StdYX in Multilevel Regression
Message/Author
 Florian Fiedler posted on Sunday, January 22, 2006 - 8:58 am
Is there a short example how to interpret StdYX of a given parameter? My explanation for Std is like that:

Model: Y=aX+bZ+c

MPlus
Y ON X + Z;

Output
Std (a): a/Var(Y)
Std (b): b/Var(Y)

So Std is just parameter/Var(latent variable).

But I have no idea what I should devide by the estimates to get StdYX. The user's guide just gives "[...] These coefficients are standardized USING the variances of the cont. latent variables as well as the variances of the background AND/OR outcome variables."

1) What does USING mean?
2) What does AND/OR mean?
3) Is there anything special about StdYX in multilevel-regression analysis?

Thank you for a short explanation and an equation how to compute StdYX from parameter estimates.

Florian Fiedler.
 bmuthen posted on Sunday, January 22, 2006 - 9:56 am
In regression of y on x you simply create Stdyx from the raw slope b as usual,

Stdyx = b * SD(x)/SD(y)

Then the Stdyx value has the regular interpretation: how much of a y SD the y variable changes for a 1 SD change in x.

The text you referred to tries to cover more general cases than standard regression, including latent variables.
 Florian Fiedler posted on Sunday, January 22, 2006 - 10:37 am
So far I understand it. But I'm interested in regressions containing two or more observed variables another (2-level) variable is regressed on. And since it's a dependent variable on two levels it's getting a bit more complicated I guess ...

The model I've got now is the following:

WITHIN ARE X1 X2 X3 X4;
BETWEEN ARE Z1 Z2 Z3;

WITHIN
Y ON X1 + X2 + X3 + X4;

BETWEEN
Y ON Z1 + Z2 + Z3;

How is, for instance, StdYX for variable X1 computed and interpreted? Sorry for being impatient, will I get answers on the questions 1) (USING = sum of variances; product of SDs?), 2) and 3)?

Thank you for your work (even on sundays).

Florian Fiedler.
 bmuthen posted on Sunday, January 22, 2006 - 7:42 pm
StdYX for X1 in your example uses as the SD(x) and SD(y) of my example, the estimated within-level SDs of x1 and y. Hope that helps.
 Linda K. Muthen posted on Monday, January 23, 2006 - 8:48 am
1) What does USING mean?

Multiplying or dividing.

2) What does AND/OR mean?

Observed variable variance when no latent variables in the model - both observed and latent variable variances when latent variables are in the model.

3) Is there anything special about StdYX in multilevel-regression analysis?

No.
 Fred Smyth posted on Sunday, February 05, 2006 - 12:02 pm
How can I constrain two parameter estimates to be equal, but with opposite sign?

Thanks,
Fred Smyth
 Linda K. Muthen posted on Sunday, February 05, 2006 - 5:09 pm
Use the MODEL CONSTRAINT command and say:

p1 = -p2;