Extraordinary accuracy of mcmcsamp?
On 2/22/07, T.C. Cameron <T.C.Cameron at leeds.ac.uk> wrote:
Dear Mixed models List
Thanks to the R help pages and contributors I have built a Generalised Linear mixed model with Gamma errors for a block experiment testing the effects of environment, food availability and harvesting strategie on the age at maturity in soil mite populations
The model is
m3<-lmer(dev~env*har*treat+dens + (1|pop/rep), family = Gamma)
The output of the mcmcsamp function gives estimates for the fixed factor coefficients that are similar or identical to the model output, but without any SE or deviation!
The MCMC chain is stuck, which can happen with generalized linear mixed models. The Metropolis-Hastings algorithm that I had concocted for MCMC sampling from GLMMs worked well on the examples that I tried but does not work as well as I had hoped in general. You will need to formulate your own sampler or use the z statistics.
As I think I am performing this task to test in the coefficients are
significantly different from zero this makes the job easy but for now,
untrustworthy!
Iterations = 1:10000
Thinning interval = 1
Number of chains = 1
Sample size per chain = 10000
1. Empirical mean and standard deviation for each variable,
plus standard error of the mean:
Mean SD Naive SE Time-series SE
(Intercept) 2.054e-01 0.000e+00 0.000e+00 0.000e+00
envL -4.141e-02 0.000e+00 0.000e+00 0.000e+00
harA 4.613e-03 0.000e+00 0.000e+00 0.000e+00
harJ 6.227e-03 0.000e+00 0.000e+00 0.000e+00
treatP -5.690e-03 0.000e+00 0.000e+00 0.000e+00
treatV -4.232e-03 0.000e+00 0.000e+00 0.000e+00
dens -4.647e-01 0.000e+00 0.000e+00 0.000e+00
envL:harA 8.621e-03 0.000e+00 0.000e+00 0.000e+00
envL:harJ 2.384e-02 0.000e+00 0.000e+00 0.000e+00
envL:treatP 3.398e-02 0.000e+00 0.000e+00 0.000e+00
envL:treatV 3.414e-02 0.000e+00 0.000e+00 0.000e+00
harA:treatP -7.164e-03 0.000e+00 0.000e+00 0.000e+00
harJ:treatP -3.926e-02 0.000e+00 0.000e+00 0.000e+00
harA:treatV 7.309e-03 0.000e+00 0.000e+00 0.000e+00
harJ:treatV -2.751e-03 0.000e+00 0.000e+00 0.000e+00
envL:harA:treatP 1.845e-02 0.000e+00 0.000e+00 0.000e+00
envL:harJ:treatP 3.589e-02 0.000e+00 0.000e+00 0.000e+00
envL:harA:treatV -7.708e-03 0.000e+00 0.000e+00 0.000e+00
envL:harJ:treatV -5.037e-03 0.000e+00 0.000e+00 0.000e+00
rp:p.(In) 2.987e+01 3.800e+00 3.800e-02 3.247e-02
pop.(In) 2.133e-13 8.073e-14 8.073e-16 1.054e-09
2. Quantiles for each variable:
2.5% 25% 50% 75% 97.5%
(Intercept) 2.054e-01 2.054e-01 2.054e-01 2.054e-01 2.054e-01
envL -4.141e-02 -4.141e-02 -4.141e-02 -4.141e-02 -4.141e-02
harA 4.613e-03 4.613e-03 4.613e-03 4.613e-03 4.613e-03
harJ 6.227e-03 6.227e-03 6.227e-03 6.227e-03 6.227e-03
treatP -5.690e-03 -5.690e-03 -5.690e-03 -5.690e-03 -5.690e-03
treatV -4.232e-03 -4.232e-03 -4.232e-03 -4.232e-03 -4.232e-03
dens -4.647e-01 -4.647e-01 -4.647e-01 -4.647e-01 -4.647e-01
envL:harA 8.621e-03 8.621e-03 8.621e-03 8.621e-03 8.621e-03
envL:harJ 2.384e-02 2.384e-02 2.384e-02 2.384e-02 2.384e-02
envL:treatP 3.398e-02 3.398e-02 3.398e-02 3.398e-02 3.398e-02
envL:treatV 3.414e-02 3.414e-02 3.414e-02 3.414e-02 3.414e-02
harA:treatP -7.164e-03 -7.164e-03 -7.164e-03 -7.164e-03 -7.164e-03
harJ:treatP -3.926e-02 -3.926e-02 -3.926e-02 -3.926e-02 -3.926e-02
harA:treatV 7.309e-03 7.309e-03 7.309e-03 7.309e-03 7.309e-03
harJ:treatV -2.751e-03 -2.751e-03 -2.751e-03 -2.751e-03 -2.751e-03
envL:harA:treatP 1.845e-02 1.845e-02 1.845e-02 1.845e-02 1.845e-02
envL:harJ:treatP 3.589e-02 3.589e-02 3.589e-02 3.589e-02 3.589e-02
envL:harA:treatV -7.708e-03 -7.708e-03 -7.708e-03 -7.708e-03 -7.708e-03
envL:harJ:treatV -5.037e-03 -5.037e-03 -5.037e-03 -5.037e-03 -5.037e-03
rp:p.(In) 2.327e+01 2.723e+01 2.959e+01 3.219e+01 3.816e+01
pop.(In) 1.082e-13 1.585e-13 1.962e-13 2.486e-13 4.205e-13
There does not appear to be any significant degree of skew as the
quantiles for the fixed factors are also identical!
