star.fit: STARX: spatiotemporal autoregressive model with exogenous...

In funstatpackages/STARX: Spatiotemporal Autoregressive Model with Exogenous Variables

Description

This function fits a spatiotemporal autoregressive (STAR) model with exogenous variables.

Usage

star.fit(
  data,
  Lambda,
  V,
  Tri,
  d,
  r,
  time.knots,
  rho,
  time.bound,
  intercept = TRUE,
  det.func = Matrix::det,
  return.se = FALSE,
  Weight.type = "normal"
)

Arguments

data	A list of five containing the data to fit model. Y is the response variable. Z is exogenous variables with constant linear coefficients. X is exogenous variables with varying linear coefficients. location is the location of data points. W is the weight matrix in STAR.
Lambda	A matrix of tuning parameters of the smoothness penalty.
V	The N by two matrix of verities of a triangulation, where N is the number of vertices. Each row is the coordinates for a vertex.
Tri	The triangulation matrix of dimension nTr by three, where nTr is the number of triangles in the triangulation. Each row is the indices of vertices in V.
d	The degree of piecewise polynomials – default is 2, and usually d is greater than one. -1 represents piecewise constant.
r	The smoothness parameter – default is 1, and 0 ≤ r < d.
time.knots	The vector of interior time.knots for univariate spline.
rho	The order of univariate spline.
time.bound	The vector of two. The boundary of univariate spline.
intercept	A logical number indicating whether to include intercept term in the model – default is TRUE.
det.func	A function used to calculate determinate of a matrix – default is det in the R package Matrix.
return.se	A logical number indicating whether to calculate standard deviation of the linear estimators.
Weight.type	The type of weight matrix. "normal" means the weight matrix does not have special structure. "upper" means the weight matrix is upper triangle matrix.

Value

n.Z	number of linear coefficients.
n.X	number of varying coefficient functions.
best.lambda	the selected smoothing tuning parameters.
theta.hat	Estimated coefficents.
alpha.hat	Estimated alpha in STAR.
gamma.hat	Estimated tensor spline coefficients.
beta.hat	Estimated tensor spline coefficients with matrix Q_2.
se.eta	Standard deviation of α, σ^2 and linear coefficients.
Y.hat	Estimated response variable.
mse	Estimated σ^2.
mle	MLE of fitted model.
MSE.Y	Mean squared error of response variable.

funstatpackages/STARX documentation built on Jan. 30, 2021, 11:47 p.m.