[R-sig-ME] multilevel cross-correlation model

[Олег Бурский]

Dear masters! I study the influence of climate change on the bird community
of 45 species over 31 years. Most species show a positive population trend,
which should be driven by two climatic factors, A and W, in two ways:
directly here and now and indirectly via broad ecosystem productivity with
~10-year lag. To prove that as the cause of the trends, I fit
log-transformed detrended standardized population abundance X with lmer
(lme4 R):

M <- lmer (X ~ 0 + (0 + Xo | S) + Xo : fRepr +
            (A0 + … + A12 + W0 + … + W12) : fGroup, data = data2, REML = F),

where Xo is previous year abundance, Xo | S is species-specific AR(1)-like
autocorrelation due to density dependence, Xo : fRepr is data dependence on
2-level representativeness of the study plot to the regional population
likely influencing density dependence, A0 … W12 are detrended standardized
climatic variables A and W with lag 0 to 12 years each, and fGroup is
3-level grouping of species by life-history traits.

It works, but several problems still exist:
1.       Climate variables consume much df and yield odd beta estimates
depending on the number of A and W lags (i.e. lagged variables) in the
model:
No. of lags      AIC    Approx.aver. |beta|   Approx.aver. |t|
…                     …                      …                      …
  8                    3670                 ~0.1                    ~2
  9                    3667                 ~0.1                    ~2
10                    3669                 ~0.1                   ~1.5
11                    3672                 ~0.1                    ~1
12                    3656                 ~0.8                   ~3.5
13                    3660                 ~1.2                   ~0.3
14                   Rank deficiency…

That is, long lags seem to be influential, but the model structure is
getting unstable.
2.       Species differ by mean abundance for two orders of magnitude, and
their contribution to the model should be weighted by square root of
abundance, which is incompatible with lmer.
3.       I am not sure with correctness of applying Xo|S term instead of
AR(1), though it is more supported by AIC and compatible with other terms
in lmer model.
4.       I doubt the overall model structure. There are 31 years of
observations on abundance (or 30 after Xo is subtracted) for each species,
though climate predictors of 40-50 years could influence. How can I arrange
them together without NAs? Perhaps there is a way to represent climatic
variables as something like …A0 + W0 + A1 + W1 + crosscorrelation (A
lagged) + crosscorrelation (W lagged) in any package other than lme4, which
explores short multilevel time series.
Any advice would be highly appreciated. The DataFile is attached.
Oleg Bourski