Am I doing something wrong or is this result genuine?
Data and script below
Thankyou and best wishes
pop treat har rep env dev fed dens
4 C 0 3 H 4 1 9
4 C 0 3 H 4 1 9
4 C 0 3 H 4 1 9
4 C 0 3 H 4 1 9
4 C 0 3 H 4 1 9
4 C 0 4 H 4 1 8
4 C 0 4 H 4 1 8
4 C 0 4 H 4 1 8
4 C 0 4 H 4 1 8
4 C 0 4 H 4 1 8
4 C 0 4 H 4 1 8
4 C 0 4 H 4 1 8
4 C 0 5 H 4 1 5
4 C 0 5 H 4 1 5
4 C 0 5 H 4 1 5
4 C 0 6 H 4 1 9
4 C 0 6 H 4 1 9
4 C 0 6 H 4 1 9
4 C 0 6 H 4 1 9
4 C 0 6 H 4 1 9
4 C 0 6 H 4 1 9
4 C 0 7 H 4 1 4
4 C 0 7 H 4 1 4
4 C 0 7 H 4 1 4
4 C 0 7 H 4 1 4
4 C 0 1 H 5 1 9
4 C 0 1 H 5 1 9
4 C 0 1 H 5 1 9
4 C 0 1 H 5 1 9
4 C 0 1 H 5 1 9
4 C 0 1 H 5 1 9
4 C 0 2 H 5 1 4
4 C 0 2 H 5 1 4
4 C 0 2 H 5 1 4
4 C 0 3 H 5 1 6
4 C 0 3 H 5 1 6
4 C 0 3 H 5 1 6
4 C 0 3 H 5 1 6
4 C 0 3 H 5 1 6
4 C 0 4 H 5 1 13
4 C 0 4 H 5 1 13
4 C 0 4 H 5 1 13
4 C 0 4 H 5 1 13
4 C 0 4 H 5 1 13
4 C 0 5 H 5 1 9
4 C 0 5 H 5 1 9
4 C 0 5 H 5 1 9
4 C 0 6 H 5 1 10
4 C 0 6 H 5 1 10
4 C 0 6 H 5 1 10
4 C 0 6 H 5 1 10
4 C 0 6 H 5 1 10
4 C 0 6 H 5 1 10
4 C 0 6 H 5 1 10
4 C 0 7 H 5 1 16
4 C 0 7 H 5 1 16
4 C 0 7 H 5 1 16
4 C 0 7 H 5 1 16
4 C 0 7 H 5 1 16
4 C 0 7 H 5 1 16
4 C 0 7 H 5 1 16
4 C 0 7 H 5 1 16
4 C 0 7 H 5 1 16
4 C 0 7 H 5 1 16
4 C 0 7 H 5 1 16
4 C 0 1 H 6 1 2
4 C 0 1 H 6 1 2
4 C 0 2 H 6 1 9
4 C 0 2 H 6 1 9
4 C 0 2 H 6 1 9
4 C 0 2 H 6 1 9
4 C 0 2 H 6 1 9
4 C 0 2 H 6 1 9
4 C 0 3 H 7 1 2
4 C 0 3 H 7 1 2
4 C 0 5 H 7 1 2
4 C 0 5 H 7 1 2
4 C 0 6 L 7 0 1
4 C 0 7 L 7 0 1
4 C 0 1 L 8 1 1
4 C 0 3 L 8 1 2
4 C 0 5 L 8 1 1
4 C 0 2 L 9 0 1
4 C 0 3 L 9 0 1
4 C 0 5 L 9 0 2
4 C 0 6 L 9 0 1
4 C 0 2 L 10 1 2
4 C 0 2 L 10 1 2
4 C 0 3 L 10 1 4
4 C 0 3 L 10 1 4
4 C 0 4 L 10 1 3
4 C 0 6 L 10 1 2
4 C 0 1 L 11 0 3
4 C 0 1 L 11 0 3
4 C 0 2 L 11 0 1
4 C 0 7 L 11 0 1
4 C 0 5 L 12 1 5
4 C 0 7 L 12 1 2
4 C 0 4 L 13 0 1
4 C 0 1 L 14 1 1
4 C 0 1 L 15 0 1
4 C 0 4 L 15 0 2
4 C 0 1 L 16 1 3
4 C 0 2 L 16 1 1
4 C 0 5 L 16 1 1
4 C 0 2 L 17 0 5
4 C 0 2 L 17 0 5
4 C 0 2 L 17 0 5
4 C 0 2 L 17 0 5
4 C 0 2 L 17 0 5
4 C 0 2 L 18 1 2
4 C 0 2 L 18 1 2
5 C 0 3 H 4 1 9
5 C 0 3 H 4 1 9
5 C 0 3 H 4 1 9
5 C 0 3 H 4 1 9
5 C 0 4 H 4 1 11
5 C 0 4 H 4 1 11
5 C 0 4 H 4 1 11
5 C 0 4 H 4 1 11
5 C 0 4 H 4 1 11
5 C 0 4 H 4 1 11
5 C 0 4 H 4 1 11
5 C 0 4 H 4 1 11
5 C 0 1 H 5 1 16
5 C 0 1 H 5 1 16
5 C 0 1 H 5 1 16
5 C 0 1 H 5 1 16
5 C 0 1 H 5 1 16
5 C 0 1 H 5 1 16
5 C 0 2 H 5 1 5
5 C 0 2 H 5 1 5
