# fit a model with given tuning parameters This function performs penalized variable selection based on spike-and-slab quantile LASSO (ssQLASSO), spike-and-slab LASSO (ssLASSO), spike-and-slab quantile group LASSO varying coefficient mixed model (ssQVCM) and spike-and-slab group LASSO varying coefficient mixed model (ssVCM). Typical usage is to first obtain the optimal spike scale and slab scale using cross-validation, then specify them in the 'emBayes' function. ```r emBayes( y, clin = NULL, X, W = NULL, nt = NULL, group = NULL, quant, s0, s1, func, error = 0.01, maxiter = 100 ) ``` ## Arguments - `y`: a vector of response variable. - `clin`: a matrix of clinical factors. It has default value NULL. - `X`: a matrix of genetic factors. - `W`: a matrix of random factors. - `nt`: a vector of number of repeated measurements for each subject. They can be same or different. - `group`: a vector of group sizes. They can be same or different. - `quant`: value of quantile. - `s0`: value of the spike scale $s_{0}$. - `s1`: value of the slab scale $s_{1}$. - `func`: methods to perform variable selection. Four choices are available. For non longitudinal analysis: "ssLASSO" and "ssQLASSO". For longitudinal varying-coefficient analysis: "ssVCM" and "ssQVCM". - `error`: cutoff value for determining convergence. The algorithm reaches convergence if the difference in the expected log-likelihood of two iterations is less than the value of error. The default value is 0.01. - `maxiter`: the maximum number of iterations that is used in the estimation algorithm. The default value is 200. ## Returns A list with components: - **alpha**: a vector containing the estimated intercept and clinical coefficients. - **intercept**: value of the estimated intercept. - **clin.coe**: a vector of estimated clinical coefficients. - **r**: a vector of estimated ranodm effect coefficients. - **beta**: a vector of estimated beta coefficients. - **sigma**: value of estimated asymmetric Laplace distribution scale parameter $\sigma$. - **theta**: value of estimated probability parameter $\theta$. - **iter**: value of number of iterations. - **ll**: a vector of expectation of likelihood at each iteration. ## Details The current version of emBayes supports four types of methods: "ssLASSO", "ssQLASSO", "ssVCM" and "ssQVCM". * ssLASSO: spike-and-slab LASSO fits a Bayesian linear regression through the EM algorithm. * ssQLASSO: spike-and-slab quantile LASSO fits a Bayesian quantile regression (based on asymmetric Laplace distribution) through the EM algorithm. * ssVCM: spike-and-slab group LASSO varying coefficient mixed model fits a Bayesian linear mixed model through the EM algorithm. * ssQVCM: spike-and-slab quantile group LASSO varying coefficient mixed model fits a Bayesian quantile mixed model through the EM algorithm. Users can choose the desired method by setting func="ssLASSO", "ssQLASSO", "ssVCM" or "ssQVCM". ## Examples ```r data(data) ##load the clinical factors, genetic factors, response and quantile data clin=data$clin X=data$X y=data$y quant=data$quant ##generate tuning vectors of desired range t0 <- seq(0.01,0.015,length.out=2) t1 <- seq(0.1,0.5,length.out=2) ##perform cross-validation and obtain tuning parameters based on check loss CV <- cv.emBayes(y,clin,X,W=NULL,nt=NULL,group=NULL,quant,t0,t1,k=5, func="ssQLASSO",error=0.01,maxiter=200) s0 <- CV$CL.s0 s1 <- CV$CL.s1 ##perform BQLSS under optimal tuning and calculate value of TP and FP for selecting beta EM <- emBayes(y,clin,X,W=NULL,nt=NULL,group=NULL,quant,s0,s1,func="ssQLASSO", error=0.01,maxiter=200) fit <- EM$beta coef <- data$coef tp <- sum(fit[coef!=0]!=0) fp <- sum(fit[coef==0]!=0) list(tp=tp,fp=fp) ```

emBayes function