Package 'FLORAL' reference manual

Title:	Fit Log-Ratio Lasso Regression for Compositional Data
Description:	Log-ratio Lasso regression for continuous, binary, and survival outcomes with (longitudinal) compositional features. See Fei and others (2024) <doi:10.1016/j.crmeth.2024.100899>.
Authors:	Teng Fei [aut, cre, cph] , Tyler Funnell [aut] , Nicholas Waters [aut] , Sandeep Raj [aut]
Maintainer:	Teng Fei <[email protected]>
License:	GPL (>= 3)
Version:	0.4.0
Built:	2025-02-17 03:38:45 UTC
Source:	https://github.com/vdblab/floral

Comparing prediction performances under different choices of weights for lasso/ridge penalty

Description

Summarizing FLORAL outputs from various choices of a

Usage

a.FLORAL(
  a = c(0.1, 0.5, 1),
  ncore = 1,
  seed = NULL,
  x,
  y,
  ncov = 0,
  family = "gaussian",
  longitudinal = FALSE,
  id = NULL,
  tobs = NULL,
  failcode = NULL,
  corstr = "exchangeable",
  scalefix = FALSE,
  scalevalue = 1,
  pseudo = 1,
  length.lambda = 100,
  lambda.min.ratio = NULL,
  ncov.lambda.weight = 0,
  mu = 1,
  pfilter = 0,
  maxiter = 100,
  ncv = 5,
  intercept = FALSE,
  step2 = FALSE,
  progress = TRUE
)
a.FLORAL(
  a = c(0.1, 0.5, 1),
  ncore = 1,
  seed = NULL,
  x,
  y,
  ncov = 0,
  family = "gaussian",
  longitudinal = FALSE,
  id = NULL,
  tobs = NULL,
  failcode = NULL,
  corstr = "exchangeable",
  scalefix = FALSE,
  scalevalue = 1,
  pseudo = 1,
  length.lambda = 100,
  lambda.min.ratio = NULL,
  ncov.lambda.weight = 0,
  mu = 1,
  pfilter = 0,
  maxiter = 100,
  ncv = 5,
  intercept = FALSE,
  step2 = FALSE,
  progress = TRUE
)

Arguments

`a`	vector of scalars between 0 and 1 for comparison.
`ncore`	Number of cores used for parallel computation. Default is to use only 1 core.
`seed`	A random seed for reproducibility of the results. By default the seed is the numeric form of `Sys.Date()`.
`x`	Feature matrix, where rows specify subjects and columns specify features. The first `ncov` columns should be patient characteristics and the rest columns are microbiome absolute counts corresponding to various taxa. If `x` contains longitudinal data, the rows must be sorted in the same order of the subject IDs used in `y`.
`y`	Outcome. For a continuous or binary outcome, `y` is a vector. For survival outcome, `y` is a `Surv` object.
`ncov`	An integer indicating the number of first `ncov` columns in `x` that will not be subject to the zero-sum constraint.
`family`	Available options are `gaussian`, `binomial`, `cox`, `finegray`.
`longitudinal`	`TRUE` or `FALSE`, indicating whether longitudinal data matrix is specified for input `x`. (`Longitudinal=TRUE` and `family="cox"` or `"finegray"` will fit a time-dependent covariate model. `Longitudinal=TRUE` and `family="gaussian"` or `"binomial"` will fit a GEE model.)
`id`	If `longitudinal` is `TRUE`, `id` specifies subject IDs corresponding to the rows of input `x`.
`tobs`	If `longitudinal` is `TRUE`, `tobs` specifies time points corresponding to the rows of input `x`.
`failcode`	If `family = finegray`, `failcode` specifies the failure type of interest. This must be a positive integer.
`corstr`	If a GEE model is specified, then `corstr` is the corresponding working correlation structure. Options are `independence`, `exchangeable`, `AR-1` and `unstructured`.
`scalefix`	`TRUE` or `FALSE`, indicating whether the scale parameter is estimated or fixed if a GEE model is specified.
`scalevalue`	Specify the scale parameter if `scalefix=TRUE`.
`pseudo`	Pseudo count to be added to `x` before taking log-transformation
`length.lambda`	Number of penalty parameters used in the path
`lambda.min.ratio`	Ratio between the minimum and maximum choice of lambda. Default is `NULL`, where the ratio is chosen as 1e-2.
`ncov.lambda.weight`	Weight of the penalty lambda applied to the first `ncov` covariates. Default is 0 such that the first `ncov` covariates are not penalized.
`mu`	Value of penalty for the augmented Lagrangian
`pfilter`	A pre-specified threshold to force coefficients with absolute values less than pfilter times the maximum value of absolute coefficient as zeros in the GEE model. Default is zero, such that all coefficients will be reported.
`maxiter`	Number of iterations needed for the outer loop of the augmented Lagrangian algorithm.
`ncv`	Folds of cross-validation. Use `NULL` if cross-validation is not wanted.
`intercept`	`TRUE` or `FALSE`, indicating whether an intercept should be estimated.
`step2`	`TRUE` or `FALSE`, indicating whether a second-stage feature selection for specific ratios should be performed for the features selected by the main lasso algorithm. Will only be performed if cross validation is enabled.
`progress`	`TRUE` or `FALSE`, indicating whether printing progress bar as the algorithm runs.

