leastsquares: (Nonnegative) least squares

In nspope/radish: Fast gradient-based optimization of resistance surfaces

Description

A function of class measurement_model that calculates likelihood, gradient, hessian, and partial derivatives of nuisance parameters and the Laplacian generalized inverse, using nonnegative least squares.

Usage

leastsquares(
  E,
  S,
  phi,
  nu = NULL,
  gradient = TRUE,
  hessian = TRUE,
  partial = TRUE,
  nonnegative = TRUE,
  validate = FALSE
)

Arguments

E	A submatrix of the generalized inverse of the graph Laplacian (e.g. a covariance matrix)
S	A matrix of observed genetic distances
phi	Nuisance parameters (see details)
nu	Unused
gradient	Compute gradient of negative loglikelihood with regard to phi?
hessian	Compute Hessian matrix of negative loglikelihood with regard to phi?
partial	Compute second partial derivatives of negative loglikelihood with regard to phi, E, S?
nonnegative	Force slope to be nonnegative?
validate	Numerical validation via package numDeriv (very slow, use for debugging small examples)

Details

The nuisance parameters phi are the intercept ("alpha"), slope ("beta"), and negative log residual standard deviation ("tau") of the least squares regression. If not supplied, phi is estimated via maximum likelihood by nlme::gls.

TODO: formula

Value

A list containing:

covariance	rows/columns of the generalized inverse of the graph Laplacian for a subset of target vertices
objective	(if objective) the negative loglikelihood
fitted	((if objective) a matrix of expected genetic distances among target vertices
boundary	(if objective) is the MLE on the boundary (e.g. no genetic structure)?
gradient	(if gradient) gradient of negative loglikelihood with respect to phi
hessian	(if hessian) Hessian matrix of the negative loglikelihood with respect to phi
gradient_E	(if partial) gradient with respect to the generalized inverse of the graph Laplacian
partial_E	(if partial) Jacobian of gradient_E with respect to phi
partial_S	(if partial) Jacobian of gradient with respect to S
jacobian_E	(if partial) a function used for reverse algorithmic differentiation
jacobian_S	(if partial) a function used for reverse algorithmic differentiation

See Also

radish_measurement_model

Examples

library(raster)

data(melip)

covariates <- raster::stack(list(altitude=melip.altitude, forestcover=melip.forestcover))
surface <- conductance_surface(covariates, melip.coords, directions = 8)

# inverse of graph Laplacian at null model (IBD) 
laplacian_inv <- radish_distance(theta = matrix(0, 1, 2), 
                                 formula = ~forestcover + altitude,
                                 data = surface,
                                 radish::loglinear_conductance, 
                                 covariance = TRUE)$covariance[,,1]

leastsquares(laplacian_inv, melip.Fst) #without 'phi': return MLE of phi
leastsquares(laplacian_inv, melip.Fst, phi = c(0., 0.5, -0.1))

nspope/radish documentation built on July 12, 2020, 11:50 a.m.