cox: cox: A package for estimating Cox process regression models

In wrbrooks/cox: Estimate Cox process regression models

Description

The cox package is used to estimate Cox process regression models. The Cox process is a kind of mixed-effect model for spatial point processes. In particular it includes a systematic or fixed effect regression portion and a stochastic random effect portion. This package uses a fixed rank spatial random effect (Cressie and Johannesson, 2008) for the stochastic portion and estimates the regression parameters via a Poisson generalized linear model, making use of numerical quadrature as in Renner et al. (2015). Finally, the estimation is based on maximizing the model likelihood, marginal to the random effects. Thus, the random effects are integrated out of the model via a variational approximation.

Estimate the regression parameters of a Cox process model using the variational approximation.

Usage

cox(y, X, S, wt, beta.start, tau.start = 100,
  tol = sqrt(.Machine$double.eps), verbose = TRUE, hess = TRUE,
  diagV = FALSE)

Arguments

y	vector of response data
X	design matrix for fized effects
S	design matrix for the spatial random effects
wt	vector of observation weights
beta.start	starting values for iteration to estimate the fixed effect coefficients
tau.start	initial value of the precision of the random effects
tol	tolerance for judging convergence of the algorithm
verbose	logical indicating whether to write detailed progress reports to standard output
hess	logical indicating whether to estimate the Hessian matrix
diagV	logical: should the variational approximation to the covariance matrix of the random effects be diagonal?

Details

cox uses a variational approximation to estimate the parameters of a Cox process regression model with spatial random effects. The variational approximation to the posterior distribution of the spatial random effects is a multivariate normal.

Estimate regression coefficients of a spatial Cox process via the variational approximation.

Value

list of results containing the following elements:

beta: estimated vector of fixed effect regression coefficients

M: estimated mean vector for the posterior of the spatial random effects at the converged value of the variational approximation

V: estimated covariance matrix for the posterior of the spatial random effects at the converged value of the variational approximation

ltau: estimated precision component for the spatial random effect

hessian: estimated hessian matrix for beta, M, and ltau at convergence (estimated by call to optim)

neg.log.lik: negative of the variational lower bound on the marginal log-likelihood at convergence

wrbrooks/cox documentation built on May 4, 2019, 11:58 a.m.