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First public version.
Raster, misaligned, and restricted-regression covariates
for the spatio-temporal model. SDALGCP2_ST() (and
sdalgcp(..., time =)) now accept rasters =
(intensity-scale continuous covariates), covariates =
(kriged covariates measured on a different support, with the Berkson
correction), and confounding = "restricted" (restricted
spatial regression against space-time confounding) — the same extensions
previously available only for spatial fits. The raster/misaligned fits
use a Gauss-Newton tilting loop around the Kronecker-free space-time
likelihood; the restricted fit reduces exactly to the spatial restricted
fit at T = 1.
Spatio-temporal prediction now returns a long
sf too. predict() on an
SDALGCP2_ST fit returns a one-row-per-region-time
sf (class "SDALGCP2_ST_pred") with the same
relative_risk/adjusted_rr columns as the
spatial predictor, so both can be mapped or st_write()-en
the same way; posterior draws are kept as attributes.
Bundled datasets. sdalgcp_data — a
small simulated sf of 64 regions (cases,
x1, pop) used by the help-page examples and
the intro vignette; and liver — a real example, incident
primary biliary cirrhosis counts by LSOA in North East England (Johnson
et al. 2019), for realistic case studies.
The introductory vignette now runs live on
sdalgcp_data (no precomputed figures), so it is
fully reproducible.
Runnable examples on the exported functions, all
using sdalgcp_data.
Prediction output is now an sf with clear
public-health column names. predict() returns an
sf (class "SDALGCP2_pred") you can map or
st_write() directly, with columns
relative_risk/relative_risk_se (the relative
risk exp(d'beta + S)) and
adjusted_rr/adjusted_rr_se (the
covariate-adjusted relative risk exp(S)). The previous
RR/ARR names are replaced everywhere
(plot(), exceedance(),
map_exceedance(), the spatio-temporal predictor) —
ARR was dropped because it conventionally means
absolute risk reduction in epidemiology. Posterior draws are
retained as object attributes so exceedance probabilities still work for
either quantity.
Kronecker-free spatio-temporal model
(SDALGCP2_ST()): separable space-time SDA-LGCP for counts
over the same regions at several times. The likelihood never forms the
(N*T)x(N*T) covariance, using
tr(Rs^-1 M Rt^-1 M') for the quadratic form and
N log|Rt| + T log|Rs| for the log-determinant (both
verified vs the brute-force Kronecker product). Spatial scale on a grid,
temporal Matern range estimated continuously (analytic gradient verified
vs numDeriv). No geoR.
Covariate-tilted raster model
(SDALGCP2_raster(tilt_spatial = TRUE)): rebuilds the
correlation from intensity-tilted weights with a log-normal aggregation
correction.
General Matern smoothness for the direct method:
corr_and_grad_cpp now provides closed-form phi-derivatives
for Matern kappa in {0.5, 1.5, 2.5}, so continuous-phi
(phi_method = "direct") estimation works for all three (was
exponential only). Derivatives verified against finite
differences.
Nugget / overdispersion term
(nugget = TRUE, with phi_method = "direct"):
fits covariance sigma2 (R(phi) + nu I) and estimates the
relative nugget nu = tau2/sigma2 with a standard error,
absorbing region-level overdispersion beyond the spatial structure.
Analytic gradient and Hessian (including the nugget and all cross terms)
verified against numerical differentiation.
Re-anchored (iterated) MCML
(reanchor =): re-simulates the latent field at the current
optimum and refits, keeping the importance weights near-uniform. On a
64-region example it lifts the effective sample size from ~0% to ~96%
and cuts the log-likelihood MC standard error ~100x, correcting the
variance estimate.
Importance-sampling diagnostics
(mc_diagnostics(), shown in summary()):
effective sample size of the importance weights at the optimum and a
Monte Carlo SE for the maximised log-likelihood; warns on
collapse.
Spatially continuous (raster) covariates
(SDALGCP2_raster()): covariates given as rasters enter the
LGCP intensity at the candidate-point level and are aggregated on the
intensity (exp) scale via a log-sum-exp offset
b_i(beta) = log sum_k w_ik exp(z(x_ik)'beta) – the correct
alternative to averaging the predictor over polygons (which is biased
under the log link). Fit by a Gauss-Newton fixed point reusing
mcml_fit(). On a sharp-peak covariate, naive areal
averaging is biased +67% while this recovers the truth to ~6%.
Continuous-phi (“direct”) estimation
(phi_method = "direct"): optimises the spatial scale
phi continuously inside the MCML objective instead of
profiling a grid, using analytic first/second derivatives of the
aggregated double integral (corr_and_grad_cpp). Gives a
genuine standard error for phi from the joint Hessian and
avoids grid-boundary artefacts; phi_method = "grid" stays
the default. Gradient and Hessian verified against numerical
differentiation. The full derivation is in
math/continuous-phi-derivation.pdf.
Post-fit visualisation & diagnostics: relative-risk /
uncertainty / exceedance maps, phi_profile(),
coef_plot(), model_check() (residual Moran’s
I), report().
C++ (RcppArmadillo + OpenMP) aggregated correlation assembly
(precompute_corr).
C++ Newton Laplace mode + adaptive MALA sampler
(laplace_sampling); reproducible given the same mode and
seed.
Vectorised, Cholesky-based Monte Carlo likelihood with analytic
gradient/Hessian (mcml_fit).
One-call spatial fit SDALGCP2() (points ->
correlation -> MCML).
Candidate-point generation sda_points() (SSI /
uniform / regular; sf + spatstat
Prediction predict.SDALGCP2() (discrete +
continuous) with an MCMC or a no-MCMC Laplace fast path;
exceedance() probabilities.
Vignette and reproducible benchmark scripts using entirely simulated data.
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.