Package {lnmCluster}

run main microbiome Factor Analyzer algorithm.

Description

run main microbiome Factor Analyzer algorithm.

Usage

Mico_bi_PGMM(
  W_count,
  G,
  Q_g,
  pi_g,
  mu_g,
  sig_g,
  V,
  m,
  B_K,
  T_K,
  D_K,
  cov_str,
  iter,
  const,
  beta_g,
  X
)

Arguments

Value

z_ig Estimated latent variable z

cluster Component labels

mu_g Estimated component mean

pi_g Estimated component proportion

Lambda_g Estimated loading matrix.

D_g Estimated error covariance

COV Estimated component covariance

beta_g Estimated covariates coefficients.

overall_loglik Complete log likelihood value for each iteration

ICL ICL value

BIC BIC value

AIC AIC value

run main microbiome bicluster algorithm.

Description

run main microbiome bicluster algorithm.

Usage

Mico_bi_jensens(
  W_count,
  G,
  Q_g,
  pi_g,
  mu_g,
  sig_g,
  V,
  m,
  B_g,
  T_g,
  D_g,
  cov_str,
  iter,
  const,
  beta_g,
  X
)

Arguments

Value

z_ig Estimated latent variable z

cluster Component labels

mu_g Estimated component mean

pi_g Estimated component proportion

B_g Estimated bicluster membership

T_g Estimated covariance of latent variable u

D_g Estimated error covariance

COV Estimated sparsity component covariance

beta_g Estimated covariates coefficients.

Sigma_g Estimated original component covariance

overall_loglik Complete log likelihood value for each iteration

ICL ICL value

BIC BIC value

AIC AIC value

Penalized Logistic Normal Multinomial factor analyzer main estimation process

Description

Main function will perform PLNM factor analyzer and return parameters

Usage

Mico_bi_lasso(
  W_count,
  G,
  Q_g,
  pi_g,
  mu_g,
  sig_g,
  V,
  m,
  B_K,
  T_K,
  D_K,
  cov_str,
  tuning,
  iter,
  const,
  beta_g,
  X
)

Arguments

Value

z_ig Estimated latent variable z

cluster Component labels

mu_g Estimated component mean

pi_g Estimated component proportion

Lambda_g Estimated sparsity loading matrix

D_g Estimated error covariance

COV Estimated component covariance

beta_g Estimated covariates coefficients.

overall_loglik Complete log likelihood value for each iteration

ICL ICL value

BIC BIC value

AIC AIC value

tuning display the tuning parameter you specified.

Biclustering mixture model algorithm

Description

Main function that can do initialize biclustering mixture model and run one particular model for BMM

Usage

bi_fa_T(df, mu_K, pie_K, T_K, D_K, B_K, cov_str, iter)

Arguments

Value

z_ik Estimated latent variable z

cluster Component labels

mu_K Estimated component mean

pie_K Estimated component proportion

B_K Estimated bicluster membership

T_K Estimated covariance of latent variable u

D_K Estimated error covariance

S_K Estimated sparsity component covariance

LLK Complete log likelihood value for each iteration

ICL ICL value

BIC BIC value

AIC AIC value

Biclustering mixture model algorithm

Description

Main function that can do biclustering mixture model and select the best model based on BIC, AIC or ICL.

Usage

bmm(df, range_K, range_Q, model, criteria, iter, permutation, single)

Arguments

Value

best_model contains a list of parameters: z_ik Estimated latent variable z, cluster Component labels, mu_K Estimated component mean, pie_K Estimated component proportion, B_K Estimated bicluster membership, T_K Estimated covariance of latent variable u, D_K Estimated error covariance, S_K Estimated sparsity component covariance, LLK 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

set.seed(123)
n=50
p=10
simp=rmultinom(n,1,c(0.6,0.4))
lab=as.factor(apply(t(simp),1,which.max))
#1 parameter comes from multinomial
mu1=c(-2.8,-1.3,-1.6,-3.9,-2.6,-2.9,-2.5,-2.7,-3.1,-2.9)
B1=matrix(c(1,0,0,1,0,0,0,0,0,0,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0,0),nrow = p)
T1=diag(c(2.9,0.5,1))
D1=diag(c(0.52, 1.53, 0.56, 0.19, 1.32, 1.77, 0.6, 0.53, 0.37, 0.4))
cov1=B1%*%T1%*%t(B1)+D1

