[R-sig-Geo] regression with Moran eigenvectors for multiple

[Thomas Young]

Many thanks Roberto for these very helpful references and R code.
They are just what I am looking for and much appreciated. It is interesting
that such approaches don't seem very common.

Thank you again,
Thomas

On Tue, Jun 5, 2018 at 9:57 AM, Roberto Patuelli <roberto.patuelli using unibo.it>
wrote:

> Dear Thomas,
>
> I've worked with Moran eigenvectors.
> In some previous papers, I've used panel data with it.
>
> In this article
>
> Patuelli, R., D.A. Griffith, M. Tiefelsdorf and P. Nijkamp (2011). Spatial
> Filtering and Eigenvector Stability: Space-Time Models for German
> Unemployment Data. International Regional Science Review 34 (2): 253-80.
> R code: https://sites.google.com/Desktop/RPDGMTPN2011IRSR_(R_code).zip.
>
> I obtained a filter for each year and examined common eigenvectors.
>
> In this further article
>
> Patuelli, R., N. Schanne, D.A. Griffith and P. Nijkamp (2012). Persistence
> of Regional Unemployment: Application of a Spatial Filtering Approach to
> Local Labor Markets in Germany. Journal of Regional Science 52 (2): 300-23.
>
> I instead estimated dynamic panels (LSDV) using spatial filters as
> substitutes of fixed effects (in addition to using them for heterogeneous
> coefficients). I can provide you with me code for this article too, if you
> want.
>
> Best regards,
> Roberto Patuelli
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Mon, 4 Jun 2018 06:12:00 -0700
> From: Thomas Young <thomasyoungca using gmail.com>
> To: r-sig-geo using r-project.org
> Subject: [R-sig-Geo] regression with Moran eigenvectors for multiple
>         years of data
> Message-ID:
>         <CAMJGZtxbhE7ES8XPBgxqGmLsu0q--iid+nB1ysa8BG2fd4RpVA using mail.
> gmail.com>
> Content-Type: text/plain; charset="utf-8"
>
> Hello,
>
> I think this is mostly a statistics question with possibly some R details.
> Any feedback is appreciated.
>
> I have several years of spatial biological sampling data in the same
> region but the number and locations of sites vary across year.  Very strong
> spatial autocorrelation is present in the data.
>
> I want to construct a regression model using Moran' eigenvectors as
> explanatory variables to account for SAC. For example,
>
> y_ijk=intercept+x1_ijk+x2_ijk+ EV_k
>
> where x1,x2 are environmental covariates and EV are Moran eigenvectors;
> i,j are location and k is year.
> Environmental covariate relationships with response variable are assumed
> constant across years.
>
> My plan was to first estimate using all years of data:
> y=intercept+x1+x2
> then use function ME in spdep to find identify Moran eigenvectors to
> reduce residual SAC using a year specific (index k) spatial weights and
> year-specific residuals using function ME from spdep package:
> EV_k=  ME(residuals_k~1, listw=weights_k), then linearly combine resulting
> eigenvectors for a given year into a single vector and then concatenate
> each year's vector such that the final Moran eignevector used in the
> regression is EV= c(EV_2014,EV_2015,EV_2016)
>
> and add EV as an offset or covariate as in the first equation shown.
>
> This approach seems to work quite well (eliminates residual SAC, doesn't
> shift regression coefficients substantially, improves model fit), I just
> don't know if it is statistically sound?
>
> thanks!
>
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>
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