Package {spCF}

spCF: Coarse-to-Fine Spatial Modeling

Description

Provides functions for coarse-to-fine spatial modeling (CFSM), enabling fast spatial prediction, regression, and uncertainty quantification. Suitable for moderate to large samples.

Author(s)

Maintainer: Daisuke Murakami dmuraka@ism.ac.jp

Authors:

• Daisuke Murakami dmuraka@ism.ac.jp

• Alexis Comber

• Takahiro Yoshida

• Narumasa Tsutsumida

• Chris Brunsdon

• Tomoki Nakaya

Other contributors:

• Jose Luis Blanco-Claraco (Author of the bundled 'nanoflann' C++ library (src/nanoflann.h)) [contributor, copyright holder]

• Marius Muja (Copyright holder of the bundled 'nanoflann' C++ library) [copyright holder]

• David G. Lowe (Copyright holder of the bundled 'nanoflann' C++ library) [copyright holder]

See Also

Useful links:

• https://github.com/dmuraka/spCF

• Report bugs at https://github.com/dmuraka/spCF/issues

Coarse-to-fine dynamic (space-time) spatial GLMMs (CF-DGLMMs)

Description

Prediction and regression via a separable space-time cascade. Given the scales selected by cf_dglm_hv, the model is refitted on the full sample and predictions (with standard deviations) are produced at sample and, optionally, prediction sites. The link-scale linear predictor is g(\mu_{i,t}) = x_{i,t}'\beta + \sum_k f_k(s_i,t) + offset, where each scale-k field f_k couples a per-knot AR(1) Kalman smoother in time with kernel kriging in space.

Usage

cf_dglm(
  y,
  x = NULL,
  coords,
  time,
  offset = NULL,
  x0 = NULL,
  coords0 = NULL,
  time0 = NULL,
  offset0 = NULL,
  mod_hv,
  robust_se = TRUE,
  sill_cap = TRUE,
  se_type = c("prediction", "mean"),
  se_method = c("opt", "classic")
)

Arguments

Details

The full-sample fit is a SINGLE coarse-to-fine cascade sweep, mirroring the relationship between cf_glm and cf_glm_hv: it reuses the same single greedy sweep that cf_dglm_hv performs for scale selection, plus prediction. Within the sweep, for each band (coarse to fine) the GLM working response/weights are refreshed (IRLS folded into the sweep, as cf_glm's per-band glm() does), the scale is fit and accumulated, and the constant and time-varying coefficients are backfit. (The earlier outer-IRLS implementation is archived as cf_dglm_iter under misc/.)

Value

A list (class "cf_dglm") mirroring cf_glm: beta, sd_summary, e_summary, pred, pred0, pred_q, pred0_q, bands, Z, Z_sd, Z0, Z0_sd, other, call, plus

beta_tv, beta_tv_sd

Time-varying coefficients and their standard deviations, one row per time point and one column per covariate named in tvc (plus a time column). NULL when tvc was not used in cf_dglm_hv.

pred_signal, pred_q_signal

The signal (mean) predictive kept alongside the observation predictive when se_type = "prediction".

The temporal parameters of the fitted cascade are in other$rho (AR(1) autocorrelation), other$Q (innovation variance) and other$tau (holdout-calibrated field-variance factor); the first two are shown by print.

Author(s)

Daisuke Murakami

References

Murakami, D. (2026). Fast covariance-free spatiotemporal modeling via coarse-to-fine learning. *ArXiv preprint*.

See Also

cf_dglm_hv, cf_glm

Examples

### Monthly PM10 at 63 German background stations, 2001-2005 (the data set
### behind the "Demo (air, space-time)" entry of spCFmap(); see the
### spCF_dglm vignette for a fuller walk-through).
require(sf)
air    <- read.csv(system.file("shiny", "spCFmap",
                               "example_spacetime_air.csv", package = "spCF"))
pts    <- st_as_sf(air, coords = c("lon", "lat"), crs = 4326)
coords <- st_coordinates(st_transform(pts, 25832))  # UTM 32N, in metres

### The annual cycle is a fixed effect; the space-time process takes the rest
x      <- data.frame(sin12 = sin(2 * pi * air$month / 12),
                     cos12 = cos(2 * pi * air$month / 12))

