doZeroMStep: Compute the zero Maximization step.

In metagenomeSeq: Statistical analysis for sparse high-throughput sequencing

Description

Performs Maximization step calculation for the mixture components. Uses least squares to fit the parameters of the mean of the logistic distribution. $$ pi_j = sum_i^M frac1Mz_ij $$ Maximum-likelihood estimates are approximated using the EM algorithm where we treat mixture membership $delta_ij$ = 1 if $y_ij$ is generated from the zero point mass as latent indicator variables. The density is defined as $f_zig(y_ij = pi_j(S_j) cdot f_0(y_ij) +(1-pi_j (S_j))cdot f_count(y_ij;mu_i,sigma_i^2)$. The log-likelihood in this extended model is $(1-delta_ij) log f_count(y;mu_i,sigma_i^2 )+delta_ij log pi_j(s_j)+(1-delta_ij)log (1-pi_j (sj))$. The responsibilities are defined as $z_ij = pr(delta_ij=1 | data)$.

Usage

doZeroMStep(z, zeroIndices, mmZero)

Arguments

z	Matrix (m x n) of estimate responsibilities (probabilities that a count comes from a spike distribution at 0).
zeroIndices	Index (matrix m x n) of counts that are zero/non-zero.
mmZero	The zero model, the model matrix to account for the change in the number of OTUs observed as a linear effect of the depth of coverage.

Value

List of the zero fit (zero mean model) coefficients, variance - scale parameter (scalar), and normalized residuals of length sum(zeroIndices).

See Also

fitZig

metagenomeSeq documentation built on Nov. 8, 2020, 5:34 p.m.