Calculate derivative of mu_ij with respect to B

Calculate derivative of mu_ij with respect to B

Usage

mu_d_beta(
  i,
  j,
  q,
  gammas,
  B,
  X,
  Z,
  P,
  X_tilde,
  Z_tilde,
  Z_tilde_gamma_cols,
  alpha_tilde = NULL,
  Z_tilde_list = NULL,
  P_tilde,
  gamma_tilde
)

Arguments

i

The sample index (must be in 1, ..., n)

j

The taxon index (must be in 1, ..., J)

q

Which row of B to take derivative with respect to (must be in 1, ..., p)

gammas

Numeric vector of read intensities

B

Detection efficiency matrix

X

The efficiency design matrix (n x p)

Z

The sample design matrix (n x K)

P

The sample relative abundance matrix (K x J)

X_tilde

The spurious read efficiency design (K_tilde x p)

Z_tilde

The spurious read design (n x K_tilde)

Z_tilde_gamma_cols

Numeric vector containing indexes of columns of Z_tilde to scale by exp(gamma); NULL if no columns to be scaled

alpha_tilde

A numeric vector containing starting values of length \(M\). If used, Z_tilde_list must be provided.

Z_tilde_list

A list of length \(M + 1\) containing matrices \(\tilde{Z}_1,\dots,\tilde{Z}_{M + 1}\) to be linearly combined to generate Z_tilde: \(\tilde{Z} = \tilde{Z}_{(1)} + \sum_{m = 1}^M \exp(\tilde{\alpha}_m)\tilde{Z}_{(m + 1)}\). If used, alpha_tilde must be provided.

P_tilde

The spurious source relative abundance matrix (K_tilde x J)

gamma_tilde

Spurious read intensity parameter

Value

A derivative d mu_ij / d B_qj