Null distribution for Likelihood Ratio Testing

[Kasey Pham]

Hi Ryan and dadi users,

I have a question about the null distribution weights for Godambe testing for my particular circumstance. I am testing the following two 2D models:

 

Model 1: Gradual exponential size change in both species from nu1i to nu1f and nu2i to nu2f over time T

Model 4: A period T1 of neutral evolution in isolation, followed by a period T2 of gradual exponential size change in both species from nu1i to nu1f and nu2i to nu2f, as well as a asymmetric migration of rates m12 and m21.

My nested parameters for Model 1 in Model 4 would then be T1 = 0 and m12 = m21 = 0, or three parameters on the boundary in the null model for the ratio test.

Do you know what the weights on the chi-square null distribution would be for this particular circumstance? I found the suggested weights for 2 parameters on the boundary elsewhere in this group's discussions, but not 3 -- and I'll admit to not understanding the explanation given in Self and Liang 1987 very well (and to my understanding, the cases outlined in 5 through 9 don't deal with three parameters on the boundary).

Thanks very much for your help!

Kasey Pham

[Ryan Gutenkunst]

Hello Kasey,

My apologies for the slow response. I was traveling all week for conferences. (Yay TAGC.)

Yes, this gets complicated. I find the discussion in Ota 2000 to be much clearer: https://doi.org/10.1093/oxfordjournals.molbev.a026358 . If you’re testing for 3 parameters to not be zero, then it’s 1/8 chi_0^2 + 3/8 chi_1^2 + 3/8 chi_2^2 + 1/8 chi_3^2, assuming they are uncorrelated. Unfortunately, quantitatively assessing that correlation is challenging. I would probably move forward with the distribution I just mentioned, but be sure to emphasize that it assumes uncorrelated estimates, which probably don’t have. So I would take my LRT p-value with a grain of salt, don’t trust anything marginal.

Best,
Ryan

> On Mar 4, 2024, at 7:33 PM, Kasey Pham <kase.kh...@gmail.com> wrote:
>
> Hi Ryan and dadi users,
>
> I have a question about the null distribution weights for Godambe testing for my particular circumstance. I am testing the following two 2D models:
>

> <dadi_hyb_models_ratiotested.png>
> Model 1: Gradual exponential size change in both species from nu1i to nu1f and nu2i to nu2f over time T
> Model 4: A period T1 of neutral evolution in isolation, followed by a period T2 of gradual exponential size change in both species from nu1i to nu1f and nu2i to nu2f, as well as a asymmetric migration of rates m12 and m21.
>
> My nested parameters for Model 1 in Model 4 would then be T1 = 0 and m12 = m21 = 0, or three parameters on the boundary in the null model for the ratio test.
>
> Do you know what the weights on the chi-square null distribution would be for this particular circumstance? I found the suggested weights for 2 parameters on the boundary elsewhere in this group's discussions, but not 3 -- and I'll admit to not understanding the explanation given in Self and Liang 1987 very well (and to my understanding, the cases outlined in 5 through 9 don't deal with three parameters on the boundary).
>
> Thanks very much for your help!
>
> Kasey Pham
>
>
>

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> <dadi_hyb_models_ratiotested.png>

[Kasey Pham]

That's a big help, thank you!