mi() marks a predictor whose missing values should be handled by the
missing-data predictor model. Most fitted routes support one mi(x) term in
a univariate Gaussian location formula. Numeric missing predictors can use a
matching Gaussian fixed-effect, one random-intercept, or one intercept-only
structured predictor model supplied through impute, for example
impute = list(x = x ~ z) or
impute = list(x = x ~ z + relmat(1 | line, Q = Q)). Family-aware
fixed-effect predictor models supplied with impute_model() cover binary,
ordered categorical, unordered categorical, strict proportion, zero-one
boundary proportion, denominator-aware beta-binomial proportion, count,
positive continuous, and semi-continuous predictors. The non-Gaussian
response routes support one binary mi() predictor modelled by
family = binomial() for family = poisson(), binomial(), nbinom2(),
beta_family(), lognormal(), Gamma(link = "log"), student(), and
beta_binomial().
Details
Strict-proportion and zero-one boundary proportion mi() predictors
integrate the Beta prior with a fixed 15-node Gauss-Legendre rule. This is
not an adaptive rule or an accuracy guarantee for every Beta prior shape.
A successful fit warns with class drmTMB_mi_quadrature_inaccurate when the
estimated prior mean of a missing row is within 0.10 of 0 or 1. The warning
flags the limitation without changing the integration rule; treat that fit
as approximate. Absence of this warning does not certify quadrature accuracy.
Examples
bf(y ~ z + mi(x), sigma ~ 1)
#> <drm_formula>
#> y ~ z + mi(x)
#> sigma ~ 1