Solved – spatial autocorrelation for time series data

correlationrspatialspatio-temporaltime series

I have a 20-yr dataset of an annual count of species abundance for a set of polygons (~200 irregularly shaped, continuous polygons). I have been using regression analysis to infer trends (change in count per year) for each polygon, as well as aggregations of polygon data based on management boundaries.

I am sure that there is spatial autocorrelation in the data, which is sure to impact the regression analysis for the aggregated data. My question is – how do I run a SAC test for time series data? Do I need to look at the SAC of residuals from my regression for each year (global Moran's I)? Or can I run one test with all years?

Once I've tested that yes there is SAC, is there an easy was to address this? My stats background is minimal and everything I've read on spatio-temporal modeling sounds very complex. I know that R has a distance-weighted autocovariate function – is this at all simple to use?

I'm really quite confused on how to assess/addess SAC for this problem and would very much appreciate any suggestions, links, or references. Thanks in advance!

Best Answer

According to this paper, OLS is consistent in the presence of spatial autocorrelation, but standard errors are incorrect and need to be adjusted. Solomon Hsiang provides stata and matlab code for doing so. Unfortunately I'm not familiar with any R code for this.

There are certainly other approaches to this sort of problem in spatial statistics that explicitly model spatial processes. This one just inflates the standard errors.

Theoretical econometricians unfortunately seem to take pleasure in obfuscating. The linked paper is really hard to read. Basically what it says is run whatever regression you want, and then go fix the standard errors later. Space doesn't come into it until you try to estimate the variance of your estimator. Intuitively, if all the difference is close together, you're less certain that your estimate isn't just a relic of some unobserved spatial shock.

Note that you need to specify a kernel bandwidth over which you think the spatial process might be operating.

This answer is basically a copy/paste rehash of a similar answer I made here

Related Solutions

Longitudinal Count Data – How to Analyze Longitudinal Count Data with Temporal Autocorrelation in GLMM

Log transforming your response is an option although not ideal. A GLM framework is generally preferred. If you are not familiar with GLMs then start by reviewing them prior to looking at mixed model extensions. For count data Poisson or Negative Binomial distributional assumptions will be likely suitable. Negative Binomial is indicated if the variance is higher than the mean indicating over-dispersion (https://en.wikipedia.org/wiki/Overdispersion). The interpretation of the parameter estimates is equivalent for the two.

Several options exist in R with lme4 being most commonly cited in my experience.

#glmer
library(lme4) 
glmer(count ~ AirT + I(AirT^2) + RainAmt24 + I(RainAmt24^2) + RHpct + windspeed + sin(2*pi/360*DOY) + cos(2*pi/360*DOY) + (1|plot), family=poisson, data = Data) 
# use glmer.nb with identical syntax but no family for negative binomial.

# glmmADMB with negative binomial
install.packages("glmmADMB", repos=c("http://glmmadmb.r-forge.r-project.org/repos", getOption("repos")),type="source") 
require(glmmADMB)
glmmadmb(count ~ AirT + I(AirT^2) + RainAmt24 + I(RainAmt24^2) + RHpct + windspeed + sin(2*pi/360*DOY) + cos(2*pi/360*DOY) + (1|plot), 
           family="nbinom", zeroInflation=FALSE, data=Data)

# glmmPQL, requires an estimate for theta which can be obtained from a 
# glm model in which the correlation structure is ignored.
library(MASS)
glmmPQL(count ~ AirT + I(AirT^2) + RainAmt24 + I(RainAmt24^2) + RHpct + windspeed + sin(2*pi/360*DOY) + cos(2*pi/360*DOY) , random = list(~1 | plot), data = Data,family = negative.binomial(theta = 4.22, link = log))

These links may also be of assistance:

https://udrive.oit.umass.edu/xythoswfs/webui/_xy-11096203_1-t_yOxYgf1s http://www.cell.com/trends/ecology-evolution/pdf/S0169-5347(09)00019-6.pdf

Both are by Ben Bolker, author of lme4.

I haven't tested the examples but they should give you an idea of where to start. Please supply data if you wish to verify their implementation.

Pooled Time Series Regression in R – Techniques and Applications

This doesn't exactly answer what are you looking for. However, I think you need to consider these issues before doing the analysis. In other words, I focus more on the conceptual part (part a) [I thought it to include in comment but this is very long]

With the repeated cross section data, you have here the pseudo panel data (with age group (age cohort) acting as individual effect and year as time effect) and not the true panel data. Theoretical stuffs on this has been discussed here. The good news is that you can use the fixed effect, random effect,and pooled estimator as being used for the true panel data. The use of different tests to choose one over another estimator has been discussed in the plm package manual. However, it is good to start with Introductory Econometrics by Woolridge if you are beginners in panel data. That being said, consider this Oxford discussion paper as a starting one. Once you understand the concept mentioned in the paper, it won't be difficult to apply in R. Your question doesn't spell out other variables. Is that the case?

Best Answer

Related Solutions

Longitudinal Count Data – How to Analyze Longitudinal Count Data with Temporal Autocorrelation in GLMM

Pooled Time Series Regression in R – Techniques and Applications

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