Hi everyone!



I have some doubts about mixed effect models and I hope someone could help
me. I´m trying to analyze a dataset coming from samples of dung beetles in
the same forest fragments along 3 consecutive years (1994, 1995 and 1996)
and 14 years after (2010). I sampled dung beetles in 18 different fragments
with different sizes and different degrees of isolation. Each fragment was
sampled once per year, so I have a total of 72 observations. My aim is to
determine whether total species richness change over time in forest
fragments and to verify the influence of fragment size and isolation on
species richness. However, I'm trying to find a way to consider in the
analyses the temporal pseudo-replication in the data. So, I decided to use
mixed effects models to analyze this data, but I still have doubts about
how I should construct the models. When I asked for some help I received
three different answers about how to construct the model.


The first suggestion was to treat year as a fixed rather than a random
effect because it won't be practical to estimate the variance of a
random effect with only four levels. So, I constructed the model like cited
below:

m1<-lmer(riqueza~área*ano+isolamento*ano+(1|fragmento),family=poisson


The second suggestion proposed to treat year as a random effect, as cited
bellow:

m1<-lmer(riqueza~área*ano+isolamento*ano+(ano|fragmento),family=poisson


And the third suggestion also proposed to treat year as a random effect,
but to consider it *as continuous variable rather than categorical*. In the
models above I consider year as a categorical variable.

m1<-lmer(riqueza~área*ano+isolamento*ano+(ano|fragmento),family=poisson


When I analyze my dataset using the second and the third model I always
face with a singular convergence warning: *In mer finalize(ans): singular
convergence (7)**.*



I already analyzed my data using these three different models and each one
gives me a completely different response. So, I need to know which one of
these models is more appropriate to the dataset I have available. Does
anyone have some suggestions?

Thanks in advance!

-- 
*Lívia Dorneles Audino*
Doutoranda em Entomologia
Laboratório de Ecologia e Conservação de Invertebrados
Universidade Federal de Lavras

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