Prior_Setup_GLMM()Prior_Setup_GLMM() is the mixed-model counterpart of
Prior_Setup() (Core 10). It calls
model_setup() (Core 20-S01), uses the classical reference
fit, and returns calibrated default priors for both
blocks of the hierarchy:
pop.* fields).
For each random coefficient \(k\): a
Normal prior on the group-level regression coefficients \(\gamma_k\) (the lme4 fixed
effects), a centre for the between-group variance \(\tau^2_k\), and a Gamma prior on the
precision \(1/\tau^2_k\) with a
truncation window.group.*
fields). For Gaussian models, a Gamma prior on the measurement
precision. It is either pooled (\(1/\sigma^2\)) or calibrated separately for
each group (\(1/\sigma^2_j\)).As with Prior_Setup(), the defaults are set up so the
priors carry a small, explicit fraction of the information in the
data.
Passed through to model_setup().
formula, data, family,
REML, control, start,
verbose, subset, weights,
na.action, offset, contrasts,
dispformula. These have the meanings described in Core
20-S01. One difference: when control = NULL and the family
is Gaussian, Prior_Setup_GLMM() uses
lmerControl(optimizer = "bobyqa") with a larger iteration
limit.
Block 2: priors on \(\gamma_k\). Supply at most one of
pop.pwt, pop.nprior and pop.sd.
Each can be a scalar, or a list with one element per random coefficient.
Each element can be a scalar or a vector with one value per column of
W[[k]].
| Argument | Default | Role |
|---|---|---|
pop.pwt |
NULL |
Prior weight \(w \in (0,1)\); prior
covariance = reference vcov × \((1-w)/w\) |
pop.pwt_default_low,
pop.pwt_default_high |
0.01, 0.05 |
Defaults for pop.pwt, chosen per coefficient by \(p_k < 14\) or \(p_k \ge 14\) |
pop.nprior |
NULL |
Effective prior sample size in group units, \(n = J\,w/(1-w)\) |
pop.sd |
NULL |
Prior standard deviations on the coefficient scale |
pop.intercept_source |
"null_model" |
Prior mean of the overall intercept: from a random-intercept-only fit, or from the full model |
pop.effects_source |
"null_effects" |
Prior means of all other \(\gamma\): zero, or from the full model |
pop.mu |
NULL |
Explicit prior means; overrides the two *_source
arguments for the coefficients supplied |
Block 2: priors on \(\tau^2_k\).
| Argument | Default | Role |
|---|---|---|
pop.dispersion.pwt /
pop.dispersion.nprior |
NULL |
Strength of the Gamma prior on \(1/\tau^2_k\) (at most one); derived from
pop.pwt when both are NULL |
pop.max_disp_perc |
0.99 |
Tail probability for the \(\tau^2_k\) truncation window (scalar or one per coefficient) |
Block 1: priors on \(\sigma^2\) (Gaussian only).
| Argument | Default | Role |
|---|---|---|
group.dispersion.pwt /
group.dispersion.nprior |
NULL (→ 0.01) |
Strength of the Gamma prior on the measurement precision (at most
one); group.dispersion.pwt may be a vector with one value
per group |
group.max_disp_perc |
0.99 |
Tail probability for the \(\sigma^2\) truncation window(s) (scalar or one per group) |
group.alpha_target |
0.01 |
Per-group dispformula only: target rate of
out-of-bounds Block 1 draws; searches for each group’s prior weight.
