Package 'countprop'

Extended Bayesian Information Criterion

Description

Calculates the Extended Bayesian Information Criterion (EBIC) of a model. Used for model selection to asses the fit of the multinomial logit-Normal model which includes a graphical lasso penalty.

Usage

ebic(l, n, d, df, gamma)

Arguments

l	Log-likelihood estimates of the model
n	Number of rows of the data set for which the log-likelihood has been calculated
d	The size of the (k-1) by (k-1) covariance matrix of a k by k count-compositional data matrix
df	Degrees of freedom
gamma	A tuning parameter. Larger values means more penalization

Value

The value of the EBIC.

Note

The graphical lasso penalty is the sum of the absolute value of the elements of the covariance matrix Sigma. The penalization parameter lambda controls the sparsity of Sigma.

Examples

data(singlecell)
mle <- mleLR(singlecell, lambda.gl=0.5)
log.lik_1 <- mle$est[[1]]$log.lik
n <- NROW(singlecell)
k <- NCOL(singlecell)
df_1 <- mle$est[[1]]$df

ebic(log.lik_1, n, k, df_1, 0.1)

---

Extended Bayesian Information Criterion Plot

Description

Plots the extended Bayesian information criterion (EBIC) of the model fit for various penalization parameters lambda.

Usage

ebicPlot(fit, xlog = TRUE, col = "darkred")

Arguments

fit	The model fit object from mleLR()
xlog	TRUE or FALSE. Renders plot with the x-axis in the log-scale if TRUE
col	Colour of the plot (character)

Value

Plot of the EBIC (y-axis) against each lambda (x-axis).

Examples

data(singlecell)
mle <- mlePath(singlecell, tol=1e-4, tol.nr=1e-4, n.lambda = 2, n.cores = 1)

ebicPlot(mle, xlog = TRUE)

---

Logit Normal Variation

Description

Estimates the variation matrix of count-compositional data based on a multinomial logit-Normal distribution. Estimation is performed using only the parameters of the distribution.

Usage

logitNormalVariation(
  mu,
  Sigma,
  type = c("standard", "phi", "phis", "rho"),
  order = c("second", "first")
)

Arguments

mu	The mle estimate of the mu matrix
Sigma	The mle estimate of the Sigma matrix
type	Type of variation metric to be calculated: standard, phi, phis (a symmetrical version of phi), rho, or logp (the variance-covariance matrix of log-transformed proportions)
order	The order of the Taylor-series approximation to be used in the estimation

Value

An estimate of the requested metric of proportionality.

Examples

data(singlecell)
mle <- mleLR(singlecell)
mu.hat <- mle$mu
Sigma.hat <- mle$Sigma

logitNormalVariation(mu.hat, Sigma.hat)
logitNormalVariation(mu.hat, Sigma.hat, type="phi")
logitNormalVariation(mu.hat, Sigma.hat, type="rho")

---

Log-Likelihood

Description

Calculates the log-likelihood, under the multinomial logit-Normal model.

Usage

logLik(v, y, ni, S, invSigma)

Arguments

v	The additive log-ratio transform of y
y	Compositional dataset
ni	The row sums of y
S	Covariance of v
invSigma	The inverse of the Sigma matrix

Value

The estimated log-likelihood under the Multinomial logit-Normal distribution.

Examples

data(singlecell)
mle.sim <- mlePath(singlecell, tol=1e-4, tol.nr=1e-4, n.lambda = 2, n.cores = 1)

n <- NROW(singlecell)


logLik(mle.sim$est.min$v,
      singlecell,
      n,
      cov(mle.sim$est.min$v),
      mle.sim$est.min$Sigma.inv)

---

Full logp Variance-Covariance

Description

Estimates the variance-covariance of the log of the proportions using a Taylor-series approximation.

Usage

logVarTaylorFull(
  mu,
  Sigma,
  transf = c("alr", "clr"),
  order = c("second", "first")
)

Arguments

mu	The mean vector of the log-ratio-transformed data (ALR or CLR)
Sigma	The variance-covariance matrix of the log-ratio-transformed data (ALR or CLR)
transf	The desired transformation. If transf="alr" the inverse additive log-ratio transformation is applied. If transf="clr" the inverse centered log-ratio transformation is applied.
order	The desired order of the Taylor Series approximation

Value

The estimated variance-covariance matrix for log p.

Examples

data(singlecell)
mle <- mleLR(singlecell)
mu <- mle$mu
Sigma <- mle$Sigma

logVarTaylorFull(mu, Sigma)

---

Maximum Likelihood Estimate for multinomial logit-normal model

Description

Returns the maximum likelihood estimates of multinomial logit-normal model parameters given a count-compositional dataset. The MLE procedure is based on the multinomial logit-Normal distribution, using the EM algorithm from Hoff (2003).

Usage

mleLR(
  y,
  max.iter = 10000,
  max.iter.nr = 100,
  tol = 1e-06,
  tol.nr = 1e-06,
  lambda.gl = 0,
  gamma = 0.1,
  verbose = FALSE
)

Arguments

y	Matrix of counts; samples are rows and features are columns.
max.iter	Maximum number of iterations
max.iter.nr	Maximum number of Newton-Raphson iterations
tol	Stopping rule
tol.nr	Stopping rule for the Newton-Raphson algorithm
lambda.gl	Penalization parameter lambda, for the graphical lasso penalty. Controls the sparsity of Sigma
gamma	Gamma value for EBIC calculation of the log-likelihood
verbose	If TRUE, print information as the functions run

Value

The additive log-ratio of y (v); maximum likelihood estimates of mu, Sigma, and Sigma.inv; the log-likelihood (log.lik); the EBIC (extended Bayesian information criterion) of the log-likelihood of the multinomial logit-Normal model with the graphical lasso penalty (ebic); degrees of freedom of the Sigma.inv matrix (df).

