Generalized Estimating Equations – How to Analyze GEE with Unevenly Spaced Observations

autocorrelationgeneralized-estimating-equationspanel datarregression

I am interested in using Generalized Estimating Equations (GEE) to model longitudinal count data. I recorded animal count observations on the same sites on many days but the spacing of the observations was uneven. I was wondering if there is a way to specify this uneven structure when using an autoregressive correlation structure?

for example, when using lme from the nlme package to analyze linear mixed models it is possible to specify the correlation structure as:

correlation = corAR1(form = ~DAY | Subject)

That way the spacing of the observations for the autoregressive structure is adjusted based on DAY. Is there a way to do this in R in a GEE model using a package such as geepack, gee, or any others?

Thanks,
Dan

Best Answer

When using the geeglm fonction (in geepack), you can specify the order and the spacing between observations with the waves argument.

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.

Solved – How to perform model selection in GEE in R

If you want to select amongst pre-specified models, this should work the same with GEE as elsewhere. For example, if you were comparing a nested model to a full model, you could test that. If the models weren't nested, you could use an informational criterion (such as the QIC) to help adjudicate between them. Another approach is to use the Parametric Bootstrap Cross-fitting Method; this is a very solid approach, but computationally very expensive.

Best Answer

Related Solutions

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

Solved – How to perform model selection in GEE in R

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