spte_semiparmreg {SpTe2M}

Fit the semiparametric spatio-temporal model

Description

The function spte_semiparmreg fits the semiparametric spatio-temporal model to study the relationship between the response y and covariates \bm{x} by the method discussed in Qiu and Yang (2021), in which an iterative algorithm is used to compute the estimated regression coefficients.

Usage

spte_semiparmreg(
  y,
  st,
  x,
  ht = NULL,
  hs = NULL,
  maxIter = 1000,
  tol = 10^(-4),
  stE = NULL
)

Arguments

y

A vector of length N containing the data of the spatio-temporal response y(t,s).

st

An N \times 3 matrix specifying the spatial locations and times for all the spatio-temporal observations in y.

x

An N \times p matrix containing the data of the p covariates.

ht

The temporal kernel bandwidth ht; default is NULL and it will be chosen by the modified cross-validation mod_cv if ht=NULL.

hs

The spatial kernel bandwidth hs; default is NULL, and it will be chosen by the function mod_cv if hs=NULL.

maxIter

A positive integer specifying the maximum number of iterations allowed. Default value is 1,000.

tol

A positive numeric value specifying the tolerance level for the convergence criterion. Default value is 0.0001.

stE

A three-column matrix specifying the spatial locations and times where we want to calculate the estimate of the mean. Default is NULL, and stE=st if stE=NULL.

Value

bandwidth

The bandwidths (ht, hs) used in the estimation procedure.

stE

Same as the one in the arguments.

muhat

The estimated mean values at spatial locations and times specified by stE.

beta

The vector of the estimated regression coefficient vector.

Author(s)

Kai Yang [e-mail] and Peihua Qiu

References

Qiu, P. and Yang, K. (2021). Effective Disease Surveillance by Using Covariate Information. Statistics in Medicine, 40, 5725-5745.

Examples

library(SpTe2M)
data(sim_dat)
y <- sim_dat$y; st <- sim_dat$st; x <- sim_dat$x
ids <- 1:500; y.sub <- y[ids]; st.sub <- st[ids,]; x.sub <- x[ids]
semi.est <- spte_semiparmreg(y.sub,st.sub,x.sub,maxIter=2)