Statistical Modelling 21 (6) (2021), 479519
Streamlined variational inference for higher level group-specific curve models
M. Menictas,
School of Mathematical and Physical Sciences,
University of Technology Sydney,
Ultimo,
Australia.
T.H. Nolan,
School of Mathematical and Physical Sciences,
University of Technology Sydney,
Ultimo;
Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers,
The University of Melbourne,
Parkville,
Australia.
D.G. Simpson,
Department of Statistics,
University of Illinois at Urbana-Champaign,
Champaign,
Illinois,
United States of America.
M.P. Wand,
School of Mathematical and Physical Sciences,
University of Technology Sydney,
Ultimo;
Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers,
The University of Melbourne,
Parkville,
Australia.
e-mail: matt.wand@uts.edu.au
Abstract:
A two-level group-specific curve model is such that the mean
response of each member of a group is a separate smooth function
of a predictor of interest. The three-level extension is such
that one grouping variable is nested within another one,
and higher level extensions are analogous. Streamlined variational
inference for higher level group-specific curve models is a
challenging problem. We confront it by systematically working
through two-level and then three-level cases and making use of
the higher level sparse matrix infrastructure laid down in
Nolan and Wand (2020). A motivation is analysis of data from
ultrasound technology for which three-level group-specific curve
models are appropriate. Whilst extension to the number of levels exceeding
three is not covered explicitly, the pattern established by our
systematic approach sheds light on what is required for even
higher level group-specific curve models.
Keywords:
approximate Bayesian inference, longitudinal data analysis, multilevel models, panel data,
mean field variational Bayes
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