Fit the one-stage hierarchical model for SAD validation

Fits a single mixed model to all severity estimates of a SAD validation study, instead of first summarising each rater by Lin's statistics. The model describes how the mean estimate, the variation among raters and the residual variation change along the severity range in each condition.

Usage

sad_fit(
  x,
  structure = c("auto", "full", "noim", "sep", "base"),
  dispersion = c("quad", "lin"),
  family = c("gaussian", "ordbeta"),
  center = 10,
  scale = 10
)

Arguments

x

An object returned by sad_data().

structure

Random-effects structure for raters. "auto" (default) tries "full", "noim", "sep" and "base" in this order and keeps the first that converges with a positive definite Hessian and finite standard errors. See Details.

dispersion

Model for the residual variance: "quad" (default), a quadratic function of severity in each condition, which allows larger errors at intermediate severity; or "lin", a log-linear function.

family

"gaussian" (estimates in %) or "ordbeta" (ordered beta regression on the 0-1 scale, which handles the bounds at 0 and 100% and accepts exact zeros and ones). "ordbeta" is useful as a sensitivity analysis.

center, scale

Severity is entered as z = (actual - center) / scale. The defaults (10% and 10 percentage points) give intercepts that refer to 10% severity and help convergence.

Value

An object of class sad_fit: a list with the model, the structure used, the data (with z), center, scale, family, dispersion, conditions and methods.

Details

The mean model is estimate ~ z * condition, so each condition has its own intercept (bias at center) and slope (calibration). Random-effects structures:

full

(0 + method + method:z | rater) + (1 | image) + (1 | image:condition): a random intercept and slope per rater and method, all correlated, an image effect (intrinsic difficulty) and an image x condition effect.

noim

as full without the image x condition effect.

sep

(0 + method | rater) + (0 + method:z | rater) + (1 | image): intercepts and slopes uncorrelated.

base

(1 + z | rater) + (1 | image): rater effects common to all methods.

The dispersion formula is ~ condition * (z + I(z^2)) or ~ condition * z. Models are fitted with glmmTMB::glmmTMB().

See also

sad_curve(), sad_raters(), sad_images(), sad_compare()

Examples

# \donttest{
if (requireNamespace("glmmTMB", quietly = TRUE)) {
  x <- sad_data(SADRustSoybean, wide = c(UN = "unaided", SAD = "aided"), group = "sad")
  fit <- sad_fit(x)
  fit
}
#> Structure 'full' did not converge; trying the next one.
#> Structure 'noim' did not converge; trying the next one.
#> One-stage model for SAD validation
#>   family: gaussian | dispersion: quad | rater structure: sep
#>   severity centred at 10%, in units of 10 percentage points
#>   40 raters, 50 images, 4000 estimates; conditions: UN_Old, UN_New, SAD_Old, SAD_New
#>   AIC = 28896.6
# }