Comparing two regressions with a likelihood ratio test

[Max Haberl]

Dear all,

I want to test the hypothesis that all coefficients are the same across two equations of two subsamples using a likelihood ratio test.
So it's not a default test to choose the "best" model between two nested models.
Do you have any ideas how to run this test?

Thanks for your support.
Max

[Carlo Lazzaro]

Max:
welcome to this forum .
You may want to take a look at -help suest- and/or -help sureg-.

[Richard Williams]

You can also set this up using interaction effects. See

https://www3.nd.edu/~rwilliam/stats2/l51.pdf

When you think about "all" coefficients think about whether that includes the constants too. It is more common to let them differ across groups.

[Max Haberl]

Thanks for your help!
Unfortunately I must use the likelihood ratio test. But I don't know how to run it with my specification as stated above...

[Richard Williams]

You can use an LR test when using the interactions approach:

webuse nhanes2f, clear
regress health i.female c.weight c.height
est store m1
regress health i.female##(c.weight c.height)
est store m2
lrtest m1 m2, stats

Last part of output:

. lrtest m1 m2, stats

Likelihood-ratio test                                 LR chi2(2)  =     42.18
(Assumption: m1 nested in m2)                         Prob > chi2 =    0.0000

Akaike's information criterion and Bayesian information criterion

-----------------------------------------------------------------------------
       Model |        Obs  ll(null)  ll(model)      df         AIC        BIC
-------------+---------------------------------------------------------------
          m1 |     10,335 -16601.75  -16355.54       4    32719.07   32748.05
          m2 |     10,335 -16601.75  -16334.45       6    32680.89   32724.35
-----------------------------------------------------------------------------
               Note: N=Obs used in calculating BIC; see [R] BIC note.

Note that I allowed females and males to have different constant terms. If you want to run a baseline model where the constants for the two groups are equal too, then just drop i.female from the first regression.

I used regress here, but you could use logit or probit or several other commands where a lrtest is appropriate.

As Carlo notes, there are other approaches. I like using interactions because I can adopt an intermediate position, e.g. allow for interactions with some variables but not others.

[Ghazal Khan]

Hello, i am trying to compare two multivariate regression models, the difference therefore from the above model is that there are more than one y variable, and i use the mvreg command to estimate the models, unfortunately, when i run the lrtest after storing the regression results, it keeps returning the error "xxxx does not contain scalar e(ll)". Does that mean that the mvreg command does not store log likelihood? but how is it that the regress command works with lrtest and the mvreg does not.. is there a multivariate regression version of the lrtest command? i will appreciate any advice

[Richard Williams]

Hi Ghazal. It is usually better to start a new thread rather than revive a very old one.

If you type

help mvreg

you see that it does not return e(ll).

What exactly is it you want to do? Showing code and output could add clarity to your question.

You might see if sureg will do what you want. It does return e(ll).

[smith Jason]

You can use an LR test when using the interactions approach:

webuse nhanes2f, clear
regress health i.female c.weight c.height
est store m1
regress health i.female##(c.weight c.height)
est store m2
lrtest m1 m2, stats

Last part of output:

. lrtest m1 m2, stats

Likelihood-ratio test LR chi2(2) = 42.18
(Assumption: m1 nested in m2) Prob > chi2 = 0.0000

Akaike's information criterion and Bayesian information criterion

-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
m1 | 10,335 -16601.75 -16355.54 4 32719.07 32748.05
m2 | 10,335 -16601.75 -16334.45 6 32680.89 32724.35
-----------------------------------------------------------------------------
Note: N=Obs used in calculating BIC; see [R] BIC note.

Note that I allowed females and males to have different constant terms. If you want to run a baseline model where the constants for the two groups are equal too, then just drop i.female from the first regression.

I used regress here, but you could use logit or probit or several other commands where a lrtest is appropriate.

As Carlo notes, there are other approaches. I like using interactions because I can adopt an intermediate position, e.g. allow for interactions with some variables but not others.

Where is the value of chi2(2) = 42.18 from? Can you explain?
Thank you!

[Bruce Weaver]

. // LR chi2(2) = change in -2LL
. display -2*(-16355.54 - (-16334.45))
42.18