# Penalized Logistic Normal Multinomial factor analyzer algorithm Main function that can do PLNM factor analyzer and select the best model based on BIC, AIC or ICL. ```r plnmfa(W_count, range_G, range_Q, model, criteria, range_tuning, iter, X) ``` ## Arguments - `W_count`: The microbiome count matrix - `range_G`: All possible number of components. A vector. - `range_Q`: A specific number of latent dimension. - `model`: The covaraince structure you choose, there are 2 different models belongs to this family:UUU and GUU. You can choose more than 1 covarance structure to do model selection. - `criteria`: one of AIC, BIC or ICL. The best model is depends on the criteria you choose. The default is BIC - `range_tuning`: A range of tuning parameters specified, ranged from 0-1. - `iter`: Max iterations, default is 150. - `X`: The regression covariate matrix, which is generated by model.matrix. ## Returns z_ig Estimated latent variable z cluster Component labels mu_g Estimated component mean pi_g Estimated component proportion B_g Estimated bicluster membership D_g Estimated error covariance COV Estimated component covariance beta_g Estimated covariate coefficients overall_loglik Complete log likelihood value for each iteration ICL ICL value BIC BIC value AIC AIC value all_fitted_model display all names of fitted models in a data.frame. ## Examples ```r #'#generate toy data with n=100, K=5, #set up parameters n<-100 p<-5 mu1<-c(-2.8,-1.3,-1.6,-3.9,-2.6) B1<-matrix(c(1,0,1,0,1,0,0,1,0,1),nrow = p, byrow=TRUE) T1<-diag(c(2.9,0.5)) D1<-diag(c(0.52, 1.53, 0.56, 0.19, 1.32)) cov1<-B1%*%T1%*%t(B1)+D1 mu2<-c(1.5,-2.7,-1.1,-0.4,-1.4) B2<-matrix(c(1,0,1,0,0,1,0,1,0,1),nrow = p, byrow=TRUE) T2<-diag(c(0.2,0.003)) D2<-diag(c(0.01, 0.62, 0.45, 0.01, 0.37)) cov2<-B2%*%T2%*%t(B2)+D2 #generate normal distribution library(mvtnorm) simp<-rmultinom(n,1,c(0.6,0.4)) lab<-as.factor(apply(t(simp),1,which.max)) df<-matrix(0,nrow=n,ncol=p) for (i in 1:n) { if(lab[i]==1){df[i,]<-rmvnorm(1,mu1,sigma = cov1)} else if(lab[i]==2){df[i,]<-rmvnorm(1,mu2,sigma = cov2)} } #apply inverse of additive log ratio and transform normal to count data f_df<-cbind(df,0) z<-exp(f_df)/rowSums(exp(f_df)) W_count<-matrix(0,nrow=n,ncol=p+1) for (i in 1:n) { W_count[i,]<-rmultinom(1,runif(1,10000,20000),z[i,]) } #if run one model let range_G, and range_tuning be an integer #remember you can always overspecify Q, so we don't suggest to run models with a range of Q. res<-plnmfa(W_count,2,2,model="UUU",range_tuning=0.6) #if run model selection let any \code{range_} parameters be a vector. res<-plnmfa(W_count,c(2:3),3,range_tuning=seq(0.5,0.8,by=0.1)) ```

plnmfa function