### Holdout validation optimizing the number of spatial scales
mod_hv <- cf_dglm_hv(y = air$pm10, x = x, coords = coords, time = air$time)

### Space-time modeling; the 63 stations are also predicted one month beyond
### the data (time = 61), which the AR(1) predict step turns into a forecast
uni    <- !duplicated(air$station)
n0     <- sum(uni)
mod    <- cf_dglm(y = air$pm10, x = x, coords = coords, time = air$time,
                  x0 = data.frame(sin12 = rep(sin(2 * pi / 12), n0),
                                  cos12 = rep(cos(2 * pi / 12), n0)),
                  coords0 = coords[uni, ], time0 = rep(61, n0),
                  mod_hv = mod_hv)
mod

round(mod$bands / 1000, 1)              # accepted bandwidths, in km
round(c(rho = mod$other$rho, Q = mod$other$Q), 3)  # AR(1) parameters

### Mapping the forecast for January 2006 at the station locations
fc     <- st_as_sf(data.frame(pred = mod$pred0$pred, coords[uni, ]),
                   coords = c("X", "Y"), crs = 25832)
plot(fc[, "pred"], pch = 20, cex = 1.3, axes = TRUE, key.pos = 4, nbreaks = 20)

### Multiscale extraction, averaged over the observed months
mod_s1 <- sp_scalewise(mod, bw_range = c(150000, Inf))  # large scale
mod_s2 <- sp_scalewise(mod, bw_range = c(0, 150000))    # small scale

### The same fit, explored interactively over a basemap
# spCFmap(mod, crs = 25832)

Holdout validation for coarse-to-fine dynamic (space-time) spatial GLMMs

Description

Trains a coarse-to-fine dynamic spatial GLMM (CF-DGLMM) and selects the spatial scales of a separable space-time cascade through progressive holdout validation. The companion cf_dglm refits the selected structure on the full sample and predicts. The model decomposes the link-scale linear predictor as g(\mu_{i,t}) = x_{i,t}'\beta + \sum_k f_k(s_i,t) + offset, where each scale-k field f_k is a per-knot AR(1) Kalman smoother in time combined with kernel kriging in space.

Usage

cf_dglm_hv(
  y,
  x = NULL,
  coords,
  time,
  offset = NULL,
  train_rat = 0.75,
  id_train = NULL,
  alpha = 0.9,
  kernel = "exp",
  family = gaussian(),
  rho = NULL,
  Q = NULL,
  tvc = NULL,
  q_tvc = NULL,
  seed = 1234
)

Arguments

Value

A list of class "cf_dglm_hv" with the following elements:

loss_hv

Holdout deviance of the selected model, evaluated at the validation locations. Fits of the same data share the same split, so this value compares models directly, whatever number of scales each selected.

loss_hv_all

The validation loss after every learning step.

e_summary

Out-of-sample accuracy at the validation locations of the model trained on the training locations only: deviance-based pseudo R-squared (validation_Pseudo-R2, ordinary R-squared in the Gaussian case), validation_RMSE and validation_MAE. Unlike the e_summary of cf_dglm, which scores the full-sample refit at those same points, this one never saw them.

val_pred

The validation predictions behind e_summary: one row per held-out observation with its location index (loc), time point (time), observed response (y) and predicted mean (pred) on the response scale.

id_train

Row indices of the training observations.

other

Internal objects reused by cf_dglm.

call

The matched call.

Author(s)

Daisuke Murakami

References

Murakami, D. (2026). Fast covariance-free spatiotemporal modeling via coarse-to-fine learning. *ArXiv preprint*.

See Also

cf_dglm, cf_glm_hv

Coarse-to-fine spatial downscaling (CF-DS)

Description

Scalable downscaling via CF-DS for predicting disaggregate-level responses from aggregate-level response Y, while ensuring that predictions aggregate exactly to the observed aggregate-level values.

