 STDYX standardization    Message/Author  Eric Teman posted on Monday, April 28, 2014 - 5:14 pm
I'm trying to compute the STDYX estimates for an observed path analysis by hand. The Mplus manual says SD(Y) is the model estimated standard deviation of Y. Is there a way to see this computed SD(Y) in the output?  Linda K. Muthen posted on Monday, April 28, 2014 - 6:11 pm
Take the square root of the model estimated variance.  Eric Teman posted on Monday, April 28, 2014 - 6:14 pm
The residual variance?  Eric Teman posted on Monday, April 28, 2014 - 6:25 pm
Oh...I think you mean from the covariance matrix. But the STDYX estimates are a bit off when I do the calculation by hand. Is this normal, or is there something else to account for?  Eric Teman posted on Monday, April 28, 2014 - 6:35 pm
Where are the model-estimated variances located in Mplus output??  Linda K. Muthen posted on Monday, April 28, 2014 - 9:30 pm
TECH4 or RESIDUAL.  Eric Teman posted on Tuesday, April 29, 2014 - 9:06 am
You're a life saver! Thanks, Linda!! Can't wait on version 7.2!!  mboer posted on Wednesday, November 27, 2019 - 6:01 am
Dear Prof. Muthen,

I would like to compare standardized coefficients of a cross-lagged panel model across groups using the MODEL CONSTRAINT specification:

MODEL BOY:
wy2 ON wy1 wx1 (bb1 bb2);
wy3 ON wy2 wx2 (bb3 bb4);
wx2 ON wy1 wx1 (bb5 bb6);
wx3 ON wy2 wx2 (bb7 bb8);
wx1 WITH wy1 (cb1);
wx2 WITH wy2 (cb2);
wx3 WITH wy3 (cb3);
wx1-wx3 (vb1-vb3);
wy1-wy3 (vb4-vb6);

MODEL GIRL:
wy2 ON wy1 wx1 (bg1 bg2);
wy3 ON wy2 wx2 (bg3 bg4);
wx2 ON wy1 wx1 (bg5 bg6);
wx3 ON wy2 wx2 (bg7 bg8);
wx1 WITH wy1 (cg1);
wx2 WITH wy2 (cg2);
wx3 WITH wy3 (cg3);
wx1-wx3 (vg1-vg3);
wy1-wy3 (vg4-vg6);

MODEL CONSTRAINT: new(s_bb2 s_bg2 s_diff);
s_bb2 = bb2*SQRT(vb1)/SQRT(vb5);
s_bg2 = bg2*SQRT(vg1)/SQRT(vg5);
s_diff = s_bg2 - s_bb2 ;

Here, wx1-wy3 are latent variables. My computation of standardized estimates does not reproduce the STDYX output. Perhaps because I don't take into account the covariances? Can you see what I'm doing wrong? I would also like to compare the standardized endogenous predictors wy2 and wx2 across groups, as well as the covariances (e.g. wx1 with wy1) across groups. Does this require a different computation?  Bengt O. Muthen posted on Wednesday, November 27, 2019 - 1:21 pm
Note that for a DV like wy2, (vb5) is the residual variance, not the total variance. The total variance is the residual variance plus the variance due to wy1 plus the variance due to wx1 plus the covariance contribution from them.

All computations can be done in Model Constraint.  mboer posted on Tuesday, December 10, 2019 - 5:41 am
Dear Prof. Muthen,

Thank you for your quick response. I would like to ask some follow-up questions related to your response:

1. Could you maybe show me what the correct specification is for the calculation of the stdyx effect of wy1 on wy2 in MODEL CONSTRAINT (given my model specification in my post from November 27)? I don't know how to specify the variance of wy2 due to wy1 and the other (co)variances you mentioned.
2. Which additional parameters do I need to add to calculate the stdyx effects of wy2 on e.g. wy3?
3. How can I compute correlations via MODEL constraint (of e.g. wx2 WITH wy2)?  Bengt O. Muthen posted on Tuesday, December 10, 2019 - 5:28 pm
If you have

y = b1*x1+b2*x2+e

the variance of y is

b1^2*V(x1)+b2^*V(x2)+2*b1*b2*Cov(x1, x2)+V(e).

SEMNET is suitable for these question. You can also read our RMA book.  mboer posted on Sunday, February 02, 2020 - 2:34 am
Dear Prof. Muthen,

Thank you for your answer. I have a follow-up question related to your reply on December 10th. How can I compute cov(x1,x2) when x1 and x2 are endogenous? The mplus provides the covariance between the residuals. Is there a way how I can compute the covariance between endogenous variables x1 and x2 using MODEL CONSTRAINT?  Bengt O. Muthen posted on Sunday, February 02, 2020 - 4:53 pm
Yes, you can use Model Constraint. When variables are endogenous, you have to express them in terms of their linear regression on the exogenous variables. Such an expression is similar to what I did above for the variance of y.  mboer posted on Monday, February 03, 2020 - 3:16 am
Dear Prof. Muthen,

Thank you for your quick response, I greatly appreciate it. I am still not sure how to compute the covariance for endogenous variables. I have the following cross-lagged panel model:

MODEL:
x2 ON x1 y1 (bx2x1 bx2y1);
y2 ON x1 y1 (by2x1 by2y1);
y3 ON x2 y2 (by3x2 by3y2);
x3 ON x2 y2 (bx3x2 bx2y3);
x1 WITH y1 (c1);
x2 WITH y2 (c2);
x3 WITH y3 (c3);
x1-x3 (vx1 vx2 vx3);
y1-y3 (vy1 vy2 vy3);

! I want to estimate the variance of all variables using model constraint
! (because I want to calculate standardized estimates and then constrain
! the standardized estimates):

MODEL CONSTRAINT:
new(var_x1 var_y1 var_x2 var_y2 var_x3 var_y3);
var_x1 = vx1;
var_y1 = vy1;
var_x2 = bx2x1^2*var_x1 + bx2y1^2*var_y1 + 2*bx2x1*bx2y1*c1 + vx2;
var_y2 = by2x1^2*var_x1 + by2y1^2*var_y1 + 2*by2x1*by2y1*c1 + vy2;
var_x3 = by3x2^2*var_x2 + by3y2^2*var_y2 + 2*by3x2*by3y2*cov(x2,y2)? + vx3;
var_y3 = bx3x2^2*var_x2 + bx2y3^2*var_y2 + 2*bx3x2*bx2y3*cov(x2,y2)? + vy3;

My question is how do I specify the covariance between x2 and y2 in model constraint, as the mplus output only provides their residual correlation?  Bengt O. Muthen posted on Monday, February 03, 2020 - 4:54 pm
Cov(x2, y2) can be expressed in model parameter terms. See any stat intro book or our RMA book, page 492 which gives the definition of Cov as

Cov(x, z) = E(x*z) - E(x)*E(z).

If you prefer, you can consult a statistics lab.    Topics | Tree View | Search | Help/Instructions | Program Credits Administration