mu2=c(1.5,-2.7,-1.1,-0.4,-1.4,-2.6,-3,-3.9,-2.7,-3)
B2=matrix(c(1,0,0,1,0,0,0,0,0,0,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0,0),nrow = p)
T2=diag(c(0.2,0.003,0.15))
D2=diag(c(0.01, 0.62, 0.45, 0.01, 0.37, 0.42, 0.08, 0.16, 0.23, 0.27))
cov2=B2%*%T2%*%t(B2)+D2
library(mvtnorm)
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)}
}

#if run model for UUU, UUG, UUD, or UUC
res <- bmm(df,2,range_Q=c(2,3),model="UUU")#it will run 2 combinations of Q=2 or 3

#following will run 4 combinations of Q: 2 2, 3 3, 2 3 and 3 2
res <- bmm(df,2,range_Q=c(2,3),model="UUU", permutation=TRUE)


#if run model selection let range_Q and range_K be a vector.
res <- bmm(df,c(2:3),c(2:3)) #use BIC as criteria to do models selection for all 16 models

#if run one single model
res <- bmm(df,range_K=3, range_Q=c(3,3,2),model=c("UUU"),single=TRUE)
#notice that the different biclusters for each component only works for UUU, UUD, UUG and UUC model.

#do not run:
#because G stands for same structure for all components
#res <- bmm(df,3,c(2,3,3),model="GUU",single = TRUE)

#run:
res <- bmm(df,3,c(3,3,3),model="GUU",single = TRUE)#3 biclusters for each component

Gives default initial guesses for logistic-normal multinomial Factor analyzer algorithm.

Description

Gives default initial guesses for logistic-normal multinomial Factor analyzer algorithm.

Usage

initial_variational_PGMM(W_count, G, Q_g, cov_str, X)

Arguments

Value

new_pi_g Initial guess of proportion

new_mu_g Initial guess of mean vector

new_sig_g Initial guess of covariance matrix for each component

new_B_g Initial guess of loading matrix.

new_T_g The identity matrix of latent variable: u

new_D_g Initial guess of error matrix

new_m Initial guess of variational mean

new_V Initial guess of variational varaince

new_beta_g Initial guess of covariates coefficients.

Gives default initial guesses for logistic-normal multinomial biclustering algorithm.

Description

Gives default initial guesses for logistic-normal multinomial biclustering algorithm.

Usage

initial_variational_gaussian(W_count, G, Q_g, cov_str, X)

Arguments

Value

new_pi_g Initial guess of proportion

new_mu_g Initial guess of mean vector

new_sig_g Initial guess of covariance matrix for each component

new_T_g Initial guess of covariance of latent variable: u

new_B_g Initial guess of bicluster membership

new_D_g Initial guess of error matrix

new_m Initial guess of variational mean

new_V Initial guess of variational varaince

new_beta_g Initial guess of covariates coefficients.

Gives default initial guesses for penalized logistic-normal multinomial Factor analyzer algorithm.

Description

Gives default initial guesses for penalized logistic-normal multinomial Factor analyzer algorithm.

Usage

initial_variational_lasso(W_count, G, Q_g, cov_str, X)

Arguments

Value

new_pi_g Initial guess of proportion

new_mu_g Initial guess of mean vector

new_sig_g Initial guess of covariance matrix for each component

new_B_g Initial guess of loading matrix.

new_T_g The identity matrix of latent variable: u

new_D_g Initial guess of error matrix

new_m Initial guess of variational mean

new_V Initial guess of variational varaince

new_beta_g Initial guess of covariates coefficients.

Logistic Normal Multinomial Biclustering algorithm

Description

Main function that can do LNM biclustering and select the best model based on BIC, AIC or ICL.