Usage

cf_downscale(
  Y,
  x = NULL,
  prop_weight = NULL,
  coords,
  agg_id,
  mod_hv,
  adj = TRUE,
  nonneg = TRUE
)

Arguments

Value

A list with the following elements:

beta

Regression coefficients, their standard errors, and the lower and upper limits of the 95 percent confidence intervals.

sd_summary

Standard deviation of the regression term (xb), spatial processes (spatial_scale1, spatial_scale2,...), and residuals.

e_summary

Aggregate-level holdout validation accuracy, evaluated on the validation units: R-squared (validation_R2), root mean squared error (validation_RMSE), and mean absolute error (validation_MAE). All are NA when no validation areas are available (e.g. train_rat = 1).

pred

Predictive mean (pred) and standard deviation (pred_sd) of the disaggregate-level response. The spatial-process contribution to pred_sd is rescaled by a holdout-calibrated factor (stored as other$tau) estimated on the validation areas.

bands

Bandwidth values for each accepted scale during the holdout validation in cf_downscale_hv.

Z

Predictive mean of each single-scale spatial process at the disaggregate-level (data.frame; one column per scale).

Z_sd

Predictive standard deviation of the single-scale process at the disaggregate-level units (data.frame).

other

Other internally used output objects.

Author(s)

Daisuke Murakami

References

Murakami, D., Chun, Y., Yoshida, T., & Seya, H. (2026). Scalable coarse-to-fine spatial downscaling. *ArXiv preprint*.

See Also

cf_downscale_hv, cf_lm

Examples

set.seed(123)
require(sf); require(CARBayesdata)
data(GGHB.IZ)
data(pollutionhealthdata)
d  <- pollutionhealthdata[pollutionhealthdata$year == 2010, ]
ar <- merge(GGHB.IZ, d, by = "IZ")

### Disaggregate-level data (271 units)
coords <- st_coordinates(suppressWarnings(st_centroid(ar)))
x      <- data.frame(pm10 = ar$pm10, jsa = ar$jsa, price = ar$price)
prop_weight <- as.numeric(ar$expected)

### Aggregate-level data (30 units).
agg_id <- as.integer(stats::kmeans(coords, centers = 30)$cluster)

### Two types of response variables are possible:
# Y_type = "sum"  : Y_I = sum(response variable for each aggregate unit)
# Y_type = "mean" : Y_I = mean(response variable for each aggregate unit)
Y_type <- "sum"   # change to "mean" for the density-type data
Y      <- as.numeric(stats::aggregate(ar$observed, by = list(agg_id),
                       FUN = if (Y_type == "sum") sum else mean)[, 2])

### Downscaling
mh <- cf_downscale_hv(Y = Y, Y_type = Y_type, x = x,
                      prop_weight = prop_weight,
                      coords = coords, agg_id = agg_id)
md <- cf_downscale(Y = Y, x = x, prop_weight = prop_weight,
                   coords = coords, agg_id = agg_id, mod_hv = mh)

### Mapping
ar$agg_id <- agg_id
agg_poly  <- stats::aggregate(ar["agg_id"], by = list(agg_id = agg_id),
                              FUN = function(z) z[1])
agg_poly$Y<- Y
ar$pred   <- md$pred$pred
plot(agg_poly["Y"], nbreaks = 20, main = "Aggregated data")
plot(ar["pred"], nbreaks = 20, main = "Downscaling result")

Holdout validation for the coarse-to-fine spatial downscaling (CF-DS)

Description

Trains the CF-DS model and selects the number of spatial scales through sequential holdout validation.

Usage

cf_downscale_hv(
  Y,
  Y_type = "sum",
  x = NULL,
  prop_weight = NULL,
  coords,
  agg_id,
  train_rat = 0.75,
  id_train = NULL,
  alpha = 0.9,
  kernel = "exp",
  rel_tol = 1e-04,
  seed = 123
)

Arguments

Value

A list with the following elements:

sse_hv

Final sum-of-squared error (SSE) for validation samples.

sse_hv_all

SSEs obtained at each learning step.

id_train

ID of training aggregate-level units.

other

Other internally used output objects.

Author(s)

Daisuke Murakami

References

Murakami, D., Chun, Y., Yoshida, T., & Seya, H. (2026). Scalable coarse-to-fine spatial downscaling. *ArXiv preprint*.