Value

A ggplot2 object of cross-validated prediction metric versus lambda, stratified by a. Detailed data can be retrieved from the ggplot2 object itself.

Author(s)

Teng Fei. Email: [email protected]

References

Fei T, Funnell T, Waters N, Raj SS et al. Scalable Log-ratio Lasso Regression Enhances Microbiome Feature Selection for Predictive Models. bioRxiv 2023.05.02.538599.

Examples


set.seed(23420)

dat <- simu(n=50,p=30,model="linear")
pmetric <- a.FLORAL(a=c(0.1,1),ncore=1,x=dat$xcount,y=dat$y,family="gaussian",ncv=2,progress=FALSE)

set.seed(23420)

dat <- simu(n=50,p=30,model="linear")
pmetric <- a.FLORAL(a=c(0.1,1),ncore=1,x=dat$xcount,y=dat$y,family="gaussian",ncv=2,progress=FALSE)

Fit Log-ratio lasso regression for compositional covariates

Description

Conduct log-ratio lasso regression for continuous, binary and survival outcomes.

Usage

FLORAL(
  x,
  y,
  ncov = 0,
  family = "gaussian",
  longitudinal = FALSE,
  id = NULL,
  tobs = NULL,
  failcode = NULL,
  corstr = "exchangeable",
  scalefix = FALSE,
  scalevalue = 1,
  pseudo = 1,
  length.lambda = 100,
  lambda.min.ratio = NULL,
  ncov.lambda.weight = 0,
  a = 1,
  mu = 1,
  pfilter = 0,
  maxiter = 100,
  ncv = 5,
  ncore = 1,
  intercept = FALSE,
  foldid = NULL,
  step2 = TRUE,
  progress = TRUE,
  plot = TRUE
)
FLORAL(
  x,
  y,
  ncov = 0,
  family = "gaussian",
  longitudinal = FALSE,
  id = NULL,
  tobs = NULL,
  failcode = NULL,
  corstr = "exchangeable",
  scalefix = FALSE,
  scalevalue = 1,
  pseudo = 1,
  length.lambda = 100,
  lambda.min.ratio = NULL,
  ncov.lambda.weight = 0,
  a = 1,
  mu = 1,
  pfilter = 0,
  maxiter = 100,
  ncv = 5,
  ncore = 1,
  intercept = FALSE,
  foldid = NULL,
  step2 = TRUE,
  progress = TRUE,
  plot = TRUE
)