NULL disables the search. |
| Field(s) | Block | Content |
|---|---|---|
pop.prior_list |
2 | Named list, one entry per random coefficient: mu,
Sigma, dispersion (\(\hat\tau^2_k\) centre) |
pop.pwt, pop.nprior, pop.sd,
pop.mu |
2 | The values actually used, in the same shape the matching argument accepts |
pop.dispersion.pwt,
pop.dispersion.nprior |
2 | Strength of the \(\tau^2_k\) prior, one value per coefficient |
pop.ing_prior |
2 | One entry per coefficient: Gamma shape,
rate, disp_lower, disp_upper,
max_disp_perc |
pop.dispersion.ref |
2 | Classical \(\hat\tau^2_k\) from the reference fit (diagnostic) |
group.ing_prior |
1 | Pooled: one list (shape, rate,
disp_lower, disp_upper, …). Per group: a named
list with one entry per group |
group.dispersion |
1 | \(\hat\sigma^2\) centre (pooled
scalar or per-group vector), with a "source" attribute |
group.dispersion.pwt,
group.dispersion.nprior, group.max_disp_perc,
group.alpha_target, group.pwt_calibration |
1 | Block 1 prior strength, windows and (per group) the
alpha_target search table |
group.Sigma, group.tau_sd |
1 | Diagonal random-effect covariance \(\mathrm{diag}(\hat\tau^2_k)\) and its square roots |
group.dispersion.ref,
group.dispersion.fit |
1 | Per-group classical \(\hat\sigma^2_j\) and the
glmmTMB fit (per-group dispformula only) |
design, mer_fit, fit_ref,
calibration_source |
— | The model_setup() object, the lme4 fit,
the fit used for calibration and which one it was ("lme4"
or "glmmTMB") |
block_formula |
— | Within-group formula y ~ 1 + <random slopes> used
for Block 1 calibration |
formula, family, data,
dispformula, pop.intercept_source,
pop.effects_source |
— | Inputs |
This vignette uses the full-rank Big Word Club data from Core 20-S01.
data(big_word_club, package = "bayesrules")
dat <- big_word_club
dat$school_id <- factor(dat$school_id)
dat <- subset(
dat,
!is.na(score_ppvt) &
!is.na(invalid_ppvt) & invalid_ppvt == 0L &
complete.cases(dat[, c(
"score_ppvt", "distracted_a1", "distracted_ppvt",
"private_school", "title1", "free_reduced_lunch", "school_id"
)])
)
form_lmer <- score_ppvt ~
private_school + title1 + free_reduced_lunch +
distracted_ppvt + distracted_a1 +
free_reduced_lunch:distracted_a1 +
(1 + distracted_ppvt + distracted_a1 || school_id)
design0 <- model_setup(form_lmer, data = dat, fit_mer = FALSE)
dat <- subset(dat, school_id %in% names(design0$groupef.rank)[design0$groupef.rank])
dat$school_id <- droplevels(dat$school_id)dispformula = ~1)ps_pooled <- Prior_Setup_GLMM(form_lmer, data = dat, pop.pwt = 0.01)
ps_pooled
#> Call: Prior_Setup_GLMM()
#>
#> --- Setup ---
#> Model family, prior-mean sources, and reference fit used for calibration.
#>
#> family : gaussian (identity link)
#> pop.intercept_source : null_model
#> pop.effects_source : null_effects
#> dispformula : ~1
#> calibration_source : lme4 (fixef / tau^2_k / sd_tau)
#>
#> --- Group dispersion (sigma^2) ---
#> Pooled Gamma prior on sigma^2 is stored in group.ing_prior.
#> (dGamma_list() requires a per-group dispformula.)
#> group.dispersion : 388.8 [pooled S_marg (A12 3.3.4)]
#> classical lmer sigma^2 : 366.4 (diagnostic)
#>
#> --- Design check (from model_setup) ---
#> Identifiability flags copied from the design object (not re-checked here).
#>
#> Full-rank groups (algebraic D_j): 34 of 34 school_id
#> Full-rank & estimable : 34 of 34 full-rank (34 of 34 total school_id)
#>
#> --- Group-effect covariance (group.Sigma) ---
#> Diagonal Psi with entries tau^2_k for each group-effect coefficient.