See Also

cf_downscale, cf_lm_hv

Coarse-to-fine spatial generalized linear mixed models (CF-GLMMs)

Description

Scalable prediction, regression, and multiscale analysis via CF-GLMMs.

Usage

cf_glm(
  y,
  x = NULL,
  coords,
  offset = NULL,
  x0 = NULL,
  coords0 = NULL,
  offset0 = NULL,
  mod_hv,
  robust_se = TRUE,
  se_type = c("prediction", "mean"),
  se_method = c("opt", "classic")
)

Arguments

Value

A list with the following elements:

beta

Regression coefficients, their standard errors, and the lower and upper limits of the 95 percent confidence intervals.

sd_summary

Standard deviation of the regression term (xb), spatial process (spatial_scale1, spatial_scale2,...), additional learning, and residuals.

e_summary

Holdout validation accuracy evaluated on the validation samples: R-squared (validation_Pseudo-R2), root mean squared error (validation_RMSE), and mean absolute error (validation_MAE).

pred

Predictive means and standard deviations (sample sites). The spatial-process contribution to the predictive SD is rescaled by a holdout-calibrated factor (stored as other$tau) estimated on the validation samples.

pred0

Predictive means and standard deviations (prediction sites).

pred_q

Predictive quantiles on the response scale at the sample sites. A data frame whose columns q0.005, q0.025, q0.05, q0.1, ..., q0.9, q0.95, q0.975, q0.995 give the corresponding quantile levels, obtained by Gaussian approximation on the link scale followed by inverse-link transformation.

pred0_q

Predictive quantiles on the response scale at the prediction sites. Column structure is identical to pred_q. NULL when prediction sites are not supplied.

bands

Bandwidth values for each scale. The i-th bandwidth corresponds to the i-th column of the Z matrix.

Z

Predictive mean of the spatial process at each scale (sample sites; list).

Z_sd

Predictive standard deviation of the spatial process at each scale (sample sites; list).

Z0

Predictive mean of the spatial process at each scale (prediction sites; list).

Z0_sd

Predictive standard deviation of the spatial process at each scale (prediction sites; list).

other

Other internally used output objects.

Author(s)

Daisuke Murakami

References

Murakami, D., Comber, A., Yoshida, T., Tsutsumida, N., Brunsdon, C., & Nakaya, T. (2025). Coarse-to-fine spatial GLMMs for scalable prediction and multiscale analysis. *ArXiv preprint*, 2605.01157. https://doi.org/10.48550/arXiv.2605.01157

See Also

cf_glm_hv, sp_scalewise

Examples

################ Example 1: Count data modeling/Disease mapping/smoothing
set.seed(1234)
require( CARBayesdata )
require( sf )
data(pollutionhealthdata)
data(GGHB.IZ)

### Data
dat      <- pollutionhealthdata[pollutionhealthdata$year==2011,]
y        <- dat[,"observed"]             # count data
x        <- dat[,c("pm10","jsa","price")]
offset   <- log(dat[,"expected"])
coords   <- st_coordinates(st_centroid(GGHB.IZ))

### Holdout validation optimizing the number of spatial scales
mod_hv   <- cf_glm_hv(y = y, x = x, offset=offset, coords = coords, family=poisson())

### Spatial modeling and prediction
mod      <- cf_glm(y = y, x = x, coords = coords, mod_hv = mod_hv)
mod

### Mapping predictive mean and standard deviations (SD)
GGHB.IZ$y      <- y
GGHB.IZ$pred   <- mod$pred$pred
GGHB.IZ$pred_sd<- mod$pred$pred_sd
plot(GGHB.IZ[,c("pred")],lwd=0.2,axes=TRUE, key.pos=4,nbreaks=50)   # Predictive mean
plot(GGHB.IZ[,c("pred_sd")],lwd=0.2,axes=TRUE, key.pos=4,nbreaks=50)# Predictive SD

### Multiscale spatial pattern/feature extraction
mod_s1      <- sp_scalewise(mod,bw_range=c(4000,Inf)) # Large scale (4000 <= bandwidth)
mod_s2      <- sp_scalewise(mod,bw_range=c(0,4000))   # Small scale (bandwidth <= 4000)
GGHB.IZ$z1  <- mod_s1$pred$pred
GGHB.IZ$z2  <- mod_s2$pred$pred
plot(GGHB.IZ[,c("z1","z2")],lwd=0.2,axes=TRUE,key.pos=4, nbreaks=50)# Extracted features

