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I have autocorrelated data that show a positive linear increase. When I model them using gls, I think the summary shows overdispersion.

When using GLMM etc I'd change error structure, but I don't think I can change family in gls. Is there a way to address overdispersion in a gls model?

library(nlme)

nest <- c(4087,2761,3807,4158,2046,4757,2984,3316,3143,
3042,4429,3335,5124,2464,3713,3028,5739,4671,3799,6167,2937,5031)

y <- seq(1997,2018,1)

m1 <- glm(nest~y)
summary(m1)
acf(resid(m1),type="p")

#residuals show autocorrelation at one year, so I need to use gls

m1.gls <- gls(nest~y,correlation=corARMA(p=1), method="ML")
summary(m1.gls)
acf(resid(m1.gls))
acf(resid(m1.gls),type="p")

m0.gls <- gls(nest~y,correlation=NULL,method="ML")
AIC(m0.gls,m1.gls)
anova(m1.gls,m0.gls)

#L.Ratio = chisqu = 7.382355;p = 0.0066
#autocorrelation is significant

null.gls <- gls(nest~1,correlation=corARMA(p=1), method="ML")
anova(m1.gls,null.gls)

#L.Ratio = chisq = 7.956113; p = 0.0048
#trend is significant

summary(m1.gls)

#residual se = 970 over 22 df

Does this show overdispersion?

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I have realised that a gls model is not subject to overdispersion. A gls model is based on the gaussian distribution, which cannot be overdispersed, just more or less widely distributed. Overdispersion applies only to other families such as poisson.

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