It is a complete suite to estimate models based on moment conditions. It includes the two step Generalized method of moments (Hansen 1982; <doi:10.2307/1912775>), the iterated GMM and continuous updated estimator (Hansen, Eaton and Yaron 1996; <doi:10.2307/1392442>) and several methods that belong to the Generalized Empirical Likelihood family of estimators (Smith 1997; <doi:10.1111/j.0013-0133.1997.174.x>, Kitamura 1997; <doi:10.1214/aos/1069362388>, Newey and Smith 2004; <doi:10.1111/j.1468-0262.2004.00482.x>, and Anatolyev 2005 <doi:10.1111/j.1468-0262.2005.00601.x>).

Perform association tests using generalized linear mixed models (GLMMs) in genome-wide association studies (GWAS) and sequencing association studies. First, GMMAT fits a GLMM with covariate adjustment and random effects to account for population structure and familial or cryptic relatedness. For GWAS, GMMAT performs score tests for each genetic variant as proposed in Chen et al. (2016) <DOI:10.1016/j.ajhg.2016.02.012>. For candidate gene studies, GMMAT can also perform Wald tests to get the effect size estimate for each genetic variant. For rare variant analysis from sequencing association studies, GMMAT performs the variant Set Mixed Model Association Tests (SMMAT) as proposed in Chen et al. (2019) <DOI:10.1016/j.ajhg.2018.12.012>, including the burden test, the sequence kernel association test (SKAT), SKAT-O and an efficient hybrid test of the burden test and SKAT, based on user-defined variant sets.

Likelihood-based boosting approaches for generalized mixed models are provided.

Generating, evaluating, and selecting initialization strategies for Gaussian Mixture Models (GMMs), along with functions to run the Expectation-Maximization (EM) algorithm. Initialization methods are compared using log-likelihood, and the best-fitting model can be selected using BIC. Methods build on initialization strategies for finite mixture models described in Michael and Melnykov (2016) <doi:10.1007/s11634-016-0264-8> and Biernacki et al. (2003) <doi:10.1016/S0167-9473(02)00163-9>, and on the EM algorithm of Dempster et al. (1977) <doi:10.1111/j.2517-6161.1977.tb01600.x>. Background on model-based clustering includes Fraley and Raftery (2002) <doi:10.1198/016214502760047131> and McLachlan and Peel (2000, ISBN:9780471006268).