2](is1 is2 id1 id2);
s1 ON T (t1);s2 ON T (t1);d1 ON T (t2);d2 ON T (t2);
T ON L1 L2 ONE (a b c);[T$1@0];
Model priors:

I used bayes to tackle underidentification using prior knowledge. Because of slow convergence, I fixed threshold at 0 and simulated an intercept with an auxiliary variable. The convergence improved (still slow).

1) Do you think that fitting an underidentified model using external information embedded in priors is a reasonable approach?
2) When I fit the model, I get an error message for singular sample covariance matrix. I understand why, but is there a way to obtain posterior p-values in this case?
3) Any suggestion to improve convergence?

Thank you
 Bengt O. Muthen posted on Tuesday, March 03, 2015 - 11:55 am
I don't recognize this as an endogenous treatment model. T is regressed on 2 factors at the same time as the factor indicators are regressed on T - what does that mean?
 Annibale Cois posted on Tuesday, March 03, 2015 - 8:59 pm
The idea is that the observed values of the continuous indicators are affected by treatment status T, which, in turn, is not independent by the values of the underlying factors.

In the model, L1 and L2 represent blood pressure values (systolic and diastolic) in absence of treatment. With increasing L1 and/or L2, the probability of being treated increases, and this affects the observed values s1-d2. Treatment is endogenous in this sense.

Do you think that this reasoning makes sense?

 Bengt O. Muthen posted on Wednesday, March 04, 2015 - 9:48 am
That is like a reciprocal interaction model (in econometrics). It makes substantive sense, but seems hard to identify. Usually with reciprocal interaction you need exogenous variables to identify. Or you need longitudinal data.
 Annibale Cois posted on Wednesday, March 04, 2015 - 10:32 am
I have various exogenous covariates (omitted from the model I posted, for simplicity). But I suppose you are thinking to instrumental variables, correlated with T but not with s1-d2. Am I interpreting correctly your comment?
 Bengt O. Muthen posted on Wednesday, March 04, 2015 - 3:47 pm
I am thinking of an econometric reciprocal model like

y1 on y2 x1;
y2 on y1 x2;

Here, the fact that y1 and y2 both have a unique predictor makes the model identified, whereas this model is not:

y1 on y2 x1 x2;
y2 on y1 x1 x2;
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