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Re: st: Hierarchical CFA problem


From   "JVerkuilen (Gmail)" <jvverkuilen@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Hierarchical CFA problem
Date   Mon, 22 Apr 2013 11:07:00 -0400

On Mon, Apr 22, 2013 at 10:33 AM, John Antonakis <John.Antonakis@unil.ch> wrote:
> BTW, by "look at your output," I meant when you force Stata to stop
> iterating:
>
> -------------+----------------------------------------------------------------
> Variance     |
>         e.x1 |   .5509189   .1985341 .2718573    1.116437
>         e.x2 |   1.086973   .1179499 .8787249    1.344574
>         e.x3 |   .8554162   .1292344 .6361797    1.150205
>         e.x4 |    .345022   .0468115 .264459    .4501272
>         e.x5 |   .4623856   .0608402 .3572761    .5984178
>         e.x6 |   .3636892   .0440637 .2868144    .4611688
>         e.x7 |   .5784454    .110548 .3977291    .8412739
>         e.x8 |   .5318421   .0899317 .3818115    .7408264
>         e.x9 |   .7004508   .0882214 .5472292    .8965738
>         e.L1 |  -1.00e-09   .2417215 .           .
>         e.L2 |   .9446486   .1340474 .7152918    1.247548
>         e.L3 |   .5939406   .1637864 .3459504      1.0197
>            G |   .7258514   .2259537 .3943421    1.336049
> ------------------------------------------------------------------------------
>
> In any case, the chi-square overidentification test shows that this model is
> no good.

Yes, it's a Heywood case in latent variable L1. lavaan was heading to
it but didn't quite get there. That can happen with different
estimation algorithms. This model is not properly specified and given
that it's not regular any chi square statistics for it are misleading.
One of the surest signs in standard output is a variance parameter
that is about the same size as its standard error, and the point
estimate for e.L1 here is clearly numerically 0 (negative only due to
rounding error). The only way that can possibly happen is when the
likelihood for that parameter is piling up on 0. A variance
parameter's log-likelihood should be essentially the same shape as
that of a chi square distribution's. When the DF gets very low the chi
square is substantially right-skewed and eventually has a mode at 0.
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