##### Random Effects


###import the data


datum=read.csv(file.choose())
head(datum)


###Import appropriate package
# random- and mixed-effects models can't be analysized with lm
# analyze with either lme in the nlme package
# or with lmer in the lme4 package


library(nlme) ###load the nlme package
help(lme) ###check out the lme function


###create a random-effects model


results=lme(Abundance~1,data=datum,random=~1|Year) ### random effect model
# no fixed effects included, hence reason for ~1 in formula
# random effects listed separately
summary(results) ### look at output
# notice summary out put similar to lm, but with estimates for se for random effects


###Test whether random effects are significant source of variation


# Compare more complex model (with random effect) to simpler model (no random effect)
results2=lm(Abundance~1,data=datum) 
# must use lm - lme MUST have a random effect
anova(results,results2) 
# notice that test is done using likelihood, rather than sse


###Repeat analysis using lmer


library(lme4)
help(lmer) ### check out lmer function


### create a random-effects model in lmer


results3=lmer(Abundance~1+(1|Year),data=datum) 
# simliar to lme, but random effects
# included in formula statement.
summary(results3)