Hi guys,
I'm very new to R and have been teaching myself over the past few months - it's
a great tool and I'm hoping to use it to analyse my PhD data.As I'm a bit of a
newb, I'd really appreciate any feedback and/or guidance with regards to the
following questions that relate to generalized linearmixed modelling (or, at
least, I think they do!)(if there is a 'better', more appropriate way that I
could attempt to answer my questions, please let me know).
I've spent a lot of time researching this approach on the internet, but
can'tseem to find any directly applicable examples.
Thanks in advance, and, if you need any further information, please let me know.
# My experiment:# I have 1 site on 3 different rivers (independent)(sites 1,2
and 3). # I visit each site 2 times (time 1 and 2). # On each visit, I take 5x
replicate insect samples and calculate total abundance for each replicate.#
Site 1 is in an area called "yellow" and sites 2 and 3 are in an area called
"blue".
# My data frame:
data=data.frame(site=c(rep(1,10),rep(2,10),rep(3,10)),replicate=c(rep(1:5,6)),time=c(rep(1,5),rep(2,5),rep(1,5),rep(2,5),rep(1,5),rep(2,5)),abundance=c(1,2,1,2,1,2,1,2,1,2,30,32,30,32,30,32,30,32,30,32,30,31,33,32,31,31,33,32,31,32),sitetype=c(rep("yellow",10),rep("blue",20)))
data$site=factor(data$site)data$replicate=factor(data$replicate)data$time=factor(data$time)
data
# Initial remarks: # As each replicate (1-5) was taken from within each site
(1-3) on both sampling times (1-2),# I figure that 'replicate' should be
treated as nested within 'site' and that both should be treated as random
factors?
# First question: Is there is difference in abundance between sites?# Second
question: Is there is difference in abundance between sitetypes (blue or
yellow)?
#If my 'initial remarks' statement is correct (please tell me if not),
then I think a generalized linear mixed model is appropriate and would be
something along these lines:
# Fitting the model:
require(lme4)
glmm1=glmer(abundance~time+sitetype+(1|site/replicate),family="poisson",data=data)
#I chose to use poisson as abundance is count data... not sure if that's
a good reason... summary(glmm1) #Output:
################################################################Generalized
linear mixed model fit by the Laplace approximation Formula: abundance ~ time +
sitetype + (1 | site/replicate) Data: data AIC BIC logLik deviance
12.31 19.31 -1.153 2.306Random effects: Groups Name Variance
Std.Dev. replicate:site (Intercept) 0 0 site
(Intercept) 0 0 Number of obs: 30, groups: replicate:site, 15;
site, 3
Fixed effects: Estimate Std. Error z value Pr(>|z|)
(Intercept) 3.43579 0.05641 60.91 <2e-16 ***time2 0.01560
0.07900 0.20 0.843 sitetypeyellow -3.03815 0.26127 -11.63
<2e-16 ***---Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
Correlation of Fixed Effects: (Intr) time2 time2 -0.706
sitetypyllw -0.108
0.000################################################################
# Inferences:
#I'm unsure how to assess the variance and std dev scores for
site... some guidance here would be appreciated....i.e. how do I answer my
original question: Is there is difference in abundance between sites?
#There is no statistically significant difference between the two time periods
(P=>0.05) #Using the above output, the model suggests that there
is a statistically significant difference between site types (p<0.05)
# Further questions:
#1 Are the above inferences correct? #2 I have read
about overdispersion.... how would I test for this in this example?
#3 How could I build an interaction term into the model and answer the
following: "Is there a statistically significant site*time interaction?"
#4 Finally, are there any obvious steps or things I should be doing in order
to get a 'robust' or 'correct' answer from this problem? i.e. further tests...
alternative models and comparisons...
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