Constrained log-likelihood \(\ell_{\boldsymbol{y}\,|\,\boldsymbol{\zeta}}(\boldsymbol{\psi}(\boldsymbol{z}))\)

Composes loglik_multivariate() with isometric_logistic(), so that optimisation may be performed over unconstrained ILR coordinates \(\boldsymbol{z}\in\mathbb{R}^{J-1}\).

Usage

loglik_multivariate_constrained(z, y, mean_signature_matrix, Sigma, V = NULL)

Arguments

z

Numeric vector \(\boldsymbol{z}\in\mathbb{R}^{J-1}\).

y

Numeric vector (or one-column matrix) \(\boldsymbol{y}\in\mathbb{R}^{G}\).

mean_signature_matrix

Numeric matrix \(\boldsymbol{\mu}\in\mathcal{M}_{G\times J}\) (plug-in means).

Sigma

Array of cell-type covariances in \(\mathcal{M}_{G\times G\times J}\).

V

Optional ILR basis; see isometric_logistic().

Value

Scalar log-likelihood on the constrained manifold.

Examples

mu <- matrix(c(20, 22, 22, 20), 2)
Sigma <- array(c(diag(2), diag(2)), dim = c(2, 2, 2))
p <- c(0.6, 0.4)
y <- drop(mu %*% p)
loglik_multivariate_constrained(isometric_log_ratio(p), y, mu, Sigma)
#> [1] 0.6539265