5 C 0 2 H 5 1 5
5 C 0 2 H 5 1 5
5 C 0 3 H 5 1 6
5 C 0 3 H 5 1 6
5 C 0 3 H 5 1 6
5 C 0 3 H 5 1 6
5 C 0 4 H 5 1 7
5 C 0 4 H 5 1 7
5 C 0 4 H 5 1 7
5 C 0 4 H 5 1 7
5 C 0 4 H 5 1 7
5 C 0 4 H 5 1 7
5 C 0 4 H 5 1 7
5 C 0 5 H 5 1 10
5 C 0 5 H 5 1 10
5 C 0 5 H 5 1 10
5 C 0 5 H 5 1 10
5 C 0 5 H 5 1 10
5 C 0 6 H 5 1 18
5 C 0 6 H 5 1 18
5 C 0 6 H 5 1 18
5 C 0 6 H 5 1 18
5 C 0 6 H 5 1 18
5 C 0 6 H 5 1 18
5 C 0 6 H 5 1 18
5 C 0 7 H 5 1 10
5 C 0 7 H 5 1 10
5 C 0 7 H 5 1 10
5 C 0 7 H 5 1 10
5 C 0 7 H 5 1 10
5 C 0 4 L 6 1 3
5 C 0 4 L 6 1 3
5 C 0 4 H 7 1 1
5 C 0 2 L 8 1 1
5 C 0 5 L 8 1 1
5 C 0 7 L 8 1 1
5 C 0 3 L 9 0 1
5 C 0 1 L 10 1 2
5 C 0 2 L 10 1 3
5 C 0 2 L 10 1 3
5 C 0 2 L 10 1 3
5 C 0 3 L 10 1 4
5 C 0 3 L 10 1 4
5 C 0 3 L 10 1 4
5 C 0 4 L 10 1 1
5 C 0 5 L 10 1 5
5 C 0 5 L 10 1 5
5 C 0 7 L 10 1 2
5 C 0 1 L 11 0 1
5 C 0 2 L 11 0 2
5 C 0 3 L 11 0 2
5 C 0 4 L 11 0 1
5 C 0 6 L 11 0 2
5 C 0 7 L 11 0 2
5 C 0 1 L 12 1 6
5 C 0 1 L 12 1 6
5 C 0 1 L 12 1 6
5 C 0 1 L 12 1 6
5 C 0 1 L 12 1 6
5 C 0 2 L 12 1 2
5 C 0 2 L 12 1 2
5 C 0 3 L 12 1 1
5 C 0 4 L 12 1 3
5 C 0 6 L 12 1 3
5 C 0 7 L 12 1 1
5 C 0 1 L 14 1 1
5 C 0 3 L 14 1 1
5 C 0 6 L 14 1 1
5 C 0 1 L 15 0 2
5 C 0 6 L 15 0 1
5 C 0 7 L 16 1 1
10 C A 1 L 4 1 18
10 C A 1 H 4 1 18
10 C A 2 H 4 1 20
10 C A 2 H 4 1 20
10 C A 2 H 4 1 20
10 C A 5 H 4 1 17
10 C A 5 H 4 1 17
10 C A 6 H 4 1 20
10 C A 6 H 4 1 20
10 C A 6 H 4 1 20
10 C A 1 H 5 1 13
10 C A 1 H 5 1 13
10 C A 1 H 5 1 13
10 C A 1 H 5 1 13
10 C A 2 H 5 1 11
10 C A 2 H 5 1 11
10 C A 2 H 5 1 11
10 C A 2 H 5 1 11
10 C A 2 H 5 1 11
10 C A 2 H 5 1 11
10 C A 2 H 5 1 11
10 C A 2 H 5 1 11
10 C A 3 H 5 1 14
10 C A 3 H 5 1 14
10 C A 3 H 5 1 14
10 C A 3 H 5 1 14
10 C A 3 H 5 1 14
10 C A 3 H 5 1 14
10 C A 3 H 5 1 14
10 C A 3 H 5 1 14
10 C A 3 H 5 1 14
10 C A 3 H 5 1 14
10 C A 3 H 5 1 14
10 C A 3 H 5 1 14
10 C A 4 H 5 1 16
10 C A 4 H 5 1 16
10 C A 4 H 5 1 16
10 C A 4 H 5 1 16
10 C A 4 H 5 1 16
10 C A 4 H 5 1 16
10 C A 5 H 5 1 12
10 C A 5 H 5 1 12
10 C A 5 H 5 1 12
10 C A 5 H 5 1 12
10 C A 5 H 5 1 12
10 C A 5 H 5 1 12
10 C A 6 H 5 1 14
10 C A 6 H 5 1 14
10 C A 6 H 5 1 14
10 C A 6 H 5 1 14
10 C A 6 H 5 1 14
10 C A 6 H 5 1 14
10 C A 6 H 5 1 14
10 C A 6 H 5 1 14
10 C A 6 H 5 1 14
10 C A 6 H 5 1 14
10 C A 7 H 5 1 18
10 C A 7 H 5 1 18
10 C A 7 H 5 1 18
10 C A 7 H 5 1 18
10 C A 7 H 5 1 18
10 C A 7 H 5 1 18