#>
#> (Intercept) distracted_ppvt distracted_a1
#> (Intercept) 191.7847 0.0000 0.0000
#> distracted_ppvt 0.0000 26.0344 0.0000
#> distracted_a1 0.0000 0.0000 41.0503
#>
#> --- Population priors (pop.prior_list) ---
#> One prior list per group-effect coefficient (input to pfamily_list()).
#>
#> [(Intercept)]
#> pop.pwt : 0.01
#> pop.dispersion.pwt : 0.01 [derived from pwt]
#> pop.dispersion.nprior : 0.3434 (= J * pwt_disp / (1 - pwt_disp))
#>
#> mu:
#> (Intercept) private_school title1 free_reduced_lunch
#> 88.3756 0.0000 0.0000 0.0000
#>
#> Sigma:
#> (Intercept) private_school title1 free_reduced_lunch
#> (Intercept) 6154.4418 -6078.6768 733.5262 -84.0092
#> private_school -6078.6768 9380.4431 -738.9706 83.2363
#> title1 733.5262 -738.9706 10055.5989 -117.6066
#> free_reduced_lunch -84.0092 83.2363 -117.6066 2.4665
#>
#> dispersion : 159.1361 (tau^2_k; A12 3.3.4 marginal)
#> pop.dispersion.ref : 191.7847 (classical VarCorr / Psi)
#> ING tau^2 window : [91.58, 283.7] (0.01/0.99 limiting-posterior quantiles; upper/tau2 = 1.78)
#> ING shape, rate : 2.672, 266 (Gamma on 1/tau^2_k; for ptypes = "dIndependent_Normal_Gamma")
#>
#> [distracted_ppvt]
#> pop.pwt : 0.01
#> pop.dispersion.pwt : 0.01 [derived from pwt]
#> pop.dispersion.nprior : 0.3434 (= J * pwt_disp / (1 - pwt_disp))
#>
#> mu:
#> (Intercept)
#> 0
#>
#> Sigma:
#> (Intercept)
#> (Intercept) 306.4756
#>
#> dispersion : 6.7375 (tau^2_k; A12 3.3.4 marginal)
#> pop.dispersion.ref : 26.0344 (classical VarCorr / Psi)
#> ING tau^2 window : [3.877, 12.01] (0.01/0.99 limiting-posterior quantiles; upper/tau2 = 1.78)
#> ING shape, rate : 1.172, 1.157 (Gamma on 1/tau^2_k; for ptypes = "dIndependent_Normal_Gamma")
#>
#> [distracted_a1]
#> pop.pwt : 0.01
#> pop.dispersion.pwt : 0.01 [derived from pwt]
#> pop.dispersion.nprior : 0.3434 (= J * pwt_disp / (1 - pwt_disp))
#>
#> mu:
#> (Intercept) free_reduced_lunch
#> 0 0
#>
#> Sigma:
#> (Intercept) free_reduced_lunch
#> (Intercept) 1715.5404 -20.7836
#> free_reduced_lunch -20.7836 0.3412
#>
#> dispersion : 11.4785 (tau^2_k; A12 3.3.4 marginal)
#> pop.dispersion.ref : 41.0503 (classical VarCorr / Psi)
#> ING tau^2 window : [6.606, 20.47] (0.01/0.99 limiting-posterior quantiles; upper/tau2 = 1.78)
#> ING shape, rate : 1.672, 7.71 (Gamma on 1/tau^2_k; for ptypes = "dIndependent_Normal_Gamma")names(ps_pooled$pop.prior_list)
#> [1] "(Intercept)" "distracted_ppvt" "distracted_a1"
ps_pooled$pop.prior_list[["(Intercept)"]]$mu
#> (Intercept) private_school title1 free_reduced_lunch
#> 88.37564 0.00000 0.00000 0.00000
ps_pooled$pop.prior_list[["(Intercept)"]]$Sigma
#> (Intercept) private_school title1 free_reduced_lunch
#> (Intercept) 6154.44179 -6078.67680 733.5262 -84.009160
#> private_school -6078.67680 9380.44313 -738.9706 83.236339
#> title1 733.52621 -738.97062 10055.5989 -117.606611
#> free_reduced_lunch -84.00916 83.23634 -117.6066 2.466547Sigma is the reference fit’s covariance for the fixed
effects in W[["(Intercept)"]], scaled by \((1-w)/w\). This is the same convention
Prior_Setup() uses for single-level models. The prior mean
of the overall intercept comes from a random-intercept-only reference
fit, and the other means are zero (the defaults for
pop.intercept_source and
pop.effects_source).