### The same fit, explored interactively over a basemap
# spCFmap(mod, crs = 27700)   # crs = the system the coordinates are in


################ Example 2: Binary data modeling/spatial prediction
set.seed(1234)
require(sp); require(sf)
data(meuse)
data(meuse.grid)

### Data
y        <- ifelse(meuse$ffreq==1, 1, 0 )# binary data
coords   <- meuse[,c("x","y")]
x        <- meuse[,"dist"]

### Data at prediction sites
coords0  <- meuse.grid[,c("x","y")]
x0       <- meuse.grid[,"dist"]

### Holdout validation optimizing the number of spatial scales
mod_hv   <- cf_glm_hv(y = y, x = x, coords = coords, family=binomial())

### Spatial modeling and prediction
mod      <- cf_glm(y = y, x=x, coords = coords, x0=x0, coords0 = coords0,
                   mod_hv = mod_hv)
mod

### Mapping predictive mean and standard deviations (SD)
meuse.grid$pred   <- mod$pred0$pred
meuse.grid$pred_sd<- mod$pred0$pred_sd
meuse.grid_sf     <- st_as_sf(meuse.grid, coords = c("x","y"))
plot(meuse.grid_sf[,"pred"], pch = 15, cex = 0.8, nbreaks = 20)   # Predictive mean
plot(meuse.grid_sf[,"pred_sd"], pch = 15, cex = 0.8, nbreaks = 20)# Predictive SD

### Multiscale spatial pattern/feature extraction
mod_s1<- sp_scalewise(mod,bw_range=c(1000,Inf)) # Large scale (1000 <= bandwidth)
mod_s2<- sp_scalewise(mod,bw_range=c(0,1000))   # Small scale (0 <= bandwidth <= 1000)
meuse.grid_sf$z1    <- mod_s1$pred0$pred
meuse.grid_sf$z2    <- mod_s2$pred0$pred
plot(meuse.grid_sf[,c("z1","z2")], pch = 15,
     cex = 0.5, nbreaks = 20,axes=TRUE) # Predictive means

### The same fit, explored interactively over a basemap
# spCFmap(mod, crs = 28992)   # crs = the system the coordinates are in

Holdout validation for coarse-to-fine spatial generalized linear mixed models (CF-GLMMs)

Description

Trains CF-GLMMs and selects the number of spatial scales through sequential holdout validation.

Usage

cf_glm_hv(
  y,
  x = NULL,
  coords,
  offset = NULL,
  train_rat = 0.75,
  id_train = NULL,
  alpha = 0.9,
  kernel = "exp",
  family = gaussian(),
  seed = 1234
)

Arguments

Value

A list with the following elements:

loss_hv

Final deviance loss for validation samples.

loss_hv_all

Deviance losses obtained at each learning step.

id_train

ID of training samples.

other

Other internally used output objects.

Author(s)

Daisuke Murakami

References

Murakami, D., Comber, A., Yoshida, T., Tsutsumida, N., Brunsdon, C., & Nakaya, T. (2025). Coarse-to-fine spatial GLMMs for scalable prediction and multiscale analysis. *ArXiv preprint*, 2605.01157. https://doi.org/10.48550/arXiv.2605.01157

See Also

cf_glm

Coarse-to-fine spatial modeling (CFSM) for Gaussian response

Description

Scalable prediction, regression, and multiscale analysis via Gaussian CFSM.

