Rendered checks
The small example below is only a guide to the output grain. The
coordinate surface is fitted in the location predictor mu;
raw response values remain on the response scale and should not be
plotted as if they were spatial SDs or correlations.
spatial_example <- simulate_spatial_guide_data()
spatial_dat <- spatial_example$data
coords <- spatial_example$coords
fit_spatial <- drmTMB(
drm_formula(
y ~ depth + temp + spatial(1 | site, coords = coords),
sigma ~ depth
),
family = gaussian(),
data = spatial_dat
)
fit_spatial_slope <- drmTMB(
drm_formula(
y ~ depth + temp + spatial(1 + depth | site, coords = coords),
sigma ~ depth
),
family = gaussian(),
data = spatial_dat
)if (requireNamespace("ggplot2", quietly = TRUE)) {
spatial_effect <- ranef(fit_spatial, "spatial_mu")$terms[[1]]
spatial_field <- data.frame(
site = names(spatial_effect),
fitted_spatial_deviation = unname(spatial_effect),
coords[names(spatial_effect), , drop = FALSE],
row.names = NULL
)
field_limit <- max(abs(spatial_field$fitted_spatial_deviation))
if (!is.finite(field_limit) || field_limit == 0) field_limit <- 1
ggplot2::ggplot(
spatial_field,
ggplot2::aes(
x = x,
y = y,
fill = fitted_spatial_deviation
)
) +
ggplot2::geom_hline(yintercept = 0, colour = "grey90", linewidth = 0.4) +
ggplot2::geom_vline(xintercept = 0, colour = "grey90", linewidth = 0.4) +
ggplot2::geom_point(
shape = 21,
size = 7,
colour = "grey20",
stroke = 0.35
) +
ggplot2::scale_fill_gradient2(
low = "#D55E00",
mid = "white",
high = "#009E73",
midpoint = 0,
limits = c(-field_limit, field_limit),
name = "Fitted\nspatial deviation"
) +
ggplot2::coord_equal() +
spatial_guide_theme() +
ggplot2::labs(
title = "Fitted spatial location field",
subtitle = "Conditional fitted deviations; uncertainty not shown",
x = "Coordinate x",
y = "Coordinate y"
)
}
Simulated example of coordinate-spatial fitted site deviations from
ranef(fit_spatial, "spatial_mu"). Points are conditional
location-effect estimates; uncertainty is not shown.
Spatial intercept and slope SDs have different units, so placing them on one quantitative axis would imply a comparison that is not meaningful. The compact display below reports each estimate in its own unit instead.
spatial_sd <- data.frame(
Component = c("Spatial intercept SD", "Spatial depth-slope SD"),
Estimate = formatC(
summary(fit_spatial_slope)$parameters[
match(
c("sd:mu:spatial(1 | site)", "sd:mu:spatial(0 + depth | site)"),
summary(fit_spatial_slope)$parameters$parm
),
"estimate"
],
digits = 4,
format = "g"
),
Unit = c("Response units", "Response units per depth unit"),
Status = c(
"Point estimate; interval not validated",
"Near-zero boundary; interval not validated"
),
check.names = FALSE
)
knitr::kable(spatial_sd, align = c("l", "r", "l", "l"))| Component | Estimate | Unit | Status |
|---|---|---|---|
| Spatial intercept SD | 0.3808 | Response units | Point estimate; interval not validated |
| Spatial depth-slope SD | 4.396e-06 | Response units per depth unit | Near-zero boundary; interval not validated |
For the exact fixed-kappa bivariate Gaussian location model, the
calibrated M rung has 36 sites with three complete
response pairs per site and the baseline ring geometry. Native REML for
this cell requires unit weights, intercept-only sigma1,
sigma2, and rho12, no known
meta_V() covariance, and no additional ordinary random
effect, direct-SD formula, or corpair() regression.
spatial_q2_example <- simulate_spatial_q2_guide_data()
spatial_q2_dat <- spatial_q2_example$data
spatial_q2_coords <- spatial_q2_example$coords
fit_spatial_q2_example <- drmTMB(
drm_formula(
mu1 = y1 ~ x1 + spatial(1 | p | site, coords = spatial_q2_coords),
mu2 = y2 ~ x2 + spatial(1 | p | site, coords = spatial_q2_coords),
sigma1 = ~ 1,
sigma2 = ~ 1,
rho12 = ~ 1
),
family = biv_gaussian(),
data = spatial_q2_dat,
REML = TRUE,
control = drm_control(
optimizer = list(eval.max = 1000L, iter.max = 1000L),
fallback_optimizer = "BFGS"
)
)The fixed seed is the first retained M-rung baseline-ring smoke dataset. It keeps this tutorial fit reproducible without re-running the coverage campaign.
