Hello,

This is both an R and stats question.  I have some data covering
contaminant concentrations in fish over a time period of ~35 years.  Each
year, multiple samples of fish were taken (with varying sample sizes each
year). The trend is modeled using a linear regression on ln[contaminant]
and year.  The ultimate goal of this project is to do a power analysis for
a monitoring program, and to do this, I need an estimation of both random
within-year variation and random between-year variation.

I used a linear mixed model to estimate these variances.  My questions is
whether the function as I've set it up will return the estimates that I'm
looking for, and if so, which values within the output reflect those
estimates.  If someone knows of a better/alternative way to estimate these
values, that would also be useful.

> fish<-read.csv("data.csv",header=TRUE)
> fish
   SPECIES YEAR CONT
1  Walleye 1970 2.83
2  Walleye 1970 2.56
3  Walleye 1970 2.83
4  Walleye 1970 2.56
5  Walleye 1970 2.77
6  Walleye 1970 2.56
7  Walleye 1970 2.64
8  Walleye 1970 2.22
9  Walleye 1970 2.56
10 Walleye 1970 2.40
11 Walleye 1975 1.59
12 Walleye 1975 1.53
13 Walleye 1975 2.16
14 Walleye 1975 1.60
15 Walleye 1975 2.16
16 Walleye 1976 2.03
17 Walleye 1976 1.97
18 Walleye 1976 1.95
19 Walleye 1976 2.36
20 Walleye 1976 1.82
21 Walleye 1976 1.99
22 Walleye 1977 1.06
23 Walleye 1977 2.00
24 Walleye 1977 1.97
25 Walleye 1977 2.00
26 Walleye 1977 1.99
27 Walleye 1977 1.95
28 Walleye 1977 2.10
29 Walleye 1977 2.29
30 Walleye 1977 2.20
31 Walleye 1979 1.90
32 Walleye 1979 1.98
33 Walleye 1979 2.00
34 Walleye 1979 2.11
35 Walleye 1980 1.92
36 Walleye 1980 2.00
37 Walleye 1980 1.98
38 Walleye 1980 2.25
39 Walleye 1981 1.22
40 Walleye 1981 1.36
41 Walleye 1981 1.48
42 Walleye 1981 1.86
43 Walleye 1981 1.41
44 Walleye 1982 1.25
45 Walleye 1982 1.10
46 Walleye 1982 1.28
47 Walleye 1982 1.28
48 Walleye 1982 1.77
49 Walleye 1982 1.59
50 Walleye 1982 1.61
51 Walleye 1982 1.55
52 Walleye 1984 1.25
53 Walleye 1984 1.41
54 Walleye 1984 1.50
55 Walleye 1984 1.39
> year<-fish$YEAR
> cont<-fish$CONT
> reg3<-lme(year~cont,random=~1|year,method="REML")
> reg3
Linear mixed-effects model fit by REML
  Data: NULL
  Log-restricted-likelihood: 1243.336
  Fixed: year ~ cont
 (Intercept)         cont
1.978213e+03 4.947785e-14

Random effects:
 Formula: ~1 | year
        (Intercept)    Residual
StdDev:     4.23609 1.18049e-13

Number of Observations: 55
Number of Groups: 9

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