Statistical Modelling 10 (2010), 391419
Arbitrariness of models for augmented and coarse data, with emphasis on
incomplete data and random effects models
Geert Verbeke
Interuniversity Institute for Biostatistics and Statistical Bioinformatics,
Katholieke Universiteit Leuven
and
Universiteit Hasselt
Belgium
Geert Molenberghs
Interuniversity Institute for Biostatistics and Statistical Bioinformatics,
Katholieke Universiteit Leuven,
and
Universiteit Hasselt
Agovalaan 1,
BDiepenbeek
Belgium
eMail: geert.molenberghs@uhasselt.be
Abstract:
Statistical models often extend beyond the data available. First, in coarse
data, what is actually observed is less detailed than what might be, owing to
incompleteness, censoring, grouping, or a combination thereof. Second, in
augmented data, the observed data are hypothetically supplemented with random
effects, latent variables/classes, or component membership in mixture
distributions. The two settings together will be referred to as enriched
data. Reasons for modelling enriched data encompass mathematical and
computational convenience, advantages in interpretation, and substantive
plausibility. Models for enriched data combine evidence coming from empirical
data with unverifiable model components, resting entirely on assumptions.
This has acute consequences for enriched data, but knowledge about this issue
is somewhat scattered. We provide a unified framework for enriched data and
show, generally and with focus on incomplete-data models and random-effects
models on the other hand, that to any given model an entire class of models
can be assigned, with all of its members producing the same fit to the observed
data but arbitrary regarding the unobservable parts of the enriched data. The
concepts developed are illustrated using a clinical trial in toenail
dermatophyte onychomycosis and a developmental toxicity study conducted in
mice.
Keywords:
enriched data; exponential random effects; gamma random effects;
missing data model; linear mixed model
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