10 C A 7 H 5 1 18
10 C A 7 H 5 1 18
10 C A 1 H 6 1 5
10 C A 1 H 6 1 5
10 C A 2 L 10 1 2
10 C A 2 L 10 1 2
10 C A 4 L 10 1 1
10 C A 5 L 10 1 3
10 C A 5 L 10 1 3
10 C A 5 L 11 0 2
10 C A 5 L 12 1 2
10 C A 5 L 13 1 2
10 C A 7 L 13 1 2
10 C A 3 L 14 0 9
10 C A 3 L 14 0 9
10 C A 4 L 14 0 6
10 C A 4 L 14 0 6
10 C A 4 L 14 0 6
10 C A 6 L 14 0 1
10 C A 7 L 14 0 6
10 C A 7 L 14 0 6
10 C A 7 L 14 0 6
10 C A 7 L 14 0 6
10 C A 4 L 15 1 3
10 C A 4 L 15 1 3
10 C A 4 L 15 1 3
10 C A 3 L 15 1 5
10 C A 3 L 15 1 5
10 C A 3 L 15 1 5
10 C A 3 L 15 1 5
10 C A 2 L 15 1 4
10 C A 2 L 15 1 4
10 C A 6 L 15 1 3
10 C A 7 L 15 1 8
10 C A 7 L 15 1 8
10 C A 6 L 16 0 2
10 C A 2 L 17 1 3
10 C A 2 L 17 1 3
10 C A 2 L 17 1 3
10 C A 3 L 17 1 1
10 C A 5 L 17 1 1
10 C A 6 L 17 1 3
10 C A 4 L 18 0 1
10 C A 4 L 19 1 3
10 C A 4 L 19 1 3
10 C A 4 L 19 1 3
10 C A 2 L 20 0 1
11 C A 3 H 4 1 19
11 C A 3 H 4 1 19
11 C A 3 H 4 1 19
11 C A 3 H 4 1 19
11 C A 3 H 4 1 19
11 C A 3 H 4 1 19
11 C A 3 H 4 1 19
11 C A 3 H 4 1 19
11 C A 4 H 4 1 5
11 C A 4 H 4 1 5
11 C A 5 H 4 1 14
11 C A 5 H 4 1 14
11 C A 5 H 4 1 14
11 C A 5 H 4 1 14
11 C A 5 H 4 1 14
11 C A 5 H 4 1 14
11 C A 6 H 4 1 16
11 C A 6 H 4 1 16
11 C A 6 H 4 1 16
11 C A 6 H 4 1 16
11 C A 6 H 4 1 16
11 C A 6 H 4 1 16
11 C A 6 H 4 1 16
11 C A 6 H 4 1 16
11 C A 7 H 4 1 20
11 C A 7 H 4 1 20
11 C A 7 H 4 1 20
11 C A 7 H 4 1 20
11 C A 1 H 5 1 12
11 C A 1 H 5 1 12
11 C A 1 H 5 1 12
11 C A 1 H 5 1 12
11 C A 1 H 5 1 12
11 C A 1 H 5 1 12
11 C A 1 H 5 1 12
11 C A 1 H 5 1 12
11 C A 2 H 5 1 12
11 C A 2 H 5 1 12
11 C A 2 H 5 1 12
11 C A 2 H 5 1 12
11 C A 2 H 5 1 12
11 C A 2 H 5 1 12
11 C A 2 H 5 1 12
11 C A 2 H 5 1 12
11 C A 2 H 5 1 12
11 C A 2 H 5 1 12
11 C A 2 H 5 1 12
11 C A 3 H 5 1 4
11 C A 3 H 5 1 4
11 C A 3 H 5 1 4
11 C A 3 H 5 1 4
11 C A 4 H 5 1 9
11 C A 4 H 5 1 9
11 C A 4 H 5 1 9
11 C A 4 H 5 1 9
11 C A 4 H 5 1 9
11 C A 5 H 5 1 3
11 C A 6 H 5 1 1
11 C A 7 H 5 1 10
11 C A 7 H 5 1 10
11 C A 7 H 5 1 10
11 C A 7 H 5 1 10
11 C A 7 H 5 1 10
11 C A 7 H 5 1 10
11 C A 7 H 5 1 10
11 C A 7 H 5 1 10
11 C A 2 L 8 1 2
11 C A 3 L 8 1 1
11 C A 4 L 8 1 2
11 C A 2 L 9 0 2
11 C A 2 L 9 0 2
11 C A 3 L 9 0 1
11 C A 2 L 10 1 4
11 C A 2 L 10 1 4
11 C A 3 L 10 1 3
11 C A 3 L 10 1 3
11 C A 6 L 10 1 3
11 C A 6 L 10 1 3
11 C A 6 L 10 1 3
11 C A 1 L 11 0 3
11 C A 1 L 11 0 3
11 C A 3 L 11 0 1
11 C A 7 L 11 0 3
