RobustLPA - Robust Latent Profile Analysis

Provides a comprehensive toolset for estimating Latent Profile Analysis (LPA) models that are robust to multivariate outliers and missing data. By integrating a high-performance 'C++' engine via 'RcppArmadillo', it reliably extracts latent profiles using both Expectation-Maximization (EM) and Markov Chain Monte Carlo (MCMC) Bayesian estimation. Robustness is obtained either by Huber-type down-weighting or by mixtures of multivariate t distributions (a likelihood-based robust model, see Peel and McLachlan (2000) <doi:10.1023/A:1008981510081>). Missing data are handled by full information maximum likelihood with the exact EM treatment of incomplete observations (data augmentation in the MCMC engine). The EM engine also supports LASSO regularization with k-fold cross-validation for penalty tuning; the MCMC engine uses a Bayesian Lasso with Laplace priors, multiple chains, Gelman-Rubin/effective sample size diagnostics and the widely applicable information criterion. It supports six geometric variance-covariance models, along with functions for bootstrapped likelihood ratio tests (BLRT), BCH auxiliary variable analysis, and plotting. For longitudinal data, it fits robust growth mixture models and latent class growth analysis (Muthen and Shedden (1999) <doi:10.1111/j.0006-341X.1999.00463.x>) for one or several outcomes measured on unbalanced occasions, with Gaussian, Huber-weighted or multivariate-t (Pinheiro, Liu and Wu (2001) <doi:10.1198/10618600152628059>) latent classes, by EM and MCMC, and optional adaptive LASSO penalties (Zou (2006) <doi:10.1198/016214506000000735>) that identify stable trajectories and the outcomes that differentiate the classes. For methodological details on the Bootstrapped Likelihood Ratio Test, see Nylund et al. (2007) <doi:10.1080/10705510701575396>. For robust clustering methods, see Garcia-Escudero et al. (2010) <doi:10.1007/s11634-010-0064-5>. For BCH auxiliary variable analysis, see Bolck et al. (2004) <doi:10.1093/pan/mph001>.