Usage

lnmbiclust(W_count, range_G, range_Q, model, criteria, iter, permutation, X)

Arguments

Value

z_ig Estimated latent variable z

cluster Component labels

mu_g Estimated component mean

pi_g Estimated component proportion

B_g Estimated bicluster membership

T_g Estimated covariance of latent variable u

D_g Estimated error covariance

COV Estimated sparsity component covariance

beta_g Estimated covariate coefficients

Sigma_g Estimated original component covariance

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

#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_Q be an integer
res<-lnmbiclust(W_count,2,2,model="UUU")

#following will run 2 combinations of Q: 2 2, and 3 3 with G=2.
res<-lnmbiclust(W_count,2,range_Q=c(2:3),model="UUU")

#if run model selection let range_Q and range_G be a vector.
#model selection for all 16 models with G=1 to 3, Q=1 to 3.
res<-lnmbiclust(W_count,c(1:3),c(1:3))

Logistic Normal Multinomial factor analyzer algorithm

Description

Main function that can do LNM factor analyzer and select the best model based on BIC, AIC or ICL.

Usage

lnmfa(W_count, range_G, range_Q, model, criteria, iter, X)

Arguments

Value

z_ig Estimated latent variable z

cluster Component labels

mu_g Estimated component mean

pi_g Estimated component proportion

Lambda_g Estimated loading matrix

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

#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_Q be an integer
res<-lnmfa(W_count,2,2,model="UUU")

#following will run 2 combinations of Q: 2 2, and 3 3 with G=2.
res<-lnmfa(W_count,2,range_Q=c(2:3),model="UUU")

#if run model selection let range_Q and range_G be a vector.
#model selection for all 16 models with G=1 to 3, Q=1 to 3.
res<-lnmfa(W_count,c(1:3),c(1:3))

Model selections for lnmbicluster

Description

fit several models for lnmbicluster along with 3 criteria values: AIC BIC and ICL

Usage

model_selection(W_count, range_G, range_Q, model, permutation, iter, const, X)

Arguments

Value

A dataframe that contain the cov_str, K, Q, AIC, BIC, ICL values for model. There may be a lot rows if large K and Q, because of lots of combinations: it is a sum of a geometric series with multiplier max(Q) from 1 to max(K).

Model selections for lnmfa

Description

fit several models for lnmfa along with 3 criteria values: AIC BIC and ICL

Usage

model_selection_PGMM(
  W_count,
  range_G,
  range_Q,
  model,
  permutation,
  iter,
  const,
  X
)

Arguments

Value

A dataframe that contain the cov_str, K, Q, AIC, BIC, ICL values for model. There may be a lot rows if large K and Q, because of lots of combinations: it is a sum of a geometric series with multiplier max(Q) from 1 to max(K).

Model selections for bmm

Description

fit several models for bmm along with 3 criteria values: AIC BIC and ICL

Usage

model_selection_bmm(df, range_K, range_Q, model, permutation, iter)

Arguments

Value

A dataframe that contain the cov_str, K, Q, AIC, BIC, ICL values for model. There may be a lot rows if large K and Q, because of lots of combinations: it is a sum of a geometric series with multiplier max(Q) from 1 to max(K).

Model selections for plnmfa

Description

fit several models for plnmfa along with 3 criteria values: AIC BIC and ICL

Usage

model_selection_lasso(W_count, K, Q_K, model, range_tuning, iter, const, X)

Arguments

Value

A dataframe that contain the cov_str, K, Q, AIC, BIC, ICL values for model. There may be a lot rows if long range of tuning parameters.

Penalized Logistic Normal Multinomial factor analyzer algorithm

Description

Main function that can do PLNM factor analyzer and select the best model based on BIC, AIC or ICL.

Usage

plnmfa(W_count, range_G, range_Q, model, criteria, range_tuning, iter, X)

Arguments

Value

z_ig Estimated latent variable z

cluster Component labels

mu_g Estimated component mean

pi_g Estimated component proportion

Lambda_g Estimated sparsity loading matrix

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

tuning display the tuning parameter you specified.

all_fitted_model display all names of fitted models in a data.frame.

Examples

#'#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))