Initialize parameters for the ZIP case (zero-inflated)

SVD-based initialization of parameters for a zero-inflated Poisson log-normal latent factor model (ZIP-PLN). Regression coefficients for the abundance part (B) are obtained by regressing log(1+vec(Y)) on X; zero-inflation coefficients (D) come from a logistic regression of I(Y>0) on X. The latent structure is initialized from the SVD of the residual matrix.

Usage

Init_ZIP(Y, X, q)

Arguments

Y

Numeric n x p count matrix (may contain NA).

X

Numeric design matrix with n*p rows and d columns, aligned with vec(Y) (column-wise vectorization).

q

Integer, target latent dimension (rank).

Value

A list with elements:

B

Abundance (Poisson) regression coefficients (1 x d).

D

Zero-inflation (logit) regression coefficients (1 x d).

C

Loadings matrix (p x q).

M

Variational means of latent factors (n x q).

S

Variational scale parameters.

See also

Init for the non-ZI initializer; MatrixToVector, VectorToMatrix

Examples

set.seed(1)
n <- 30; p <- 10; d <- 3; q <- 2
Y <- matrix(rpois(n*p, 2), n, p)
X <- cbind(1, rnorm(n*p), rnorm(n*p))  # (n*p) x d, vectorized design
init <- Init_ZIP(Y, X, q)
str(init)
#> List of 5
#>  $ B: num [1:3, 1] 0.9676 -0.0346 -0.0303
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : chr [1:3] "X1" "X2" "X3"
#>   .. ..$ : NULL
#>  $ D: num [1:3, 1] 2.01 -0.113 -0.248
#>   ..- attr(*, "dimnames")=List of 2
#>   .. ..$ : chr [1:3] "X1" "X2" "X3"
#>   .. ..$ : NULL
#>  $ C: num [1:10, 1:2] 0.0295 -0.2115 -0.0742 -0.271 -0.2691 ...
#>  $ M: num [1:30, 1:2] -0.09895 -0.11673 0.01751 0.02207 0.00335 ...
#>  $ S: num [1:30, 1:2] 0.333 0.333 0.333 0.333 0.333 ...