interpreting modification indices relative to Wald, Lagrange multiplier tests

[Bill Shipley]

Hello.  I am relatively new to lavaan.  I am familiar with the use of Wald (fixing a free parameter to zero) and Lagrange multiplier tests (estimating a parameter than had been fixed) the context of modifications of an SEM.  However, I do not understand the output of the modindices() command in lavaan.  What tests does this command do?  I notice that there is an "epc" column (expected parameter change) but is this the change in the model X2 if a particular parameter is freed (like a LM test)?  Could someone point me to documentation (besided the help file) that explains how to interpret the output.  My email is Bill.S...@USherbrooke.ca.

 

[yrosseel]

On 02/15/2013 03:45 PM, Bill Shipley wrote:
> Hello. I am relatively new to lavaan. I am familiar with the use of
> Wald (fixing a free parameter to zero) and Lagrange multiplier tests
> (estimating a parameter than had been fixed) the context of
> modifications of an SEM. However, I do not understand the output of the
> modindices() command in lavaan. What tests does this command do?

They are Langrange multiplier tests, for a single parameter only. Often
called score tests. Or modification indices. The latter termed coined in
this paper:

Sorbom, D. (1989) Model modification. Psychometrika 54, 371�384.

> notice that there is an "epc" column (expected parameter change) but is
> this the change in the model X2 if a particular parameter is freed

No. The 'mi' column contains the 'modification index', or the (expected)
change of the chi-square test statistic. This is the score/LM test
statistic. The 'epc' column is the expected change for the parameter
estimate (if we would make it free). The remaining columns (epc.std,
...) are various standardized versions of this epc value, similar to
parameterEstimates().

The EPC values are based on

Sarris, W. E., Satorra, A., and Sorbom, D. (1987) The detection and
correction of specification errors in structural equation models. Pp.
105�129 in Clogg, C. C. (ed.), Sociological Methodology 1987. American
Sociological Association.

One day, proper documentation will be available...

Yves.