The three ways of expressing prior strength are always returned with the values actually used. You can inspect them, edit one and pass it back:
ps_pooled$pop.nprior
#> $`(Intercept)`
#> (Intercept) private_school title1 free_reduced_lunch
#> 0.3434343 0.3434343 0.3434343 0.3434343
#>
#> $distracted_ppvt
#> (Intercept)
#> 0.3434343
#>
#> $distracted_a1
#> (Intercept) free_reduced_lunch
#> 0.3434343 0.3434343
ps_pooled$pop.sd[["distracted_a1"]]
#> (Intercept) free_reduced_lunch
#> 41.4190827 0.5841062np <- ps_pooled$pop.nprior
np[["(Intercept)"]][] <- 5
ps_np <- Prior_Setup_GLMM(form_lmer, data = dat, pop.nprior = np)
rbind(
default = ps_pooled$pop.sd[["(Intercept)"]],
nprior_5 = ps_np$pop.sd[["(Intercept)"]]
)
#> (Intercept) private_school title1 free_reduced_lunch
#> default 78.45025 96.85269 100.27761 1.5705244
#> nprior_5 20.56038 25.38333 26.28094 0.4116058Raising the effective prior sample size of the intercept regression from about \(0.01 J/0.99\) to 5 schools tightens those prior standard deviations. The other coefficients keep their defaults.
For Gaussian models, pop.prior_list[[k]]$dispersion is
not the classical \(\hat\tau^2_k\). It treats the reference
fit’s group coefficients \(\hat b_{\cdot
k}\) as data for the regression \(b_{\cdot k} \sim N(W_k\gamma_k, \tau^2_k
I_J)\) under the Normal prior above, and takes the marginal
variance centre returned by compute_gaussian_prior() (Core
10). The classical value is kept in pop.dispersion.ref:
rbind(
centre = sapply(ps_pooled$pop.prior_list, `[[`, "dispersion"),
classical = ps_pooled$pop.dispersion.ref
)
#> (Intercept) distracted_ppvt distracted_a1
#> centre 159.1361 6.73747 11.47851
#> classical 191.7847 26.03443 41.05029pop.ing_prior holds the Gamma prior on \(1/\tau^2_k\) used when
pfamily_list() builds independent Normal–Gamma priors (Core
20-S03). With \(n_0\) =
pop.dispersion.nprior and \(p_k\) = ncol(W[[k]]):
\[ \text{shape} = \frac{n_0 + 1 + p_k}{2}, \qquad \text{rate} = \hat\tau^2_k \,\frac{n_0 + p_k - 1}{2}, \]
so the implied prior mean of \(\tau^2_k\) equals the centre. The
truncation window (disp_lower, disp_upper)
comes from quantiles of the limiting posterior \(\Gamma\!\left(\tfrac{J+1}{2},
\hat\tau^2_k\tfrac{J-1}{2}\right)\). This window does not widen
as the prior gets weaker. See
system.file("ING_TRUNCATION_WINDOW.md", package = "glmbayesCore").
