. .

Sometimes it is desired to “correct for” binary, continuous, or categorical variables (“covariates”) that may also be influencing the dependent variable, or for first-order interactions between these covariates. This allows the researcher to see specifically what effects there are on the dependent variable that are strictly genetic. (See 26.10.)

To do this, first, a logistic regression which includes only the dependent and the covariates is done (the “reduced model”). Then, a logistic regression which includes not only the dependent and the covariates, but also the haplotype frequencies (as determined in the same way as for HTR (26.6)) (the “full model”) is done.

We then calculate a likelihood ratio statistic to find the significance of including the haplotype frequencies vs. not including the haplotype frequencies, where L₀ is the restricted likelihood of the reduced model and L₁ is the restricted likelihood of the full model (both computed as in 26.16), and -2ln(L₀∕L₁) should be chi-squared with the degrees of freedom being the difference in the degrees of freedom between the full and the reduced models.

HelixTree also allows simply doing a regression on covariates and haplotype frequencies put together, without “correcting for” either one. Here, the likelihood ratio test is the same as for performing just HTR, except that the regressors also include the covariates (26.16).

The same remarks apply for stepwise regression, covariates, and permutation testing using a binomial response as for stepwise regression (26.9), covariates (26.10) and permutation testing (26.21) using a linear response.