Note

The graphical lasso penalty is the sum of the absolute value of the elements of the covariance matrix Sigma. The penalization parameter lambda controls the sparsity of Sigma.

This function is also used within the mlePath() function.

Examples

data(singlecell)
mle <- mleLR(singlecell)

mle$mu
mle$Sigma
mle$ebic

---

Maximum Likelihood Estimator Paths

Description

Calculates the maximum likelihood estimates of the parameters for the mutlinomial logit-Normal distribution under various values of the penalization parameter lambda. Parameter lambda controls the sparsity of the covariance matrix Sigma, and penalizes the false large correlations that may arise in high-dimensional data.

Usage

mlePath(
  y,
  max.iter = 10000,
  max.iter.nr = 100,
  tol = 1e-06,
  tol.nr = 1e-06,
  lambda.gl = NULL,
  lambda.min.ratio = 0.1,
  n.lambda = 1,
  n.cores = 1,
  gamma = 0.1
)

Arguments

y	Matrix of counts; samples are rows and features are columns.
max.iter	Maximum number of iterations
max.iter.nr	Maximum number of Newton-Raphson iterations
tol	Stopping rule
tol.nr	Stopping rule for the Newton Raphson algorithm
lambda.gl	Vector of penalization parameters lambda, for the graphical lasso penalty
lambda.min.ratio	Minimum lambda ratio of the maximum lambda, used for the sequence of lambdas
n.lambda	Number of lambdas to evaluate the model on
n.cores	Number of cores to use (for parallel computation)
gamma	Gamma value for EBIC calculation of the log-likelihood

Value

The MLE estimates of y for each element lambda of lambda.gl, (est); the value of the estimates which produce the minimum EBIC, (est.min); the vector of lambdas used for graphical lasso, (lambda.gl); the index of the minimum EBIC (extended Bayesian information criterion), (min.idx); vector containing the EBIC for each lambda, (ebic).

Note

If using parallel computing, consider setting n.cores to be equal to the number of lambdas being evaluated for, n.lambda.

The graphical lasso penalty is the sum of the absolute value of the elements of the covariance matrix Sigma. The penalization parameter lambda controls the sparsity of Sigma.

Examples

data(singlecell)
mle.sim <- mlePath(singlecell, tol=1e-4, tol.nr=1e-4, n.lambda = 2, n.cores = 1)

mu.hat <- mle.sim$est.min$mu
Sigma.hat <- mle.sim$est.min$Sigma

---

Naive (Empirical) Variation

Description

Naive (empirical) estimates of proportionality metrics using only the observed counts.

Usage

naiveVariation(
  counts,
  pseudo.count = 0,
  type = c("standard", "phi", "phis", "rho", "logp"),
  impute.zeros = TRUE,
  ...
)

Arguments

counts	Matrix of counts; samples are rows and features are columns
pseudo.count	Positive count to be added to all elements of count matrix.
type	Type of variation metric to be calculated: standard, phi, phis (a symmetric version of phi), rho, or logp (the variance-covariance matrix of log-transformed proportions)
impute.zeros	If TRUE, then cmultRepl() from the zCompositions package is used to impute zero values in the counts matrix.
...	Optional arguments passed to zero-imputation function cmultRepl()

Value

An estimate of the requested metric of proportionality.

Examples

#' data(singlecell)

naiveVariation(singlecell)
naiveVariation(singlecell, type="phi")
naiveVariation(singlecell, type="rho")

---

Plugin Variation

Description

Estimates the variation matrix of count-compositional data based on a the same approximation used in logitNormalVariation() only for this function it uses empirical estimates of mu and Sigma. Also performs zero-imputation using cmultRepl() from the zCompositions package.

Usage

pluginVariation(
  counts,
  type = c("standard", "phi", "phis", "rho"),
  order = c("second", "first"),
  impute.zeros = TRUE,
  ...
)

Arguments

counts	Matrix of counts; samples are rows and features are columns.
type	Type of variation metric to be calculated: standard, phi, phis (a symmetrical version of phi), rho, or logp (the variance-covariance matrix of log-transformed proportions).
order	The order of the Taylor-series approximation to be used in the estimation
impute.zeros	If TRUE, then cmultRepl() from the zCompositions package is used to impute zero values in the counts matrix.
...	Optional arguments passed to zero-imputation function cmultRepl()

Value

An estimate of the requested metric of proportionality.

Examples

data(singlecell)

pluginVariation(singlecell)
pluginVariation(singlecell, type="phi")
pluginVariation(singlecell, type="rho")

---

Single cell sequencing data from mouse embryonic stem cells in G1 phase

Description

A subset of single cell data from Buettner et al. 2015. Contains single cell measurements from 96 mouse embryonic stem cells all in G1 phase.

Usage

data(singlecell)

Format

## 'singlecell' A matrix with 96 rows and 10 columns.

Source

<https://www.ebi.ac.uk/biostudies/arrayexpress/studies/E-MTAB-2805>

Examples

data(singlecell)

---