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 Cecile Marguerite Povel posted on Tuesday, October 04, 2011 - 6:30 am
Dear Linda,

I am running a second-order hierarchical one factor model. I would like to test the model fit, under the assumption that the standardized parameter estimates of the second-order factors are equal. However, by default MPLUS sets the unstandardized parameters to be equal. Is there a way to program equality of standardized (instead of undstandardized) parameter estimates of second-order factors.

For a first-order model, I solved this standardization issue by inputing standardized variables, calculated in SAS. However, for a second-order hierarchical model, it is not possible to calculate the standardized values in advance.

Thanks for your help!

 Bengt O. Muthen posted on Wednesday, October 05, 2011 - 2:58 am
You can do this in Mplus. You have to use parameter labels in Model, use these to express the standardized parameters as New parameters in Model Constraint, and then test the equality either in Model Constraint or in Model test.
 Cecile Marguerite Povel posted on Thursday, October 06, 2011 - 12:35 pm
Dear Bengt,

Thanks for your quick and clear reply. I am left with one clarifying question: "Which syntax should I use to express the standardized parameters as new parameters within the model constraint statement?"


 Linda K. Muthen posted on Thursday, October 06, 2011 - 12:54 pm
See Example 5.20 for an example.
 Brooke Buckman posted on Tuesday, October 11, 2011 - 2:21 am
I'm wanting to test model fit of a fully latent structural model with the paths of two MEDIATORS contrained to equal one another both in respect to their relationship with an IV and a DV:


Y BY y1 y2 y3;
MED1 BY y4 y5 y6;
MED2 BY y7 y9 y9;
IV BY iv1 iv2 iv3;

MED1 ON IV (1);
MED2 ON IV (1);
Y ON MED1 (2);
Y ON MED2 (2);

MED1 with MED2;
. . .

Similar to an earlier question above, the default is for the program to set the UNSTANDARDIZED parameters equal to one another. Could you provide guidance re the simplest way to set the STANDARDIZED (STDYX) structural path coefficents to be equal? (all variables are continuous in this model)

Based on example 5.20 (which I'm not certain is applicable here) is the only option to define/calculate the total variance of each endogenous latent construct (e.g. MED1 and MED2) in the MODEL CONSTRAINT: prior to then defining/calculating the STANDARDIZED paramters using the traiditonal STD formula beta = b * (stddev X/ stdev y)?

If this IS the only approach, is it acceptable input values of "total variance" estimates of each latent construct from tech4 output? or do i have to calculate it with a formula?
 Linda K. Muthen posted on Tuesday, October 11, 2011 - 11:23 pm
You need to define the variance in MODEL CONSTRAINT if you have a conditional model and the residual variance is the parameter in the model.
 Brooke B posted on Wednesday, October 12, 2011 - 12:12 am
Thanks for the quick response Linda. You have referred to the type=basic output for covariance value needed to calculate total variance of endog vars, but that appears to only works for obs vars. Do you have any guidance for obtaining covar values for latent constructs?

Y BY . . .;
MED1 BY . . .;
MED2 BY. . .;
IV BY . . .;

MED1 ON IV (M1a);
MED2 ON IV (M2a);
Y ON MED1 (M1b);
Y ON MED2 (M2b)
Y on IV (IVb);

IV (tvarIV);
MED1 (resvM1);
MED2 (resvM2);
Y (resvY);

NEW (tvarM1 tvarM2 tvarY STANDM1a STANDM2a STANDM1b STANDM2b)

!calc total vars
tvarM1 = M1a**2*tvarIV + resvM1;
tvarM2 = M2a**2*tvarIV + resvM2;

tvarY = M1b**2*tvarM1 + M2b**2*tvarM2 + IVb**2*tvarIV + COVARIANCES? + resvY; (assuming covariances are the only thing i'm missing here)

!Calc IV-> MED params
STANDM1a = M1a * SQRT(tvarIV)/SQRT (tvarM1);
STANDM2a = M2a * SQRT(tvarIV)/SQRT (tvarM2);

!Calc MED -> DV params
STANDM1b = M1b * SQRT (tvarM1)/SQRT (tvarY);
STANDM2b = M2b * SQRT (tvarM2)/SQRT (tvarY);
 Linda K. Muthen posted on Friday, October 14, 2011 - 6:18 pm
The same formulas apply to latent variable variances.
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