Location Scale Parameterization
Message/Author
 Brandon Reed posted on Monday, January 08, 2018 - 2:24 pm
We were wondering whether or not it is possible to run a model like MixRegLS in the DSEM framework. If so, is there some sample code available?
 Tihomir Asparouhov posted on Monday, January 08, 2018 - 6:04 pm
Subject specific variances can be used even without DSEM. Something like that

%within%
S | Y; ! this creates a normally distributed random effect for Log (Var (Y_w))
%between%
S on W;

That would correspond to equation (4) in

https://www.jstatsoft.org/index.php/jss/article/view/v052i12/v52i12.pdf

There are some DSEM simulation examples like this in Section 5.2 http://statmodel.com/download/DSEM.zip
see page 11 in

See also page 757 from the User's guide.

We have some possibilities for within cluster change in variance but that involves cross random modeling and at this point would have to be done through random loadings. This is along the lines of the example on page 22 in
(which doesn't have changing variance but the idea is the same).

You can do the subject and time specific variance with ML and numerical integration along the lines of Web Note 3 http://statmodel.com/download/webnotes/mc3.pdf
and user's guide example 9.14

Alternatively, for shorter time series you can use multivariate modeling and the constrain= feature with any functional form for any parameter like in User's guide example 5.23.
 Brandon Reed posted on Wednesday, January 10, 2018 - 12:55 pm
1. Are there any specifications about BETWEEN and WITHIN that are necessary to obtain a similar result as MixRegLS?
 Brandon Reed posted on Wednesday, January 10, 2018 - 12:58 pm
I realize that the Bayesian estimation may not be identical to the ML, but expected more similar results.

MODEL:
%WITHIN%
LogV | AA;

%BETWEEN%
LogV on PHA;
AA on PHA;

My results differ from Hedeker's MixRegLS program
Syntax:

mixregls.results<- mixregls.combined(aa ~ pha | pha | pha, id="id", data=lss)

Model 2:
Estimate AsymStdErr z-value p-value
beta Intercept 4.45296 1.030803 4.320 3.537e-05
beta pha 0.06050 0.024678 2.452 1.976e-02
alpha Intercept -1.28358 0.980698 -1.309 1.694e-01
alpha pha 0.04846 0.020623 2.350 2.522e-02
tau Intercept 0.79211 0.090439 8.759 0.000e+00
tau pha 0.01736 0.001887 9.201 0.000e+00

VS.

Between Level

LOGV ON
PHA 0.026 0.014 0.032 -0.002 0.054

AA ON
PHA 0.050 0.022 0.010 0.007 0.092 *

Intercepts
AA 4.879 1.027 0.000 2.877 6.900 *
LOGV 0.031 0.659 0.479 -1.241 1.347

Residual Variances
AA 3.157 0.782 0.000 2.037 5.053 *
LOGV 1.313 0.314 0.000 0.866 2.102 *