Arguments

`x`	Feature matrix, where rows specify subjects and columns specify features. The first `ncov` columns should be patient characteristics and the rest columns are microbiome absolute counts corresponding to various taxa. If `x` contains longitudinal data, the rows must be sorted in the same order of the subject IDs used in `y`.
`y`	Outcome. For a continuous or binary outcome, `y` is a vector. For survival outcome, `y` is a `Surv` object.
`ncov`	An integer indicating the number of first `ncov` columns in `x` that will not be subject to the zero-sum constraint.
`family`	Available options are `gaussian`, `binomial`, `cox`, `finegray`.
`longitudinal`	`TRUE` or `FALSE`, indicating whether longitudinal data matrix is specified for input `x`. (`Longitudinal=TRUE` and `family="cox"` or `"finegray"` will fit a time-dependent covariate model. `Longitudinal=TRUE` and `family="gaussian"` or `"binomial"` will fit a GEE model.)
`id`	If `longitudinal` is `TRUE`, `id` specifies subject IDs corresponding to the rows of input `x`.
`tobs`	If `longitudinal` is `TRUE`, `tobs` specifies time points corresponding to the rows of input `x`.
`failcode`	If `family = finegray`, `failcode` specifies the failure type of interest. This must be a positive integer.
`corstr`	If a GEE model is specified, then `corstr` is the corresponding working correlation structure. Options are `independence`, `exchangeable`, `AR-1` and `unstructured`.
`scalefix`	`TRUE` or `FALSE`, indicating whether the scale parameter is estimated or fixed if a GEE model is specified.
`scalevalue`	Specify the scale parameter if `scalefix=TRUE`.
`pseudo`	Pseudo count to be added to `x` before taking log-transformation. If unspecified, then the log-transformation will not be performed.
`length.lambda`	Number of penalty parameters used in the path
`lambda.min.ratio`	Ratio between the minimum and maximum choice of lambda. Default is `NULL`, where the ratio is chosen as 1e-2.
`ncov.lambda.weight`	Weight of the penalty lambda applied to the first `ncov` covariates. Default is 0 such that the first `ncov` covariates are not penalized.
`a`	A scalar between 0 and 1: `a` is the weight for lasso penalty while `1-a` is the weight for ridge penalty.
`mu`	Value of penalty for the augmented Lagrangian
`pfilter`	A pre-specified threshold to force coefficients with absolute values less than pfilter times the maximum value of absolute coefficient as zeros in the GEE model. Default is zero, such that all coefficients will be reported.
`maxiter`	Number of iterations needed for the outer loop of the augmented Lagrangian algorithm.
`ncv`	Folds of cross-validation. Use `NULL` if cross-validation is not wanted.
`ncore`	Number of cores for parallel computing for cross-validation. Default is 1.
`intercept`	`TRUE` or `FALSE`, indicating whether an intercept should be estimated.
`foldid`	A vector of fold indicator. Default is `NULL`.
`step2`	`TRUE` or `FALSE`, indicating whether a second-stage feature selection for specific ratios should be performed for the features selected by the main lasso algorithm. Will only be performed if cross validation is enabled.
`progress`	`TRUE` or `FALSE`, indicating whether printing progress bar as the algorithm runs.
`plot`	`TRUE` or `FALSE`, indicating whether returning plots of model fitting.

Value

A list with path-specific estimates (beta), path (lambda), and others. Details can be found in README.md.

Author(s)

Teng Fei. Email: [email protected]

References

Fei T, Funnell T, Waters N, Raj SS et al. Enhanced Feature Selection for Microbiome Data using FLORAL: Scalable Log-ratio Lasso Regression bioRxiv 2023.05.02.538599.

Examples


set.seed(23420)

# Continuous outcome
dat <- simu(n=50,p=30,model="linear")
fit <- FLORAL(dat$xcount,dat$y,family="gaussian",ncv=2,progress=FALSE,step2=TRUE)

# Binary outcome
# dat <- simu(n=50,p=30,model="binomial")
# fit <- FLORAL(dat$xcount,dat$y,family="binomial",progress=FALSE,step2=TRUE)

# Survival outcome
# dat <- simu(n=50,p=30,model="cox")
# fit <- FLORAL(dat$xcount,survival::Surv(dat$t,dat$d),family="cox",progress=FALSE,step2=TRUE)

# Competing risks outcome
# dat <- simu(n=50,p=30,model="finegray")
# fit <- FLORAL(dat$xcount,survival::Surv(dat$t,dat$d,type="mstate"),failcode=1,
#               family="finegray",progress=FALSE,step2=FALSE)

# Longitudinal continuous outcome
#  dat <- simu(n=50,p=30,model="gee",geetype="gaussian",m=3,corstr="exchangeable",sdvec=rep(1,3))
#  fit <- FLORAL(x=cbind(dat$tvec, dat$xcount),y=dat$y,id=dat$id,family="gaussian",
#                ncov=1,longitudinal = TRUE,corstr = "exchangeable",lambda.min.ratio=1e-3,
#                progress=FALSE,step2=FALSE)

set.seed(23420)

# Continuous outcome
dat <- simu(n=50,p=30,model="linear")
fit <- FLORAL(dat$xcount,dat$y,family="gaussian",ncv=2,progress=FALSE,step2=TRUE)

