-----Oorspronkelijk bericht-----
Van: r-sig-mixed-models-bounces at r-project.org
[mailto:r-sig-mixed-models-bounces at r-project.org] Namens
Malcolm Fairbrother
Verzonden: zondag 26 september 2010 21:18
Aan: r-sig-mixed-models at r-project.org
Onderwerp: [R-sig-ME] multilevel time series?
Dear all,
In macro-social science, it's become fairly conventional to
analyse repeated cross-sectional survey data using
three-level models. Individual survey espondents (level-1)
are nested in state-years (level-2), which are in turn nested
within states (level-3). One big pay-off is the ability to
examine how time-constant or time-varying state-level
variables affect level-1 outcomes.
A co-author and I recently had a reviewer question whether
this approach is adequate, however. He/she suggested that
this approach could generate very misleading results, if the
data are nonstationary. (We just included a linear time
effect in our models.) So I'm thinking about how to proceed
(and I'm not particularly knowledgeable about time series
analysis). Any advice would be much appreciated. We used lme4
to fit the models in our paper, and we have several tens of
thousands of respondents nested in 48 states, each observed
about 15 or 16 times over about a 30-year period.
(1) Is the reviewer's query? Is he/she right to question this
approach?
(2) How might we test for nonstationarity? The reviewer
mentioned differencing the outcome variable, but in a
multilevel context I'm not sure how to do that... Perhaps we
could calculate an *aggregate* value for every state-year,
and check the aggregated data for autocorrelation? My
understanding is that autocorrelation across multiple lags is
a strong indicator of nonstationarity (while, conversely, the
absence of multiple-lag autocorrelation is almost a guarantee
of stationarity). I believe this can be done with nlme, as a
two-level model, with state-years nested within states.
(3) However, that approach would seem to throw away a lot of
level-1 information (about individual respondents), and I'm
not sure about the implications for any significance tests.
An alternative approach would seem to be "multilevel time
series", where autocorrelation at the *group* rather than
individual/first level is specifically allowed for in the
model. However, I can't find any references to R packages (or
other software) that allow for the specification of, for
example, AR1 processes at anything other than level-1 in
multilevel models.
In short, I'd be curious to hear what people think...
(especially if anyone out there happens to be a whiz at both
multilevel and time series analysis). I hope I've been clear
about the problem, but I'm happy to elaborate. Thanks in
advance for any help.
Cheers,
Malcolm
Dr Malcolm Fairbrother
Lecturer
School of Geographical Sciences
University of Bristol