11 C A 7 L 11 0 3
11 C A 2 L 12 1 4
11 C A 2 L 12 1 4
11 C A 2 L 12 1 4
11 C A 2 L 12 1 4
11 C A 3 L 12 1 2
11 C A 3 L 12 1 2
11 C A 6 L 12 1 6
11 C A 6 L 12 1 6
11 C A 6 L 12 1 6
11 C A 6 L 12 1 6
11 C A 6 L 12 1 6
11 C A 4 L 13 1 1
11 C A 5 L 13 1 2
11 C A 6 L 13 1 2
11 C A 1 L 14 0 3
11 C A 1 L 14 0 3
11 C A 3 L 14 0 1
11 C A 4 L 14 0 4
11 C A 5 L 14 0 7
11 C A 5 L 14 0 7
11 C A 5 L 14 0 7
11 C A 5 L 14 0 7
11 C A 5 L 14 0 7
11 C A 5 L 14 0 7
11 C A 1 L 15 1 4
11 C A 1 L 15 1 4
11 C A 3 L 15 1 3
11 C A 3 L 15 1 3
11 C A 3 L 15 1 3
11 C A 4 L 15 1 4
11 C A 4 L 15 1 4
11 C A 4 L 15 1 4
11 C A 5 L 15 1 5
11 C A 5 L 15 1 5
11 C A 5 L 15 1 5
11 C A 5 L 15 1 5
11 C A 5 L 15 1 5
11 C A 6 L 16 0 1
11 C A 4 L 17 1 1
11 C A 5 L 17 1 1
11 C A 5 L 18 0 2
11 C A 4 L 18 0 1
16 C J 1 H 4 1 4
16 C J 1 H 4 1 4
16 C J 3 H 4 1 7
16 C J 3 H 4 1 7
16 C J 3 H 4 1 7
16 C J 3 H 4 1 7
16 C J 7 H 4 1 3
16 C J 7 H 4 1 3
16 C J 1 H 5 1 7
16 C J 1 H 5 1 7
16 C J 2 H 5 1 10
16 C J 2 H 5 1 10
16 C J 2 H 5 1 10
16 C J 2 H 5 1 10
16 C J 2 H 5 1 10
16 C J 2 H 5 1 10
16 C J 2 H 5 1 10
16 C J 2 H 5 1 10
16 C J 2 H 5 1 10
16 C J 3 H 5 1 1
16 C J 4 H 5 1 14
16 C J 4 H 5 1 14
16 C J 4 H 5 1 14
16 C J 4 H 5 1 14
16 C J 4 H 5 1 14
16 C J 4 H 5 1 14
16 C J 4 H 5 1 14
16 C J 5 H 5 1 12
16 C J 5 H 5 1 12
16 C J 5 H 5 1 12
16 C J 5 H 5 1 12
16 C J 5 H 5 1 12
16 C J 5 H 5 1 12
16 C J 6 H 5 1 10
16 C J 6 H 5 1 10
16 C J 6 H 5 1 10
16 C J 7 H 5 1 7
16 C J 7 H 5 1 7
16 C J 7 H 5 1 7
16 C J 1 L 7 0 3
16 C J 1 L 7 0 3
16 C J 2 L 7 0 1
16 C J 3 L 7 0 2
16 C J 4 L 7 0 2
16 C J 4 L 7 0 2
16 C J 2 L 8 1 3
16 C J 2 L 8 1 3
16 C J 3 L 8 1 3
16 C J 3 L 8 1 3
16 C J 4 L 8 1 2
16 C J 4 L 8 1 2
16 C J 5 L 8 1 2
16 C J 7 L 8 1 1
16 C J 5 L 9 0 1
16 C J 1 L 10 1 3
16 C J 2 L 10 1 1
16 C J 3 L 10 1 1
16 C J 5 L 10 1 5
16 C J 5 L 10 1 5
16 C J 5 L 10 1 5
16 C J 5 L 10 1 5
16 C J 6 L 10 1 5
16 C J 6 L 10 1 5
16 C J 7 L 10 1 4
16 C J 7 L 10 1 4
16 C J 1 L 12 1 4
16 C J 4 L 12 1 3
16 C J 4 L 12 1 3
16 C J 7 L 12 1 3
16 C J 7 L 12 1 3
16 C J 4 L 13 0 5
16 C J 4 L 13 0 5
16 C J 5 L 13 0 2
16 C J 6 L 13 0 5
16 C J 6 L 13 0 5
16 C J 6 L 13 0 5
16 C J 1 L 14 1 1
16 C J 2 L 14 1 4
16 C J 2 L 14 1 4
16 C J 3 L 14 1 3
16 C J 3 L 14 1 3
16 C J 4 L 14 1 2
16 C J 6 L 14 1 1
16 C J 7 L 14 1 5
16 C J 7 L 14 1 5
16 C J 7 L 14 1 5
16 C J 7 L 14 1 5
