Test two models for best fit

[Laurence Vedelsdal]

Hi Stata

I want to test two models against each other to see if one's fit is significantly better than the alternative.
As one is not nested in the other I need an alternative to the LR-test.

The two regressions are in log- and quadradic form respectively.
tea = ln(gdp_cap)
tea= gdp_cap^2

Thanks for any help,

Laurence

[Joseph Coveney]

Maybe something like this.

version 15.1

clear *

set seed `=strreverse("1499483")'
quietly set obs 25

foreach var of newlist tea gdp_cap {
    generate double `var' = runiform()
}

// tea = ln(gdp_cap)
generate double ln_gc = ln(gdp_cap)
regress tea c.ln_gc
estimates store LN

// tea= gdp_cap^2
generate double gc2 = gdp_cap * gdp_cap
regress tea c.gc2
estimates store SQ

estimates stats LN SQ

exit

Or maybe you can just compare the explained variance (R²) or the mean squared error by inspection.

[Joao Santos Silva]

Dear Laurence Vedelsdal,

You can do a simple test for non-nested hypotheses using the artificial nesting approach. That is, you can estimate

tea = a*ln(gdp_cap)+b*gdp_cap^2

and test the significance of a and b. If, for example, you accept that a = 0 but reject b = 0, the quadratic model is preferred. The advantage of this approach is that it can reject both models if neither is adequate.

Best wishes,

Joao

[Laurence Vedelsdal]

Thank you both for your advice - it is much appreciated.

As it is a component in my thesis, I am curious if you have any academic papers exlpaining the metholdology that I can cite?

Best,
Laurence

[Joao Santos Silva]

Sure, search for the Davidson and MacKinnon 1981 Econometrica paper.

Joao

[Laurence Vedelsdal]

Thank you for the advice and the reference.

Laurence