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

[Roberto Patuelli]

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

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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
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	<CAMJGZtxbhE7ES8XPBgxqGmLsu0q--iid+nB1ysa8BG2fd4RpVA using mail.gmail.com>
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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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