# Binary outcome
# dat <- simu(n=50,p=30,model="binomial")
# fit <- FLORAL(dat$xcount,dat$y,family="binomial",progress=FALSE,step2=TRUE)

# Survival outcome
# dat <- simu(n=50,p=30,model="cox")
# fit <- FLORAL(dat$xcount,survival::Surv(dat$t,dat$d),family="cox",progress=FALSE,step2=TRUE)

# Competing risks outcome
# dat <- simu(n=50,p=30,model="finegray")
# fit <- FLORAL(dat$xcount,survival::Surv(dat$t,dat$d,type="mstate"),failcode=1,
#               family="finegray",progress=FALSE,step2=FALSE)

# Longitudinal continuous outcome
#  dat <- simu(n=50,p=30,model="gee",geetype="gaussian",m=3,corstr="exchangeable",sdvec=rep(1,3))
#  fit <- FLORAL(x=cbind(dat$tvec, dat$xcount),y=dat$y,id=dat$id,family="gaussian",
#                ncov=1,longitudinal = TRUE,corstr = "exchangeable",lambda.min.ratio=1e-3,
#                progress=FALSE,step2=FALSE)

Summarizing selected compositional features over multiple cross validations

Description

Summarizing FLORAL outputs from multiple random k-fold cross validations

Usage

mcv.FLORAL(
  mcv = 10,
  ncore = 1,
  seed = NULL,
  x,
  y,
  ncov = 0,
  family = "gaussian",
  longitudinal = FALSE,
  id = NULL,
  tobs = NULL,
  failcode = NULL,
  corstr = "exchangeable",
  scalefix = FALSE,
  scalevalue = 1,
  pseudo = 1,
  length.lambda = 100,
  lambda.min.ratio = NULL,
  ncov.lambda.weight = 0,
  a = 1,
  mu = 1,
  pfilter = 0,
  maxiter = 100,
  ncv = 5,
  intercept = FALSE,
  step2 = TRUE,
  progress = TRUE,
  plot = TRUE
)
mcv.FLORAL(
  mcv = 10,
  ncore = 1,
  seed = NULL,
  x,
  y,
  ncov = 0,
  family = "gaussian",
  longitudinal = FALSE,
  id = NULL,
  tobs = NULL,
  failcode = NULL,
  corstr = "exchangeable",
  scalefix = FALSE,
  scalevalue = 1,
  pseudo = 1,
  length.lambda = 100,
  lambda.min.ratio = NULL,
  ncov.lambda.weight = 0,
  a = 1,
  mu = 1,
  pfilter = 0,
  maxiter = 100,
  ncv = 5,
  intercept = FALSE,
  step2 = TRUE,
  progress = TRUE,
  plot = TRUE
)

