[R] How to plot fitted values from lmer (lme4 package)?

[Darren Norris]

I am modelling (at least trying to) the seasonal component of a variable
using lmer. I think I am just about getting the hang of building the models
but want to see what the fitted values look like.
I need to plot 2 lines on the same graph - the original data ( copy of
dataframe below) and the fitted values. I am doing this to a) start to
understand how to use R and b) start to understand how to build and compare
models. 

I have been using books (e.g. The R Book Michael Crawley) and pdf (e.g. time
series analysis with R part 1 – Walter Zuccchini and Oleg Nenadic) for
reference and if the answer is there (which it probably is) I can’t
understand it (I have a very slow dial up connection so even searching
nabble frequently crashes)!

An example of the model is:

Scale the annual cycle to be length 1.0:-
with(a_dataframe,length(mean_ind))
[1] 15
index<-1:15
15/4
[1] 3.75
time<-index/3.75

Model (index used as explanatory variable for trend, also allows different
intercepts for years as a random effect – I hope):-

mtrend<-lmer(a_dataframe$mean_ind~index+sin(time*2*pi)+cos(time*2*pi)+(1|factor(a_dataframe$YEAR)),method="ML")

using “lm” I followed the following process to produce the graph I wanted.

lmodel<-with(a_dataframe,lm(mean_ind~sin(time*2*pi)+cos(time*2*pi)))
plot(time,a_dataframe$mean_ind,pch=".")
lines(time,predict(lmodel))

How can I do the same with lmer? I have tried a variety of things with
“predict”, trying to put the results from lmer as a “groupedData” object
etc. But I can’t seem to make it work. Any simple solutions? 
Many thanks for any help.

Sample data a_dataframe below (I removed NULL rows so row references are not
concsequtive):-

  YEAR_QUARTER YEAR  a_mean
1        2004_2 2004  71.46154
2        2004_3 2004  56.30000
3        2004_4 2004  37.88889
19       2005_1 2005  37.00000
20       2005_2 2005  88.44444
21       2005_3 2005  87.28571
22       2005_4 2005  43.75000
38       2006_1 2006  50.85714
39       2006_2 2006 142.25000
40       2006_3 2006 137.57143
41       2006_4 2006  79.86667
57       2007_1 2007  73.13333
58       2007_2 2007 146.28571
59       2007_3 2007 118.07692
60       2007_4 2007  73.50000

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