Usage

cf_lm(
  y,
  x = NULL,
  coords,
  x0 = NULL,
  coords0 = NULL,
  mod_hv,
  robust_se = TRUE,
  se_type = c("prediction", "mean"),
  se_method = c("opt", "classic")
)

Arguments

Value

A list with the following elements:

beta

Regression coefficients, their standard errors, and the lower and upper limits of the 95 percent confidence intervals.

sd_summary

Standard deviation of the regression term (xb), spatial processes (spatial_scale1, spatial_scale2,...), additional learned components (effective if 'cf_lm_hv/add_learn' is not 'none'), and residuals.

e_summary

Holdout validation accuracy evaluated on the validation samples: R-squared (validation_R2), root mean squared error (validation_RMSE), and mean absolute error (validation_MAE).

pred

Predictive means and standard deviations (sample sites). When no additional learner is active, the spatial-process contribution to the predictive SD is rescaled by a holdout-calibrated factor (stored as other$tau) estimated on the validation samples.

pred0

Predictive means and standard deviations (prediction sites).

pred_q

Predictive quantiles at the sample sites (data.frame with columns q0.005, q0.025, ..., q0.975, q0.995). With add_learn = "rf"/"lightgbm" active, the combined predictive distribution is calibrated by total conformalized quantile regression (CQR) on the validation samples; otherwise the quantiles are Gaussian about the predictive mean using the (tau-calibrated) pred_sd. pred_sd is a Gaussian-equivalent summary of these quantiles.

pred0_q

Predictive quantiles at the prediction sites; identical column structure to pred_q. NULL when prediction sites are not supplied.

bands

Bandwidth values for each scale. The i-th bandwidth corresponding to the i-th column of the Z matrix.

Z

Predictive means of the single-scale processes at each scale, corresponding to each bandwidth value (sample sites; list).

Z_sd

Predictive standard deviation of the spatial processes at each scale (sample sites; list).

Z0

Predictive mean of the spatial process at each scale (prediction sites; list).

Z0_sd

Predictive standard deviation of the spatial process at each bandwidth (prediction sites; list).

other

Other internally used output objects.

Author(s)

Daisuke Murakami

References

Murakami, D., Comber, A., Yoshida, T., Tsutsumida, N., Brunsdon, C., & Nakaya, T. (2026). Coarse-to-fine spatial modeling: A scalable, machine-learning-compatible framework. *Geographical Analysis*, 58(2), e70034. https://onlinelibrary.wiley.com/doi/10.1111/gean.70034

See Also

cf_glm, cf_lm_hv, sp_scalewise

Examples

set.seed(123)
require(sp); require(sf)
data(meuse)
data(meuse.grid)

### Data
y        <- log(meuse[,"zinc"])
coords   <- meuse[,c("x","y")]
x        <- data.frame(dist   = meuse[,"dist"],
                       ffreq2 = as.integer(meuse$ffreq == 2),
                       ffreq3 = as.integer(meuse$ffreq == 3))

### Data at prediction sites
coords0  <- meuse.grid[,c("x","y")]
x0       <- data.frame(dist   = meuse.grid[,"dist"],
                       ffreq2 = as.integer(meuse.grid$ffreq == 2),
                       ffreq3 = as.integer(meuse.grid$ffreq == 3))

### Holdout validation optimizing the number of spatial scales
mod_hv   <- cf_lm_hv(y = y, x = x, coords = coords, add_learn = "none")

### Spatial modeling and prediction
mod      <- cf_lm(y = y, x = x, x0 = x0, coords = coords, coords0 = coords0,
                 mod_hv = mod_hv)
mod

### Mapping predictive mean and standard deviations (SD)
meuse.grid$pred   <- mod$pred0$pred
meuse.grid$pred_sd<- mod$pred0$pred_sd
meuse.grid_sf     <- st_as_sf(meuse.grid, coords = c("x","y"))
plot(meuse.grid_sf[,"pred"], pch = 15, cex = 0.5, nbreaks = 20)   # Predictive mean
plot(meuse.grid_sf[,"pred_sd"], pch = 15, cex = 0.5, nbreaks = 20)# Predictive SD