Arguments

`mcv`	Number of random 'ncv'-fold cross-validation to be performed.
`ncore`	Number of cores used for parallel computation. Default is to use only 1 core.
`seed`	A random seed for reproducibility of the results. By default the seed is the numeric form of `Sys.Date()`.
`x`	Feature matrix, where rows specify subjects and columns specify features. The first `ncov` columns should be patient characteristics and the rest columns are microbiome absolute counts corresponding to various taxa. If `x` contains longitudinal data, the rows must be sorted in the same order of the subject IDs used in `y`.
`y`	Outcome. For a continuous or binary outcome, `y` is a vector. For survival outcome, `y` is a `Surv` object.
`ncov`	An integer indicating the number of first `ncov` columns in `x` that will not be subject to the zero-sum constraint.
`family`	Available options are `gaussian`, `binomial`, `cox`, `finegray`.
`longitudinal`	`TRUE` or `FALSE`, indicating whether longitudinal data matrix is specified for input `x`. (`Longitudinal=TRUE` and `family="cox"` or `"finegray"` will fit a time-dependent covariate model. `Longitudinal=TRUE` and `family="gaussian"` or `"binomial"` will fit a GEE model.)
`id`	If `longitudinal` is `TRUE`, `id` specifies subject IDs corresponding to the rows of input `x`.
`tobs`	If `longitudinal` is `TRUE`, `tobs` specifies time points corresponding to the rows of input `x`.
`failcode`	If `family = finegray`, `failcode` specifies the failure type of interest. This must be a positive integer.
`corstr`	If a GEE model is specified, then `corstr` is the corresponding working correlation structure. Options are `independence`, `exchangeable`, `AR-1` and `unstructured`.
`scalefix`	`TRUE` or `FALSE`, indicating whether the scale parameter is estimated or fixed if a GEE model is specified.
`scalevalue`	Specify the scale parameter if `scalefix=TRUE`.
`pseudo`	Pseudo count to be added to `x` before taking log-transformation
`length.lambda`	Number of penalty parameters used in the path
`lambda.min.ratio`	Ratio between the minimum and maximum choice of lambda. Default is `NULL`, where the ratio is chosen as 1e-2.
`ncov.lambda.weight`	Weight of the penalty lambda applied to the first `ncov` covariates. Default is 0 such that the first `ncov` covariates are not penalized.
`a`	A scalar between 0 and 1: `a` is the weight for lasso penalty while `1-a` is the weight for ridge penalty.
`mu`	Value of penalty for the augmented Lagrangian
`pfilter`	A pre-specified threshold to force coefficients with absolute values less than pfilter times the maximum value of absolute coefficient as zeros in the GEE model. Default is zero, such that all coefficients will be reported.
`maxiter`	Number of iterations needed for the outer loop of the augmented Lagrangian algorithm.
`ncv`	Folds of cross-validation. Use `NULL` if cross-validation is not wanted.
`intercept`	`TRUE` or `FALSE`, indicating whether an intercept should be estimated.
`step2`	`TRUE` or `FALSE`, indicating whether a second-stage feature selection for specific ratios should be performed for the features selected by the main lasso algorithm. Will only be performed if cross validation is enabled.
`progress`	`TRUE` or `FALSE`, indicating whether printing progress bar as the algorithm runs.
`plot`	`TRUE` or `FALSE`, indicating whether returning summary plots of selection probability for taxa features.

Value

A list with relative frequencies of a certain feature being selected over mcv ncv-fold cross-validations.

Author(s)

Teng Fei. Email: [email protected]

References

Fei T, Funnell T, Waters N, Raj SS et al. Scalable Log-ratio Lasso Regression Enhances Microbiome Feature Selection for Predictive Models. bioRxiv 2023.05.02.538599.

Examples


set.seed(23420)

dat <- simu(n=50,p=30,model="linear")
fit <- mcv.FLORAL(mcv=2,ncore=1,x=dat$xcount,y=dat$y,ncv=2,progress=FALSE,step2=TRUE,plot=FALSE)

set.seed(23420)

dat <- simu(n=50,p=30,model="linear")
fit <- mcv.FLORAL(mcv=2,ncore=1,x=dat$xcount,y=dat$y,ncv=2,progress=FALSE,step2=TRUE,plot=FALSE)

Create data input list from phyloseq object

Description

Create data input list from phyloseq object

Usage

phy_to_floral_data(phy, y = NULL, covariates = NULL)
phy_to_floral_data(phy, y = NULL, covariates = NULL)

Arguments

`phy`	Phyloseq object
`y`	Outcome column of interest from phy's sample_data
`covariates`	Covariate column names from phy's sample_data

Value

list

Examples

library(phyloseq)
data(GlobalPatterns)
# add a covariate
sample_data(GlobalPatterns)$test <- rep(c(1, 0), nsamples(GlobalPatterns)/2)
# GlobalPatterns <- tax_glom(GlobalPatterns, "Phylum")
dat <- phy_to_floral_data(GlobalPatterns, y = "test", covariates = c("SampleType"))
# res <- FLORAL(x = dat$xcount, y=dat$y, ncov=dat$ncov, family = "binomial", ncv=NULL)

library(phyloseq)
data(GlobalPatterns)
# add a covariate
sample_data(GlobalPatterns)$test <- rep(c(1, 0), nsamples(GlobalPatterns)/2)
# GlobalPatterns <- tax_glom(GlobalPatterns, "Phylum")
dat <- phy_to_floral_data(GlobalPatterns, y = "test", covariates = c("SampleType"))
# res <- FLORAL(x = dat$xcount, y=dat$y, ncov=dat$ncov, family = "binomial", ncv=NULL)

Simulate data following log-ratio model

Description

Simulate a dataset from log-ratio model.

