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Re: st: decrease ll nested models sem


From   Volker Lang <[email protected]>
To   [email protected]
Subject   Re: st: decrease ll nested models sem
Date   Mon, 31 Mar 2014 15:23:23 +0200

Thanks Jeff Pitblado,

your feedback also helped me to solve my problems regarding model comparisons.

Best regards
Volker

Zitat von "Jeff Pitblado, StataCorp LP" <[email protected]>:

Volker Lang <[email protected]> is using -sem- and noticed that the
log-likelihood decreased when adding an exogenous variable.

I'm fitting a log-linear regression model using "sem".
(It shall later be extended to a path model with robust s.e.'s,
therefore "sem".)

Question:
Why does the log likelihood in comparison of the two nested models
estimated with "sem" decrease?
(It does not happen if I use a different estimation command, e.g.,
"sureg .. , isure".
Also, in this case coefficients and s.e.'s estimated by "sem" and
"sureg .. , isure" are identical,
so why does the log likelihood differ between these estimation
commands at all?)

Here is the output:

. sem (grade_l <- infov_l)
..
Iteration 1:   log likelihood =  -175.8425

Structural equation model                       Number of obs = 1281
Estimation method  = ml
Log likelihood     =  -175.8425
..

. sem (grade_l <- infov_l ued_l)
..
Iteration 1:   log likelihood =  -513.0155

Structural equation model                       Number of obs = 1281
Estimation method  = ml
Log likelihood     =  -513.0155
..

. sureg (grade_l infov_l), isure
Iteration 1:   tolerance =  7.234e-17
..
. di e(ll)
-677.17747

. sureg (grade_l infov_l ued_l), isure
Iteration 1:   tolerance =  1.447e-16
..
. di e(ll)
-656.64981

Notice that the reported log-likelhoods between the "equivalent" -sem- and
-sureg, isure- models do not agree.

	Model 1:	grade_l <- infov_l
	sem:		-175.8425
	sureg, isure:	-677.17747

	Model 1:	grade_l <- infov_l ued_l
	sem:		-513.0155
	sureg, isure:	-656.64981

This hints that -sem- is computing a difference log-likelihood from -sureg-.
In fact, -sem-'s log-likelihood is not conditional on the observed exogenous
variables while -sureg, isure-'s is.

If Volker intends to make direct comparisons between the reported
log-likelihoods from -sem- output, such as the -lrtest- command, then all
observed exogenous variables must be present in the fitted models; otherwise,
the likelihoods are not comparable.

Here is a silly example using the auto data. We will use -lrtest- to test the
significance of the -trunk- coefficient.

	. sysuse auto

	# constrained model
	. sem (mpg <- turn trunk@0)
	. est store sem0

	# full model
	. sem (mpg <- turn trunk)
	. est store sem1

	. lrtest sem0 sem1

We can easily verify/validate the results from -lrtest- by using -regress-:

	. regress mpg turn
	. est store reg0
	. regress mpg turn trunk
	. est store reg1
	. lrtest reg0 reg1

--Jeff
[email protected]
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