16 C J 1 L 15 0 1
16 C J 2 L 15 0 1
16 C J 6 L 15 0 1
16 C J 7 L 15 0 2
16 C J 1 L 16 1 1
16 C J 2 L 16 1 3
16 C J 2 L 16 1 3
16 C J 2 L 16 1 3
17 C J 2 H 4 1 17
17 C J 2 H 4 1 17
17 C J 2 H 4 1 17
17 C J 2 H 4 1 17
17 C J 2 H 4 1 17
17 C J 2 H 4 1 17
17 C J 2 H 4 1 17
17 C J 2 H 4 1 17
17 C J 3 H 4 1 4
17 C J 3 H 4 1 4
17 C J 3 H 4 1 4
17 C J 3 H 4 1 4
17 C J 5 H 4 1 4
17 C J 5 H 4 1 4
17 C J 5 H 4 1 4
17 C J 6 H 4 1 4
17 C J 1 H 5 1 10
17 C J 1 H 5 1 10
17 C J 1 H 5 1 10
17 C J 1 H 5 1 10
17 C J 1 H 5 1 10
17 C J 1 H 5 1 10
17 C J 1 H 5 1 10
17 C J 3 H 5 1 9
17 C J 3 H 5 1 9
17 C J 3 H 5 1 9
17 C J 3 H 5 1 9
17 C J 3 H 5 1 9
17 C J 3 H 5 1 9
17 C J 5 H 5 1 4
17 C J 5 H 5 1 4
17 C J 5 H 5 1 4
17 C J 6 H 5 1 11
17 C J 6 H 5 1 11
17 C J 6 H 5 1 11
17 C J 6 H 5 1 11
17 C J 7 H 5 1 5
17 C J 7 H 5 1 5
17 C J 7 H 5 1 5
17 C J 7 H 5 1 5
17 C J 1 L 5 0 2
17 C J 1 L 5 0 2
17 C J 1 H 6 1 1
17 C J 3 H 6 1 1
17 C J 2 L 6 1 1
17 C J 6 L 6 1 3
17 C J 6 L 6 1 3
17 C J 1 L 8 1 1
17 C J 2 L 8 1 4
17 C J 2 L 8 1 4
17 C J 3 L 8 1 3
17 C J 3 L 8 1 3
17 C J 6 L 8 1 2
17 C J 7 L 8 1 5
17 C J 7 L 8 1 5
17 C J 1 L 9 0 3
17 C J 1 L 9 0 3
17 C J 2 L 9 0 1
17 C J 5 L 9 0 3
17 C J 5 L 9 0 3
17 C J 1 L 10 1 4
17 C J 1 L 10 1 4
17 C J 1 L 10 1 4
17 C J 3 L 10 1 4
17 C J 3 L 10 1 4
17 C J 4 L 10 1 3
17 C J 7 L 10 1 1
17 C J 1 L 11 0 1
17 C J 5 L 12 1 3
17 C J 7 L 12 1 3
17 C J 7 L 12 1 3
17 C J 7 L 12 1 3
17 C J 3 L 13 0 6
17 C J 3 L 13 0 6
17 C J 5 L 13 0 3
17 C J 5 L 13 0 3
17 C J 5 L 14 1 2
17 C J 7 L 14 1 3
17 C J 7 L 14 1 3
22 V 0 1 H 4 1 1
22 V 0 3 H 4 1 1
22 V 0 4 H 4 1 1
22 V 0 1 H 5 1 6
22 V 0 1 H 5 1 6
22 V 0 1 H 5 1 6
22 V 0 1 H 5 1 6
22 V 0 2 H 5 1 5
22 V 0 2 H 5 1 5
22 V 0 3 H 5 1 13
22 V 0 4 H 5 1 3
22 V 0 4 H 5 1 3
22 V 0 4 H 5 1 3
22 V 0 5 H 5 1 10
22 V 0 5 H 5 1 10
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46 P A 6 H 4 1 3
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46 P A 1 H 5 1 10
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46 P A 1 H 5 1 10
46 P A 1 H 5 1 10
46 P A 1 H 5 1 10
46 P A 1 H 5 1 10
46 P A 1 H 5 1 10
46 P A 1 H 5 1 10
46 P A 2 H 5 1 2
46 P A 3 H 5 1 17
46 P A 3 H 5 1 17
46 P A 3 H 5 1 17
46 P A 3 H 5 1 17
46 P A 3 H 5 1 17
46 P A 3 H 5 1 17
46 P A 3 H 5 1 17
46 P A 3 H 5 1 17
46 P A 3 H 5 1 17
46 P A 3 H 5 1 17
46 P A 3 H 5 1 17