With dispformula = ~1, group.ing_prior
describes a single Gamma prior on \(1/\sigma^2\). Its centre
group.dispersion pools within-group marginal residual sums
of squares across schools (see Section 3, Stage 10). Its strength is
group.dispersion.pwt (default 0.01) relative to the total
number of observations.
ps_pooled$group.dispersion
#> [1] 388.8036
#> attr(,"source")
#> [1] "pooled S_marg (A12 3.3.4)"
#> attr(,"classical")
#> [1] 366.4058
str(ps_pooled$group.ing_prior[c("shape", "rate", "disp_lower", "disp_upper")])
#> List of 4
#> $ shape : num 4.02
#> $ rate : num 1174
#> $ disp_lower: num 117
#> $ disp_upper: num 1412dispformula = ~ school_id)With dispformula = ~ school_id (Gaussian only), each
school gets its own \(\sigma^2_j\).
model_setup() adds a glmmTMB reference fit
with a separate dispersion per school. That fit becomes the calibration
reference for every calibrated quantity
(calibration_source = "glmmTMB"), not just the Block 1
priors.
ps_group <- Prior_Setup_GLMM(
form_lmer,
data = dat,
pop.pwt = 0.01,
dispformula = ~school_id,
group.max_disp_perc = 0.8,
group.dispersion.pwt = 0.1,
group.alpha_target = NULL
)
ps_group$calibration_source
#> [1] "glmmTMB"group.ing_prior is now a named list with one entry per
school:
gi <- ps_group$group.ing_prior
fld <- function(nm) vapply(gi, function(e) {
v <- e[[nm]]
if (is.null(v)) NA_real_ else as.numeric(v)[1]
}, numeric(1))
head(data.frame(
n_j = fld("n_j"),
sigma2_hat = fld("sigma2_hat"),
shape_ING = fld("shape_ING"),
rate = fld("rate"),
disp_lower = fld("disp_lower"),
disp_upper = fld("disp_upper")
))
#> n_j sigma2_hat shape_ING rate disp_lower disp_upper
#> 2 12 1022.27935 2.666667 1703.7989 712.60456 1275.7680
#> 3 13 872.80487 2.722222 1503.1639 616.87100 1084.1978
#> 5 11 447.61608 2.611111 721.1592 307.23020 561.3532
#> 6 11 296.68442 2.611111 477.9916 203.63525 372.0705
#> 9 10 84.45595 2.555556 131.3759 56.96285 106.4661
#> 10 14 311.65922 2.777778 554.0608 223.02386 385.4533Three settings control these per-group priors:
group.dispersion.pwt: each school’s prior weight
relative to its own sample size \(n_j\). It may be one value per school.group.max_disp_perc: the tail probability for each
school’s window. Narrower windows usually raise the sampler’s acceptance
rate.group.alpha_target: when set (default 0.01), searches
for each school’s smallest prior weight that keeps the predicted rate of
Block 1 draws outside the sampler’s stable region below the target. It
only ever strengthens the prior relative to
group.dispersion.pwt. It runs a Monte Carlo calculation per
school, so it is disabled here to keep the example fast.For binomial(), poisson() and
Gamma(), the reference fit is glmer(). There
is no Block 1 measurement variance, so group.* dispersion
fields are NULL.
pop.prior_list[[k]]$dispersion is then the classical \(\hat\tau^2_k\).
Default hyperpriors need a converged reference fit, a fixed main
effect for every random slope, and \(\hat\tau^2_k > 0\) for every random
coefficient. Otherwise Prior_Setup_GLMM() stops with an
error that lists each problem. The usual fix is to add the missing fixed
effect or drop a random term whose variance is estimated at zero.
Prior_Setup_GLMM()The stages run in this order. Helper names are @noRd
internals unless marked “exported” or “internal doc”.
