Refit DeCovarT from several random starts to probe multimodality

The realised DeCovarT log-likelihood is not globally concave, so a successful convergence code, a small relative-distance-to-minimum and a negative-definite local Hessian together establish a local maximum only. Refitting from independent Dirichlet\((1,\ldots,1)\) starts and comparing the attained log-likelihoods is the cheapest direct probe of a second, equally good or better mode.

Usage

multistart_decovart(
  y,
  mean_signature_matrix,
  Sigma,
  n_starts = 5L,
  solver = deconvolute_ratios_Marquardt_Levenberg,
  loglik_tol = 1e-04,
  dirichlet_alpha = 1,
  ...
)

Arguments

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 \(\mathcal{M}_{G\times G\times J}\).

n_starts

Number of Dirichlet restarts (in addition to the equi-balanced start).

solver

Solver accepting initial_p and return_model; defaults to deconvolute_ratios_Marquardt_Levenberg().

loglik_tol

Two starts count as reaching the same mode when their log-likelihoods differ by less than this amount.

dirichlet_alpha

Concentration for those random starts (default 1). See starting_simplex().

...

Passed to solver (e.g. epsilon, itmax).

Value

A list with coefficients (best fit), loglik, loglik_range, starts (matrix of per-start estimates), logliks, and multimodal.

See also

boundary_diagnostics(), fit_decovart()

Other decovart_inference: bootstrap_decovart(), boundary_diagnostics(), chi_bar_square_pvalue(), confint_profile_decovart(), equivariance_check_decovart(), lrt_decovart(), profile_loglik_decovart(), reference_bootstrap_decovart(), restricted_mle_decovart()

Examples

mu <- matrix(c(20, 40, 15, 40, 20, 25), nrow = 3)
colnames(mu) <- paste0("ct", 1:2)
Sigma <- array(c(diag(3), diag(3)), dim = c(3, 3, 2))
y <- drop(mu %*% c(0.6, 0.4))
set.seed(1)
multistart_decovart(y, mu, Sigma, n_starts = 3L)$multimodal
#> [1] FALSE