STATA LM - lagrange multiplier test

[Anda Codreanu]

Hi everyone,
I have a question with regard to the Lagrange multiplier test used for testing the joint significance of some variables in a MLR.

First, do you happen to know the advantage of doing an LM test instead of an F-test for joint significance?

Second, what would be a the STATA line code for determining the critical value for such a test, given that it's chi^2 distributed?

Thank you!

[Andrew Musau]

Within a maximum likelihood estimation context, the Wald, Likelihood Ratio, and Lagrange Multiplier tests are asymptotically equivalent. So with a large enough sample, choose whichever you prefer.

Second, what would be a the [Stata; note the spelling] line code for determining the critical value for such a test, given that it's chi^2 distributed?

See

help chi2tail()

For example:

display chi2tail(1, 12.2)

where the test statistic is 12.2 and you have 1 degree of freedom, the tail probability is less than 0.001 below.

Res.:

. display chi2tail(1, 12.2)
.0004779

[Stephen Jenkins]

Note also

SJ-23-2 st0712 . . . Lagrange multiplier test after constrained ML estimation
(help lgrgtest if installed) . . . . . . . . . . . . . . H. Tauchmann
Q2/23 SJ 23(2):386--401
allows for straightforwardly using the Lagrange multiplier
test after constrained maximum-likelihood estimation

Found quickly using -search Lagrange multiplier test-