### Multiscale spatial pattern/feature extraction
mod_s1<- sp_scalewise(mod,bw_range=c(1000,Inf)) # Large scale (1000 <= bandwidth)
mod_s2<- sp_scalewise(mod,bw_range=c(500,1000)) # Middle scale (500 <= bandwidth <= 1000)
mod_s3<- sp_scalewise(mod,bw_range=c(0,500))    # Small scale (bandwidth <= 500)
z1    <- mod_s1$pred0$pred                      # Predictive mean
z2    <- mod_s2$pred0$pred
z3    <- mod_s3$pred0$pred
z1_sd <- mod_s1$pred0$pred_sd                   # Predictive SD
z2_sd <- mod_s2$pred0$pred_sd
z3_sd <- mod_s3$pred0$pred_sd
meuse.grid_sf3  <- cbind(meuse.grid_sf, z1, z2, z3, z1_sd, z2_sd, z3_sd)
plot(meuse.grid_sf3[,c("z1","z2","z3")], pch = 15,
     cex = 0.5, nbreaks = 20,key.pos=4,axes=TRUE) # Predictive means
plot(meuse.grid_sf3[,c("z1_sd","z2_sd","z3_sd")], pch = 15,
     cex = 0.5, nbreaks = 20,key.pos=4,axes=TRUE) # Predictive SD

### The same fit, explored interactively over a basemap
# spCFmap(mod, crs = 28992)   # crs = the system the coordinates are in

Holdout validation for the Gaussian coarse-to-fine spatial modeling (CFSM)

Description

Trains the CFSM-based Gaussian spatial regression and selects the number of spatial scales through sequential holdout validation.

Usage

cf_lm_hv(
  y,
  x = NULL,
  coords,
  train_rat = 0.75,
  id_train = NULL,
  alpha = 0.9,
  kernel = "exp",
  add_learn = "none",
  seed = 123
)

Arguments

Value

A list with the following elements:

sse_hv

Final sum-of-squared error (SSE) for validation samples.

sse_hv_all

SSEs obtained at each learning step.

id_train

ID of training samples.

other

Other internally used output objects.

Author(s)

Daisuke Murakami

References

Murakami, D., Comber, A., Yoshida, T., Tsutsumida, N., Brunsdon, C., & Nakaya, T. (2026). Coarse-to-fine spatial modeling: A scalable, machine-learning-compatible framework. *Geographical Analysis*, 58(2), e70034. https://onlinelibrary.wiley.com/doi/10.1111/gean.70034

See Also

cf_lm

Interactive mapping for coarse-to-fine spatial modelling

Description

Opens a Shiny web app for mapping CFSM results over a basemap. The function has two modes:

Usage

spCFmap(mod = NULL, crs = NULL, launch = TRUE, ...)

Arguments

Details

spCFmap()

Without mod, the full application is launched: models (cf_lm, cf_glm, cf_dglm, cf_downscale) are fitted inside the app from demo data (meuse, a space-time air-quality set, and an areal downscaling set) or from user CSV / GeoJSON uploads, and predictions can be exported as CSV or GeoJSON.

spCFmap(mod, crs)

With a fitted model, a small app maps that model directly. The layer (predictive mean / SD, covariate effect, or a scale-wise spatial component), colour scaling, and - for space-time or downscaling fits - the time range or bandwidth range are chosen interactively.

Value

If launch = TRUE, the value returned by runApp (invisibly); otherwise a shiny.appobj.

See Also

cf_lm, cf_glm, cf_dglm, cf_downscale, sp_scalewise

Examples

## Not run: 
spCFmap()                       # full app, opens in the browser
spCFmap(launch.browser = FALSE) # print the local URL instead

m <- cf_lm(y = y, x = x, x0 = x0, coords = coords, coords0 = coords0,
           mod_hv = cf_lm_hv(y = y, x = x, coords = coords))
spCFmap(m, crs = 28992)         # map an already-fitted model

## End(Not run)

Extract scale-wise spatial processes

Description

Evaluate mean and standard deviation of the (multiscale) spatial process for bandwidth values within a pre-specified range. For a spatio-temporal fit from cf_dglm, the process can additionally be averaged over a user-specified time range, returning the temporally averaged spatial process at each (sample / prediction) location.

Usage

sp_scalewise(mod, bw_range = c(0, Inf), time_range = c(-Inf, Inf))

Arguments

Value

A list with the following elements:

pred

Means and standard deviations of the spatial process at the sample sites. For a cf_dglm fit, one row per (unique) location with the temporally averaged process, together with its coordinates and the number of averaged time points.

pred0

The same at the prediction sites. NULL when mod was fitted without prediction sites, and also (with a warning) when no prediction site falls inside time_range.

Author(s)

Daisuke Murakami

See Also

cf_lm, cf_glm, cf_dglm