Reconsidering the null distribution of likelihood ratio tests for genetic linkage in multivariate variance components models Export

@article{citeulike:3138319, abstract = {Accurate knowledge of the null distribution of hypothesis tests is important for valid application of the tests. In previous papers and software, the asymptotic null distribution of likelihood ratio tests for detecting genetic linkage in multivariate variance components models has been stated to be a mixture of chi-square distributions with binomial mixing probabilities. Here we show, by simulation and by theoretical arguments based on the geometry of the parameter space, that all aspects of the previously stated asymptotic null distribution are incorrect-both the binomial mixing probabilities and the chi-square components. The true mixing probabilities give the highest probability to the case where all variance parameters are estimated positive, and mixing proportions and critical values depend on unknown nuisance parameters. Correcting the null distribution gives more conservative critical values than previously stated, yielding P values that can easily be ten times larger. We conclude that significance assessments should be done by empirical methods based on given data. In an example application to a simulated data set, we illustrate three well known methods for obtaining empirical P-values and compare their results on our data set.}, archivePrefix = {arXiv}, author = {Han, Summer S. and Chang, Joseph T.}, citeulike-article-id = {3138319}, citeulike-linkout-0 = {http://arxiv.org/abs/0808.2000}, citeulike-linkout-1 = {http://arxiv.org/pdf/0808.2000}, day = {14}, eprint = {0808.2000}, keywords = {genes, stats}, month = {Aug}, posted-at = {2008-08-20 01:55:48}, priority = {2}, title = {Reconsidering the null distribution of likelihood ratio tests for genetic linkage in multivariate variance components models}, url = {http://arxiv.org/abs/0808.2000}, year = {2008} }

TY - JOUR ID - citeulike:3138319 L3 - citeulike-article-id:3138319 N2 - Accurate knowledge of the null distribution of hypothesis tests is important for valid application of the tests. In previous papers and software, the asymptotic null distribution of likelihood ratio tests for detecting genetic linkage in multivariate variance components models has been stated to be a mixture of chi-square distributions with binomial mixing probabilities. Here we show, by simulation and by theoretical arguments based on the geometry of the parameter space, that all aspects of the previously stated asymptotic null distribution are incorrect-both the binomial mixing probabilities and the chi-square components. The true mixing probabilities give the highest probability to the case where all variance parameters are estimated positive, and mixing proportions and critical values depend on unknown nuisance parameters. Correcting the null distribution gives more conservative critical values than previously stated, yielding P values that can easily be ten times larger. We conclude that significance assessments should be done by empirical methods based on given data. In an example application to a simulated data set, we illustrate three well known methods for obtaining empirical P-values and compare their results on our data set. TI - Reconsidering the null distribution of likelihood ratio tests for genetic linkage in multivariate variance components models KW - genes KW - stats AU - Han, Summer AU - Chang, Joseph PY - 2008/Aug/14/ UR - http://arxiv.org/abs/0808.2000 ER -