The prospective campaign retained every attempted dataset. At M, all-attempt coverage was 0.938, 0.932, and 0.938 for the first spatial SD, second spatial SD, and latent spatial correlation; finite-profile rates were 1.000, 1.000, and 0.986. The higher H rung (36 sites x 8 observations) also passed jointly. The smaller L rung (12 x 3) failed and is not part of the interval claim.
spatial_q2_targets <- c(
"sd:mu:mu1:spatial(1 | p | site)",
"sd:mu:mu2:spatial(1 | p | site)",
"cor:spatial:cor(mu1:(Intercept),mu2:(Intercept) | p | site)"
)
spatial_q2_profile <- stats::confint(
fit_spatial_q2_example,
parm = spatial_q2_targets,
method = "profile",
profile_engine = "endpoint"
)
spatial_q2_target_table <- profile_targets(fit_spatial_q2_example)
spatial_q2_estimate <- spatial_q2_target_table$estimate[
match(spatial_q2_targets, spatial_q2_target_table$parm)
]
spatial_q2_eye <- data.frame(
target = factor(
c(
"Spatial SD: response 1",
"Spatial SD: response 2",
"Latent spatial correlation"
),
levels = c(
"Spatial SD: response 1",
"Spatial SD: response 2",
"Latent spatial correlation"
)
),
estimate = unname(spatial_q2_estimate),
lower = spatial_q2_profile$lower,
upper = spatial_q2_profile$upper
)
spatial_q2_eye_region <- do.call(
rbind,
lapply(seq_len(nrow(spatial_q2_eye)), function(i) {
eye_x <- seq(
spatial_q2_eye$lower[i],
spatial_q2_eye$upper[i],
length.out = 101
)
left_width <- max(
spatial_q2_eye$estimate[i] - spatial_q2_eye$lower[i],
.Machine$double.eps
)
right_width <- max(
spatial_q2_eye$upper[i] - spatial_q2_eye$estimate[i],
.Machine$double.eps
)
taper <- ifelse(
eye_x <= spatial_q2_eye$estimate[i],
(eye_x - spatial_q2_eye$lower[i]) / left_width,
(spatial_q2_eye$upper[i] - eye_x) / right_width
)
half_height <- 0.10 * sqrt(pmax(taper, 0))
data.frame(
target = spatial_q2_eye$target[i],
eye_x = c(eye_x, rev(eye_x)),
eye_y = c(half_height, rev(-half_height))
)
})
)The Confidence Eye treats each interval as a small pale tapered region and marks the estimate with a hollow circle. The eye’s horizontal span is the interval; there is no separate interval bar. Separate facet scales keep standard deviations and correlation on their own units.
if (requireNamespace("ggplot2", quietly = TRUE)) {
ggplot2::ggplot(spatial_q2_eye) +
ggplot2::geom_vline(
data = data.frame(
target = factor(
"Latent spatial correlation",
levels = levels(spatial_q2_eye$target)
),
zero = 0
),
ggplot2::aes(xintercept = zero),
inherit.aes = FALSE,
linetype = "dotted",
linewidth = 0.5,
colour = "grey55"
) +
ggplot2::geom_polygon(
data = spatial_q2_eye_region,
ggplot2::aes(
x = eye_x,
y = eye_y,
group = target,
fill = target
),
inherit.aes = FALSE,
alpha = 0.24,
colour = NA
) +
ggplot2::geom_point(
ggplot2::aes(
x = estimate,
y = 0,
colour = target
),
shape = 21,
fill = "white",
size = 4.2,
stroke = 1.2
) +
ggplot2::facet_wrap(~target, scales = "free_x", nrow = 1) +
ggplot2::scale_x_continuous(
expand = ggplot2::expansion(mult = c(0.20, 0.20))
) +
ggplot2::scale_y_continuous(
NULL,
breaks = NULL,
limits = c(-0.22, 0.32),
expand = c(0, 0)
) +
ggplot2::scale_fill_manual(
values = c(
"Spatial SD: response 1" = "#0072B2",
"Spatial SD: response 2" = "#D55E00",
"Latent spatial correlation" = "#009E73"
),
guide = "none"
) +
ggplot2::scale_colour_manual(
values = c(
"Spatial SD: response 1" = "#0072B2",
"Spatial SD: response 2" = "#D55E00",
"Latent spatial correlation" = "#009E73"
),
guide = "none"
) +
ggplot2::labs(
x = "Target value (facet-specific scale)",
title = "Profile uncertainty for the calibrated spatial q2 target set",
subtitle = "Each eye is a 95% endpoint profile interval; hollow circle marks the estimate"
) +
ggplot2::theme_minimal(base_size = 12) +
ggplot2::theme(
panel.grid.major.x = ggplot2::element_line(
colour = "grey90",
linewidth = 0.35
),
panel.grid.major.y = ggplot2::element_blank(),
panel.grid.minor = ggplot2::element_blank(),
panel.spacing.x = grid::unit(1.3, "lines"),
strip.text = ggplot2::element_text(face = "bold"),
plot.title.position = "plot"
)
}
Confidence Eye for the three direct fixed-kappa Gaussian q2 spatial targets at the tested M rung (36 sites x 3 observations, baseline ring geometry). Each coloured pale eye spans a 95% endpoint profile-likelihood interval; the larger hollow circle is the point estimate. Calibration passed jointly at the exact M and H rungs and failed at L.
This result supports inference_ready_with_caveats only
for the exact tested M/H fixed-kappa ring configurations. It does not
establish mesh intervals, estimated range, spatial slopes, q4+,
non-Gaussian spatial models, spatial scale models, derived observed
correlations, geometry robustness, or the supported
tier.