46 P A 4 H 5 1 14
46 P A 4 H 5 1 14
46 P A 4 H 5 1 14
46 P A 4 H 5 1 14
46 P A 4 H 5 1 14
46 P A 4 H 5 1 14
46 P A 4 H 5 1 14
46 P A 4 H 5 1 14
46 P A 4 H 5 1 14
46 P A 5 H 5 1 8
46 P A 5 H 5 1 8
46 P A 5 H 5 1 8
46 P A 5 H 5 1 8
46 P A 5 H 5 1 8
46 P A 5 H 5 1 8
46 P A 6 H 5 1 10
46 P A 6 H 5 1 10
46 P A 6 H 5 1 10
46 P A 6 H 5 1 10
46 P A 6 H 5 1 10
46 P A 6 H 5 1 10
46 P A 6 H 5 1 10
46 P A 6 H 5 1 10
46 P A 7 H 5 1 16
46 P A 7 H 5 1 16
46 P A 7 H 5 1 16
46 P A 7 H 5 1 16
46 P A 7 H 5 1 16
46 P A 7 H 5 1 16
46 P A 7 H 5 1 16
46 P A 7 H 5 1 16
46 P A 7 H 5 1 16
46 P A 7 H 5 1 16
46 P A 7 H 5 1 16
46 P A 7 H 5 1 16
46 P A 2 H 6 1 15
46 P A 2 H 6 1 15
46 P A 2 H 6 1 15
46 P A 2 H 6 1 15
46 P A 2 H 6 1 15
46 P A 2 H 6 1 15
46 P A 2 H 6 1 15
46 P A 2 H 6 1 15
46 P A 2 H 6 1 15
46 P A 4 H 6 1 1
46 P A 5 H 6 1 1
46 P A 7 H 6 1 1
46 P A 2 H 7 1 2
46 P A 2 H 7 1 2
46 P A 1 L 8 1 1
46 P A 5 L 8 1 3
46 P A 5 L 8 1 3
46 P A 1 L 9 0 1
46 P A 4 L 9 0 2
46 P A 4 L 9 0 2
46 P A 6 L 9 0 1
46 P A 7 L 9 0 1
46 P A 4 L 10 1 1
46 P A 5 L 10 1 1
46 P A 1 L 12 1 4
46 P A 1 L 12 1 4
46 P A 1 L 12 1 4
46 P A 1 L 12 1 4
46 P A 2 L 12 1 7
46 P A 2 L 12 1 7
46 P A 2 L 12 1 7
46 P A 2 L 12 1 7
46 P A 2 L 12 1 7
46 P A 3 L 12 1 2
46 P A 3 L 12 1 2
46 P A 4 L 12 1 6
46 P A 4 L 12 1 6
46 P A 4 L 12 1 6
46 P A 4 L 12 1 6
46 P A 6 L 12 1 2
46 P A 6 L 12 1 2
46 P A 7 L 12 1 3
46 P A 7 L 12 1 3
46 P A 7 L 12 1 3
46 P A 2 L 13 0 2
46 P A 2 L 13 0 2
46 P A 2 L 14 1 2
46 P A 3 L 14 1 3
46 P A 3 L 14 1 3
46 P A 3 L 14 1 3
46 P A 6 L 14 1 2
46 P A 1 L 15 0 3
46 P A 7 L 15 0 2
46 P A 3 L 16 1 2
46 P A 7 L 16 1 7
46 P A 7 L 16 1 7
46 P A 7 L 16 1 7
46 P A 7 L 16 1 7
46 P A 7 L 16 1 7
46 P A 3 L 17 0 1
47 P A 2 H 4 1 2
47 P A 2 H 4 1 2
47 P A 5 H 4 1 5
47 P A 5 H 4 1 5
47 P A 5 H 4 1 5
47 P A 5 H 4 1 5
47 P A 1 H 5 1 10
47 P A 1 H 5 1 10
47 P A 1 H 5 1 10
47 P A 1 H 5 1 10
47 P A 1 H 5 1 10
47 P A 1 H 5 1 10
47 P A 1 H 5 1 10
47 P A 2 H 5 1 18
47 P A 2 H 5 1 18
47 P A 2 H 5 1 18
47 P A 2 H 5 1 18
47 P A 2 H 5 1 18
47 P A 2 H 5 1 18
47 P A 2 H 5 1 18
47 P A 2 H 5 1 18
47 P A 2 H 5 1 18
47 P A 3 H 5 1 14
47 P A 3 H 5 1 14
47 P A 3 H 5 1 14
47 P A 3 H 5 1 14
47 P A 3 H 5 1 14
47 P A 4 H 5 1 14
47 P A 4 H 5 1 14
47 P A 4 H 5 1 14
47 P A 4 H 5 1 14
47 P A 4 H 5 1 14
47 P A 4 H 5 1 14
47 P A 4 H 5 1 14
47 P A 4 H 5 1 14
