[R] SEM: question regarding how standard errors are calculated

[Ned Dochtermann]

Dr. Fox,
Thank you for the reply. The discrepancy between lm and the sem package as
well as AMOS makes sense given how the se's are calculated for linear
models. This is a small dataset with non-normal data (part of the reason for
my last comment) which might contribute to the relatively large discrepancy
if the Hessian is being estimated differently. Unfortunately I can't
immediately find how AMOS does this. I might try simulating some data and
running some analyses in both AMOS and using the sem library to see how each
behaves at different sample sizes.

Thanks,
Ned




-----Original Message-----
From: John Fox [mailto:jfox at mcmaster.ca] 
Sent: Tuesday, February 08, 2011 4:16 PM
To: 'Ned Dochtermann'
Cc: r-help at r-project.org
Subject: RE: [R] SEM: question regarding how standard errors are calculated

Dear Ned,

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
> On Behalf Of Ned Dochtermann
> Sent: February-08-11 6:07 PM
> To: r-help at r-project.org
> Subject: [R] SEM: question regarding how standard errors are calculated
> 
> Sorry if this question has been asked previously, I searched but found
> little. There also doesn't seem to be a dedicated SEM list-serv so
> hopefully this will find its way to the appropriate audience.

See < http://www2.gsu.edu/~mkteer/semnet.html> for an SEM email list.

> 
> 
> 
> In discussing SEM with a colleague I mentioned that a model they were
> fitting in AMOS was equivalent to a linear regression and that the
> coefficients would be the same. This of course was the case. However, the
> standard errors associated with the paths differed dramatically between
> {sem} and AMOS and each from {lm}. Specifically, AMOS produced smaller
> standard errors with z's/cr's differing by around half a point from {sem},
> which could substantially alter one's conclusions.
> 
> 
> 
> I searched a bit and found no real information on how std. errors were
> being calculated for either AMOS or {sem}. I assume that the estimates of
> std.
> errors for lm followed normal regression methods. I also assumed that sem
> and lm differed based on the former being fit using nlm and thus being due
> to asymptotic versus exact estimates. But, does anyone have information
> about how sem and AMOS are calculating standard errors and why they would
> differ rather dramatically?

I don't use AMOS but am surprised that standard errors are very different
from those produced by the sem() function in the sem package (which I assume
is what you're referring to), since I presume that both are fitting the
model by FIML assuming multinormality. Both presumably are getting standard
errors form the square-root diagonal entries of the inverse information
matrix. In the case of sem(), a numerical estimate of the Hessian is used,
so if AMOS uses an analytic Hessian, there could be some differences, but it
would be unusual for these to be large. In my experience, using an analytic
Hessian in maximizing the likelihood slows down the computation, but there
might still be an advantage for computing standard errors. 

Finally, if you're estimating a recursive SEM in observed endogenous and
exogenous variables only, then the FIML estimates are equivalent to
equation-by-equation OLS regression. The standard errors are different,
however, since FIML is getting these from the information matrix for the
whole system and is making assumptions, such as normality of the Xs and
marginal normality of the Ys, that aren't made by OLS.

I hope that this helps,
 John

--------------------------------
John Fox
Senator William McMaster
  Professor of Social Statistics
Department of Sociology
McMaster University
Hamilton, Ontario, Canada
http://socserv.mcmaster.ca/jfox



> 
> 
> 
> SEM is really not appropriate for the dataset in question but the
> discrepancy in standard errors made me curious.
> 
> 
> 
> Thanks a lot for any help,
> 
> Ned Dochtermann
> 
> 
> 
> 
> 	[[alternative HTML version deleted]]
> 
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