Prior_Setup_GLMM(formula, data, ..., pop.*, group.*)
│
├─ STAGE 1 argument checks
│ └─ check_pwt_scalar() (local), "at most one of" checks, family normalization,
│ default lmerControl(optimizer = "bobyqa")
│
├─ STAGE 2 design and reference fits
│ └─ model_setup() exported (S01)
│
├─ STAGE 3 choose the calibration reference
│ ├─ .lmebayes_dispformula_kind() "pooled" / "group"
│ ├─ .lmebayes_mer_convergence_issues(design$lmer) must be converged
│ └─ [dispformula = ~<group>]
│ ├─ .lmebayes_glmmtmb_convergence_issues(design$glmmTMB_fit)
│ ├─ extract_glmmtmb_variance_components() tau^2_k from glmmTMB
│ └─ .lmebayes_glmmtmb_group_sigma2() classical sigma^2_j
│
├─ STAGE 4 fixed effects and structural checks
│ ├─ .lmebayes_reference_fixef(fit_ref) gamma-hat (lme4 or glmmTMB)
│ ├─ .lmebayes_reference_vcov(fit_ref) Var(gamma-hat)
│ └─ fe_name_for() (local) map W[[k]] columns → fixef names;
│ stop if missing or tau^2_k = 0
│
├─ STAGE 5 resolve prior-strength arguments
│ ├─ .lmebayes_default_pwt_list() pop.pwt = NULL → 0.01 / 0.05 per k
│ ├─ .lmebayes_resolve_pwt() scalar/list → named list per k
│ ├─ .lmebayes_resolve_mu_override() ┐
│ ├─ .lmebayes_resolve_nprior_override() ├─ .lmebayes_resolve_override_list()
│ ├─ .lmebayes_resolve_sd_override() ┘
│ └─ .lmebayes_resolve_disp_prior() pop.dispersion.pwt <-> nprior
│
├─ STAGE 6 null intercept fit [pop.intercept_source = "null_model"]
│ ├─ lme4::lmer/glmer(y ~ 1 + (1 | g)) or .lmebayes_fit_glmmtmb_reference()
│ └─ .lmebayes_mer_convergence_issues() / .lmebayes_glmmtmb_convergence_issues()
│
├─ STAGE 7 Block 2 Normal priors → pop.prior_list[[k]]$mu, $Sigma
│ └─ Sigma_k = vcov[fe_k, fe_k] * outer(s, s), s = sqrt((1 - w) / w)
│
├─ STAGE 8 Block 2 tau^2_k centres [gaussian] → pop.prior_list[[k]]$dispersion
│ ├─ .lmebayes_block_formula_from_re() block_formula (used in Stage 10)
│ └─ for each k:
│ ├─ .lmebayes_reference_b_component() b-hat_.k from coef(fit_ref)
│ │ └─ .lmebayes_reference_coef()
│ └─ .lmebayes_compute_ing_prior_cal_tau2_hyper()
│ └─ compute_gaussian_prior() exported (Core 10)
│
├─ STAGE 9 Block 2 Gamma priors and windows → pop.ing_prior
│ ├─ .lmebayes_expand_scalar_or_vector(pop.max_disp_perc)
│ └─ .lmebayes_ing_limiting_posterior_window()
│
├─ STAGE 10 Block 1 sigma^2 priors [gaussian] → group.ing_prior, group.dispersion
│ ├─ .lmebayes_resolve_measurement_disp_prior() pooled strength (n-scale)
│ ├─ [pooled]
│ │ ├─ .lmebayes_pooled_measurement_smarg_from_groups()
│ │ │ └─ .lmebayes_measurement_group_smarg_cal() (each group, see below)
│ │ └─ .lmebayes_calibrate_ing_prior_measurement()
│ │ └─ .lmebayes_ing_prior_quantile_window()
│ └─ [per group]
│ ├─ .lmebayes_resolve_measurement_disp_prior_group() per-group strength
│ ├─ .lmebayes_expand_scalar_or_vector(group.max_disp_perc)
│ └─ .lmebayes_calibrate_ing_prior_measurement_group()
│ ├─ .lmebayes_measurement_group_smarg_cal() (each group)
│ ├─ .lmebayes_ing_prior_quantile_window()
│ └─ .lmebayes_ing_prior_list_from_cal()
│
│ .lmebayes_measurement_group_smarg_cal() shared by both branches
