Neither (1) fitting the null distribution parameters (to all test statistics) by way of maximum likelihood nor (2) use of a null distribution, yielded calibrated P-values.
As before, the test is carried out by fitting the general model as well as the restricted model under the null hypothesis and calculating the likelihood ratio statistic.
For the 10 SNPs, we fitted the null distribution using permutation method in a balanced way.
A separate 10 permutations were used to fit the null distribution.
Amongst unilaterally deaf dogs in which the side of deafness was identified, the correlation in the side affected (ie left- or right-hand side) between dogs within the same litter was explored by fitting a null multilevel logistic model using Stata's -xtmelogit- command (Stata version 11, StataCorp, College Station, Texas, USA) with dog fitted within litter within the dog's kennel of origin.
We inferred the APC and AAAP gene family evolution using CAFE by fitting null models with a single parameter throughout the host phylogeny, and comparing those to models in which λ was allowed to differ in branches past the Sternorrhyncha MRCA (Table 3).
Step 1: Fit the null model defined by (1) to the data to obtain estimates μ ^ and τ ^ 2. Step 2a: Generate a new data vector y * = μ ^ 1 n + u * + e *, where u * is randomly generated as N (0, τ ^ 2 I n ), and e* is randomly generated as N 0, R ).
However, one can use many fewer permutations by instead assuming a parametric form of the null distribution and then fitting the few required parameters to the test statistics generated from the permutations (Lee et al., 2012b).
When computing p-values, a normal distribution was fit to the null distribution obtained from the resampling to increase the precision beyond 10−3.
In order for the method to scale, we also provide a model-based approximation by fitting an exponential distribution to the 95th percentile of the null distribution.
