%\VignetteIndexEntry{Lucas County Housing Example}
%\VignetteEngine{knitr::knitr}
%\VignetteEncoding{UTF-8}
\documentclass{article}
\usepackage[margin=1in]{geometry}
\usepackage{hyperref}
\title{Lucas County Housing Example}
\author{Houjian Hou}
\begin{document}
\maketitle

This vignette illustrates the package interface on a small sample of the Lucas
County housing data. The full empirical analysis requires external data and a
separate preprocessing workflow; the current standalone replication script uses
only this package sample.

<<setup, include=FALSE>>=
knitr::opts_chunk$set(collapse = TRUE, comment = "#>")
@

<<lucas-fit>>=
library("sssvcqr")

data("lucas_housing_sample")
housing <- lucas_housing_sample

y <- housing$log_price
Z <- model.matrix(~ log_TLA + log_lotsize + sale_year, data = housing)
X <- as.matrix(housing[, c("age_scaled", "age2_scaled")])
u <- as.matrix(housing[, c("longitude", "latitude")])
u <- scale(u)

fit <- ss_svcqr(
  y = y,
  Z = Z,
  X = X,
  u = u,
  tau = 0.5,
  lambda1 = 3,
  lambda2 = 1,
  k_nn = 8,
  control = list(max_iter = 40, warn_nonconvergence = FALSE)
)

summary(fit)
@

The coefficient surface returned by \verb|predict(type = "coefficients")| gives
the local total effect for each candidate spatially varying covariate.

<<lucas-coef>>=
local_coef <- predict(fit, type = "coefficients")
head(local_coef)
colMeans(local_coef)
@

\end{document}