│ ├─ .lmebayes_ing_prior_measurement_group_glm_inputs() within-group lm, V0, sd
│ │ └─ .lmebayes_block_formula_prior_mu() Prior_Setup-style means
│ ├─ Omega_j[k,k] = W_j[[k]] Sigma_k W_j[[k]]' gamma uncertainty
│ └─ .lmebayes_compute_ing_prior_cal_from_sigma()
│ └─ compute_gaussian_prior()
│
├─ STAGE 11 group.alpha_target search [gaussian, per group, non-NULL target]
│ ├─ .lmebayes_calibrate_pwt_measurement_group()
│ │ ├─ .lmebayes_reference_fixef()
│ │ ├─ .lmebayes_ing_prior_quantile_window()
│ │ ├─ .two_block_truncated_omega_moments()
│ │ └─ stats::uniroot() per group
│ ├─ .lmebayes_resolve_measurement_disp_prior_group() with calibrated weights
│ └─ .lmebayes_calibrate_ing_prior_measurement_group() re-run with them
│
└─ STAGE 12 assemble the "Prior_Setup_GLMM" objectReference-fit accessors
(R/glmmtmb_reference_helpers.R). These hide the difference
between an lme4 fit and a glmmTMB fit, so
Stages 4–11 work unchanged for both.
| Helper | Role |
|---|---|
.lmebayes_dispformula_kind() |
Validates dispformula; returns "pooled" or
"group" |
.lmebayes_fit_glmmtmb_reference() |
Fits glmmTMB() with the given dispformula
(also used for the null fit in Stage 6) |
.lmebayes_glmmtmb_convergence_issues() |
Convergence code and Hessian checks for a glmmTMB
fit |
.lmebayes_reference_fixef(),
.lmebayes_reference_vcov(),
.lmebayes_reference_coef() |
Conditional-model fixef(), vcov(),
coef() from either fit type |
extract_glmmtmb_variance_components() (internal
doc) |
Psi (\(\hat\tau^2_k\))
from a glmmTMB fit, aligned with
groupef.names |
.lmebayes_glmmtmb_group_sigma2() |
Per-group classical \(\hat\sigma^2_j\) from the dispersion model |
Argument resolvers
(R/Prior_Setup_GLMM.R,
R/mer_prior_helpers.R)
| Helper | Role |
|---|---|
.lmebayes_default_pwt_list() |
Default pop.pwt per coefficient:
pop.pwt_default_low if \(p_k <
14\), else pop.pwt_default_high |
.lmebayes_resolve_pwt() |
Validates pop.pwt and converts it to a named list of
named vectors aligned with W[[k]] columns |
.lmebayes_resolve_override_list() |
Shared resolver for list-shaped overrides (NULL
elements keep defaults) |
.lmebayes_resolve_mu_override(),
.lmebayes_resolve_nprior_override(),
.lmebayes_resolve_sd_override() |
pop.mu, pop.nprior, pop.sd
through the shared resolver |
.lmebayes_resolve_disp_prior() |
Converts between pop.dispersion.pwt and
pop.dispersion.nprior (\(n_k = J
w_k/(1-w_k)\)); default from mean pop.pwt |
.lmebayes_expand_scalar_or_vector() |
“Scalar or one value per unit” expander for
*.max_disp_perc (also used by
dGamma_list()) |
.lmebayes_resolve_measurement_disp_prior() |
Pooled Block 1 strength: \(n_{\mathrm{prior}} = w/(1-w)\,n\) |
.lmebayes_resolve_measurement_disp_prior_group() |
Per-group Block 1 strength: \(n_{\mathrm{prior},j} = w_j/(1-w_j)\,n_j\) |
.lmebayes_ing_prior_is_grouped() |
Tells the pooled and per-group shapes of
group.ing_prior apart (used by print and
dGamma_list()) |
Dispersion calibration
(R/mer_prior_helpers.R)
| Helper | Role |
|---|---|
.lmebayes_block_formula_from_re() |
Builds the within-group formula
