[R-sig-ME] multilevel time series?

[ONKELINX, Thierry]

Dear Malcolm,

Your design requires IMHO crossed random effects instead of nested
random effects. Individual is clearly crossed with year. Each individual
can be surveyed in more that one year and vice versa. If they were
nested, all data from a specific individual would come from only one
specific year. The same goes for state and year, they are rather crossed
than nested.

Fitting year as a crossed random effect will take nonstationarity along
time into account. The size of variance of this random effect will
indicate how strong this nonstationarity is.

HTH,

Thierry

------------------------------------------------------------------------
----
ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek
team Biometrie & Kwaliteitszorg
Gaverstraat 4
9500 Geraardsbergen
Belgium

Research Institute for Nature and Forest
team Biometrics & Quality Assurance
Gaverstraat 4
9500 Geraardsbergen
Belgium

tel. + 32 54/436 185
Thierry.Onkelinx at inbo.be
www.inbo.be

To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to
say what the experiment died of.
~ Sir Ronald Aylmer Fisher

The plural of anecdote is not data.
~ Roger Brinner

The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of
data.
~ John Tukey
  

> -----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
> 
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> R-sig-mixed-models at r-project.org mailing list 
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> 

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