stgam: Spatially and Temporally Varying Coefficient Models Using Generalized Additive Models (GAMs)

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This package provides a framework for specifying spatially, temporally and spatially-and-temporally varying coefficient models using Generalized Additive Models (GAMs) with smooths. It builds on GAM functionality from the mgcv package. The smooths are parameterised with location, time and predictor variables. The framework supports the investigation of the presence and nature of any space-time dependencies in the data by evaluating multiple model forms (specifications) using a Generalized Cross-Validation (GCV) score. The workflow sequence is to i) Prepare the data (data.frame, tibble or sf object) by lengthening it to have a single location and time variables for each observation. ii) Evaluate all possible spatial and/or temporal models in which each predictor is specified in different ways. iii) Evaluate the models via their GCV score and to pick the best model (the one with the lowest GCV). iv) Create the final model. v) Calculate the varying coefficient estimates to quantify how the relationships between the target and predictor variables vary over space, time or space-time. vi) Create maps, time series plots etc. For more details see: Comber et al (2023) [https://doi.org/10.4230/LIPIcs.GIScience.2023.22], Comber et al (2024) [https://doi.org/10.1080/13658816.2023.2270285] and Comber et al (2004) [https://doi.org/10.3390/ijgi13120459].

Installation

You can install the CRAN version of stgam : r install.packages("stgam") Or the development version: ``` r

just the package

remotes::install_github("lexcomber/stgam")

with the vignettes - takes a bit longer

remotes::installgithub("lexcomber/stgam", buildvignettes = TRUE, force = T) ```

Example

This code below loads the package and undertakes the proposed workflow for a spatially varying coefficient model using GAMs with spatial smooths:

``` r

a spatially varying coefficient model example

library(stgam) library(dplyr) library(ggplot2) library(cols4all)

define input data

data("hpdata") inputdata <- hp_data |> # create Intercept as an addressable term mutate(Intercept = 1)

evaluate different model forms

svcmods <- evaluatemodels( inputdata = inputdata, targetvar = "priceper", vars = c("pef", "beds"), coordsx = "X", coordsy = "Y", VCtype = "SVC", time_var = NULL, ncores = 2 )

rank the models

modcomp <- gammodelrank(svcmods)

have a look

mod_comp |> select(-f)

select best model

f = as.formula(mod_comp$f[1])

put into a mgcv GAM model

gam.m = gam(f, data = input_data)

calculate the Varying Coefficients

terms = c("Intercept", "pef") vcs = calculatevcs(inputdata, gam.m, terms) vcs |> select(priceper, yot, X, Y, startswith(c("b", "se_")), yhat)

map them

data(lb) tit <-expression(paste(""beta[pef]"")) ggplot() + geomsf(data = lb, col = "lightgrey") + geompoint(data = vcs, aes(x = X, y = Y, col = bpef)) + scalecolourcontinuousc4adiv("brewer.rdylbu", name = tit) + themebw() + coord_sf() + xlab("") + ylab("")

```