st: RE: multilevel model and gllamm

 From Jeffrey Simons To statalist@hsphsun2.harvard.edu Subject st: RE: multilevel model and gllamm Date Wed, 22 Sep 2004 08:50:47 -0500

```I see now. I first understood that both varx and vary are the
measurement variables. Then your setup looks correct. There should
also be a way of making varz and varw regressors for the latent
variable, but whether you want to do that or not depends on your
interpretation on whether they affect the random coeffcients, or
directly the outcome.

Then also the unit correlations would indicate that you are making up
a model that is too complicated. All higher constants require lower
slopes means that all of your lines, i.e. the curves across all
individuals, are passing through the same point in varx / vary plane.
Does this seem plausible to you? Does it make sense in terms of your
problem?

I am unsure of this. I was wondering whether the distribution of the
response variable would be problematic. For example, on most (i.e., 84%) of
the measurement occasions the individuals are not drinking. Thus, there is
an overrepresentation of zero values and then a positively skewed
distribution of positive values. Also, I do not have all of the data yet and
am using a subset of early data to learn the analysis. Hence there are only
22 level two units (participants) and 1331 level 1 units. I did not receive
any convergence diagnostic messages when I ran the analysis. What you
mentioned about the model being too complicated makes sense in that when I
simplify it then the correlation , though still very high, goes down below
1. For example, here is a simplified model I ran (I realize , now, that I
should have used the canonical link, but this gives an idea of what it looks
like). Even with simple models however, if I context center the level 1
predictor I seem to be getting a intercept and slope corr of -1.

gllamm drink30sum C_negafflag1 C_dts ,i(id) family(gamma) link(identity)

number of level 1 units = 1331
number of level 2 units = 22

Condition Number = 20.368537

gllamm model

log likelihood = -957.30155

----------------------------------------------------------------------------
--
drink30sum |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
C_negafflag1 |   -.035851   .0070699    -5.07   0.000    -.0497078
-.0219942
C_dts |   .0035777   .0037784     0.95   0.344    -.0038279
.0109833
_cons |   1.325152   .0577773    22.94   0.000      1.21191
1.438393
----------------------------------------------------------------------------
--

Squared Coefficient of Variation
----------------------------------------------------------------------------
-
.15615195 (.00604391)

Variances and covariances of random effects
----------------------------------------------------------------------------
-

***level 2 (id)

var(1): .06730144 (.02305949)
cov(1,2): -.00582862 (.00219853) cor(1,2): -.95641864

var(2): .00055184 (.00033866)
----------------------------------------------------------------------------
-

This is also where the model would become computationally
truciky and unstable, I suppose: the likelihood is going to be flat in
some directions, and the maximizer will stumble over it. Also, Stata's
-ml- does not like problems on the boundary when it cannot step
further than 1 for correlation coefficients. Did you receive any lack
of convergence diagnostic messages along with unit correlations?

Stas

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