Usage

simu(
  n = 100,
  p = 200,
  model = "linear",
  weak = 4,
  strong = 6,
  weaksize = 0.125,
  strongsize = 0.25,
  pct.sparsity = 0.5,
  rho = 0,
  timedep_slope = NULL,
  timedep_cor = NULL,
  geetype = "gaussian",
  m = 4,
  corstr = "exchangeable",
  sdvec = NULL,
  rhogee = 0.8,
  geeslope = 2.5,
  longitudinal_stability = TRUE,
  ncov = 0,
  betacov = 0,
  intercept = FALSE
)
simu(
  n = 100,
  p = 200,
  model = "linear",
  weak = 4,
  strong = 6,
  weaksize = 0.125,
  strongsize = 0.25,
  pct.sparsity = 0.5,
  rho = 0,
  timedep_slope = NULL,
  timedep_cor = NULL,
  geetype = "gaussian",
  m = 4,
  corstr = "exchangeable",
  sdvec = NULL,
  rhogee = 0.8,
  geeslope = 2.5,
  longitudinal_stability = TRUE,
  ncov = 0,
  betacov = 0,
  intercept = FALSE
)

Arguments

`n`	An integer of sample size
`p`	An integer of number of features (taxa).
`model`	Type of models associated with outcome variable, can be "linear", "binomial", "cox", "finegray", "gee" (scalar outcome with time-dependent features), or "timedep" (survival endpoint with time-dependent features).
`weak`	Number of features with `weak` effect size.
`strong`	Number of features with `strong` effect size.
`weaksize`	Actual effect size for `weak` effect size. Must be positive.
`strongsize`	Actual effect size for `strong` effect size. Must be positive.
`pct.sparsity`	Percentage of zero counts for each sample.
`rho`	Parameter controlling the correlated structure between taxa. Ranges between 0 and 1.
`timedep_slope`	If `model` is "timedep", this parameter specifies the slope for the feature trajectories. Please refer to the Simulation section of the manuscript for more details.
`timedep_cor`	If `model` is "timedep", this parameter specifies the sample-wise correlations between longitudinal features. Please refer to the Simulation section of the manuscript for more details.
`geetype`	If `model` is "gee", `geetype` is the type of GEE outcomes. Now support "gaussian" and "binomial".
`m`	If `model` is "gee", `m` is the number of repeated measurements per subject.
`corstr`	If `model` is "gee", `corstr` is the working correlation structure. Now support "independence", "exchangeable", and "AR-1".
`sdvec`	If `model` is "gee" and `geetype` is "gaussian", `sdvec` is the vector of standard deviations of each outcome variable.
`rhogee`	If `model` is "gee", `rhogee` is the correlation parameter between longitudinal outcomes under the selected working correlation structure.
`geeslope`	If `model` is "gee", `geeslope` is the linear time effect.
`longitudinal_stability`	If `model` is "timedep", this is a binary indicator which determines whether the trajectories are more stable (`TRUE`) or more volatile (`FALSE`).
`ncov`	Number of covariates that are not compositional features.
`betacov`	Coefficients corresponding to the covariates that are not compositional features.
`intercept`	Boolean. If TRUE, then a random intercept will be generated in the model. Only works for `linear` or `binomial` models.

Value

A list with simulated count matrix xcount, log1p-transformed count matrix x, outcome (continuous y, continuous centered y0, binary y, or survival t, d), true coefficient vector beta, list of non-zero features idx, value of intercept intercept (if applicable).

Author(s)

Teng Fei. Email: [email protected]

References

Fei T, Funnell T, Waters N, Raj SS et al. Enhanced Feature Selection for Microbiome Data using FLORAL: Scalable Log-ratio Lasso Regression bioRxiv 2023.05.02.538599.

Examples


set.seed(23420)
dat <- simu(n=50,p=30,model="linear")

set.seed(23420)
dat <- simu(n=50,p=30,model="linear")

Package 'FLORAL'

Help Index

Comparing prediction performances under different choices of weights for lasso/ridge penalty

Description

Usage

Arguments

Value

Author(s)

References

Examples

Fit Log-ratio lasso regression for compositional covariates

Description

Usage

Arguments

Value

Author(s)

References

Examples

Summarizing selected compositional features over multiple cross validations

Description

Usage

Arguments

Value

Author(s)

References

Examples

Create data input list from phyloseq object

Description

Usage

Arguments

Value

Examples

Simulate data following log-ratio model

Description

Usage

Arguments

Value

Author(s)

References

Examples