y ~ 1 + <random slopes> |
.lmebayes_reference_b_component() |
Group coefficients \(\hat b_{\cdot
k}\) (one per group, in level order) from
coef(fit_ref) |
.lmebayes_compute_ing_prior_cal_tau2_hyper() |
Block 2 \(\hat\tau^2_k\) centre:
OLS of \(\hat b_{\cdot k}\) on \(W_k\), then
compute_gaussian_prior() with the Stage 7 prior |
.lmebayes_ing_limiting_posterior_window() |
\(\tau^2_k\) window from limiting-posterior Gamma quantiles |
.lmebayes_ing_prior_measurement_group_glm_inputs() |
One group’s within-group regression inputs: design, response, OLS
covariance \(V_0\), and prior standard
deviations from group.tau_sd |
.lmebayes_block_formula_prior_mu() |
Prior_Setup()-style prior means on one group’s
data |
.lmebayes_measurement_group_smarg_cal() |
Per-group prior covariance plus \(\Omega_j\) (uncertainty in \(\gamma\) carried through group \(j\)’s row of each \(W_k\)), then
compute_gaussian_prior() |
.lmebayes_compute_ing_prior_cal_from_sigma() |
Thin wrapper calling compute_gaussian_prior() with the
group inputs |
.lmebayes_pooled_measurement_smarg_from_groups() |
Pooled \(\hat\sigma^2 = \sum_j S_{\mathrm{marg},j} / (n - J p_{\mathrm{re}})\); falls back to intercept-only residuals for a group whose within-group design is singular |
.lmebayes_calibrate_ing_prior_measurement() |
Pooled Block 1 Gamma shape/rate matched to
the pooled centre, plus window |
.lmebayes_calibrate_ing_prior_measurement_group() |
Per-group Block 1 calibration: sigma2_hat,
shape_ING, rate, n_j, window,
max_disp_perc for each group |
.lmebayes_ing_prior_list_from_cal() |
Packs one group’s compute_gaussian_prior() output into
its group.ing_prior entry |
.lmebayes_ing_prior_quantile_window() |
disp_lower/disp_upper from Gamma quantiles
at a given tail probability |
.lmebayes_print_ing_prior_measurement_group_compare() |
Developer diagnostic; not called by
Prior_Setup_GLMM() |
group.alpha_target search
(R/pwt_measurement_group_calibration.R)
| Helper | Role |
|---|---|
.lmebayes_calibrate_pwt_measurement_group() |
For each group, simulates the Block 1 draw distribution and uses
uniroot() to find the smallest prior weight meeting the
target. The result is never below the supplied weight; it also returns
the table stored as group.pwt_calibration |
.two_block_truncated_omega_moments() |
Mean and variance of a truncated Gamma precision, used by the search criterion |
| Returned field | Produced in stage |
|---|---|
design, mer_fit |
2 |
fit_ref, calibration_source,
group.dispersion.ref,
group.dispersion.fit |
3 |
pop.pwt, pop.nprior, pop.sd,
pop.mu, pop.dispersion.pwt,
pop.dispersion.nprior |
5, 7 |
pop.prior_list[[k]]$mu, $Sigma |
6, 7 |
pop.prior_list[[k]]$dispersion,
block_formula |
8 |
pop.dispersion.ref, group.Sigma,
group.tau_sd |
3, 8 |
pop.ing_prior, pop.max_disp_perc |
9 |
group.ing_prior, group.dispersion,
group.dispersion.pwt, group.dispersion.nprior,
group.max_disp_perc |
10, 11 |
group.alpha_target,
group.pwt_calibration |
11 |
Core 20-S03 converts ps_pooled and ps_group
into pfamily objects with pfamily_list() and
dGamma_list().