doCountMStep: Compute the Maximization step calculation for features still active.
Description
Maximization step is solved by weighted least squares. The function also
computes counts residuals.
Usage
doCountMStep(z, y, mmCount, stillActive, fit2 = NULL, dfMethod = "modified")
Arguments
z
Matrix (m x n) of estimate responsibilities (probabilities that a
count comes from a spike distribution at 0).
y
Matrix (m x n) of count observations.
mmCount
Model matrix for the count distribution.
stillActive
Boolean vector of size M, indicating whether a feature
converged or not.
fit2
Previous fit of the count model.
dfMethod
Either 'default' or 'modified' (by responsibilities)
Value
Update matrix (m x n) of estimate responsibilities (probabilities
that a count comes from a spike distribution at 0).
Details
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
$f_zig(y_ij = pi_j(S_j)*f_0(y_ij) +(1-pi_j (S_j)) *
f_count(y_ij;mu_i,sigma_i^2)$. The log-likelihood in this extended model is
$(1-delta_ij) log f_count(y;mu_i,sigma_i^2 )+delta_ij log
pi_j(s_j)+(1-delta_ij)log (1-pi_j (s_j))$. The responsibilities are defined
as $z_ij = pr(delta_ij=1 | data)$.