Generalised least squares with a fixed residual covariance

Fits \(\boldsymbol{y}\approx\boldsymbol{\mu}\boldsymbol{p}\) by MASS::lm.gls() with a known \(G\times G\) residual covariance W that does not depend on \(\boldsymbol{p}\), then repair_simplex(). Use fixed_gls_covariance() for the global-diagonal competitor \(\operatorname{diag}\{\sum_j \bar p_j^2\boldsymbol{\Sigma}_j\}\). This is the mean-only GLS gold standard for covariance-structure benchmarks, not the DeCovarT convolution \(\boldsymbol{\Sigma}(\boldsymbol{p})=\sum_j p_j^2\boldsymbol{\Sigma}_j\).

Usage

deconvolute_ratios_gls(y, mean_signature_matrix, W, inverse = TRUE)

Arguments

y

Numeric bulk vector of length \(G\).

mean_signature_matrix

Numeric matrix \(G\times J\).

W

Residual covariance (when inverse = TRUE) or precision (when inverse = FALSE), of size \(G\times G\).

inverse

Passed to MASS::lm.gls(); TRUE means W is a covariance matrix.

Value

Named simplex vector of length \(J\).

See also

fixed_gls_covariance(), deconvolute_ratios_deconrnaseq()

Examples

mu <- cbind(ct1 = c(20, 40), ct2 = c(40, 20))
y <- drop(mu %*% c(0.4, 0.6))
Sigma <- array(c(diag(2), 2 * diag(2)), dim = c(2, 2, 2))
deconvolute_ratios_gls(y, mu, fixed_gls_covariance(Sigma))
#> ct1 ct2 
#> 0.4 0.6