Estimating sparse direct effects in multivariate regression with the spike-and-slab LASSO

Abstract : The multivariate regression interpretation of the Gaussian chain graph model simultaneously parametrizes (i) the direct effects of p predictors on q outcomes and (ii) the residual partial covariances between pairs of outcomes. We introduce a new method for fitting sparse Gaussian chain graph models with spike-and-slab LASSO (SSL) priors. We develop an Expectation Conditional Maximization algorithm to obtain sparse estimates of the p x q matrix of direct effects and the q x q residual precision matrix. Our algorithm iteratively solves a sequence of penalized maximum likelihood problems with self-adaptive penalties that gradually filter out negligible regression coefficients and partial covariances. Because it adaptively penalizes individual model parameters, our method is seen to outperform fixed-penalty competitors on simulated data. We establish the posterior contraction rate for our model, buttressing our method’s excellent empirical performance with strong theoretical guarantees. We use our method to reanalyze a dataset from a study of the effects of diet and residence type on the composition of the gut microbiome of elderly adults.

An R package implementing cgSSL is available at this GitHub repo.

Download the journal version of the paper here.

A pre-print is available here.

Recommended citation: Shen, Y., Solís-Lemus, C., and Deshpande, S.K. (2024). "Estimating sparse direct effects in multivariate regression with the spike-and-slab LASSO." Bayesian Analysis