47 P A 4 H 5 1 14
47 P A 5 H 5 1 10
47 P A 5 H 5 1 10
47 P A 5 H 5 1 10
47 P A 5 H 5 1 10
47 P A 5 H 5 1 10
47 P A 6 H 5 1 4
47 P A 7 H 5 1 18
47 P A 7 H 5 1 18
47 P A 7 H 5 1 18
47 P A 7 H 5 1 18
47 P A 7 H 5 1 18
47 P A 7 H 5 1 18
47 P A 7 H 5 1 18
47 P A 7 H 5 1 18
47 P A 7 H 5 1 18
47 P A 7 H 5 1 18
47 P A 7 H 5 1 18
47 P A 3 H 6 1 1
47 P A 4 H 6 1 1
47 P A 3 L 7 0 1
47 P A 3 L 8 1 4
47 P A 5 L 8 1 1
47 P A 6 L 8 1 1
47 P A 2 L 9 0 1
47 P A 5 L 9 0 2
47 P A 3 L 10 1 3
47 P A 3 L 10 1 3
47 P A 5 L 10 1 4
47 P A 5 L 10 1 4
47 P A 5 L 10 1 4
47 P A 2 L 11 0 4
47 P A 2 L 11 0 4
47 P A 6 L 11 0 4
47 P A 6 L 11 0 4
47 P A 4 L 12 1 2
47 P A 5 L 12 1 3
47 P A 6 L 12 1 4
47 P A 6 L 12 1 4
47 P A 7 L 12 1 2
47 P A 4 L 13 0 1
47 P A 6 L 13 0 1
47 P A 7 L 13 0 3
47 P A 2 L 14 1 3
47 P A 4 L 14 1 2
47 P A 6 L 14 1 3
47 P A 6 L 14 1 3
47 P A 7 L 14 1 1
47 P A 7 L 15 0 5
47 P A 7 L 15 0 5
47 P A 7 L 15 0 5
47 P A 1 L 16 1 1
47 P A 2 L 16 1 2
47 P A 4 L 16 1 5
47 P A 4 L 16 1 5
47 P A 4 L 16 1 5
47 P A 4 L 16 1 5
47 P A 7 L 16 1 3
47 P A 7 L 16 1 3
47 P A 1 L 17 0 2
47 P A 1 L 17 0 2
47 P A 4 L 17 0 1
47 P A 7 L 17 0 1
47 P A 4 L 18 1 2
47 P A 7 L 19 0 1
47 P A 1 L 20 1 1
52 P J 4 H 5 1 2
52 P J 4 H 5 1 2
52 P J 6 H 5 1 3
52 P J 6 H 5 1 3
52 P J 7 H 5 1 3
52 P J 1 H 6 1 6
52 P J 1 H 6 1 6
52 P J 1 H 6 1 6
52 P J 2 H 6 1 17
52 P J 2 H 6 1 17
52 P J 2 H 6 1 17
52 P J 2 H 6 1 17
52 P J 2 H 6 1 17
52 P J 2 H 6 1 17
52 P J 2 H 6 1 17
52 P J 2 H 6 1 17
52 P J 2 H 6 1 17
52 P J 2 H 6 1 17
52 P J 3 H 6 1 13
52 P J 3 H 6 1 13
52 P J 3 H 6 1 13
52 P J 3 H 6 1 13
52 P J 3 H 6 1 13
52 P J 3 H 6 1 13
52 P J 3 H 6 1 13
52 P J 3 H 6 1 13
52 P J 3 H 6 1 13
52 P J 3 H 6 1 13
52 P J 4 H 6 1 16
52 P J 4 H 6 1 16
52 P J 4 H 6 1 16
52 P J 4 H 6 1 16
52 P J 4 H 6 1 16
52 P J 4 H 6 1 16
52 P J 4 H 6 1 16
52 P J 4 H 6 1 16
52 P J 4 H 6 1 16
52 P J 4 H 6 1 16
52 P J 5 H 6 1 12
52 P J 5 H 6 1 12
52 P J 5 H 6 1 12
52 P J 6 H 6 1 10
52 P J 6 H 6 1 10
52 P J 6 H 6 1 10
52 P J 6 H 6 1 10
52 P J 6 H 6 1 10
52 P J 6 H 6 1 10
52 P J 6 H 6 1 10
52 P J 7 H 6 1 8
52 P J 7 H 6 1 8
52 P J 7 H 6 1 8
52 P J 7 H 6 1 8
52 P J 7 H 6 1 8
52 P J 7 H 6 1 8
52 P J 7 H 6 1 8
52 P J 3 H 7 1 1
52 P J 6 H 7 1 1
52 P J 5 L 7 1 2
52 P J 5 L 7 1 2
52 P J 7 L 7 1 1
52 P J 1 L 8 0 1
52 P J 2 L 9 1 1
52 P J 5 L 9 1 1
52 P J 7 L 9 1 2
52 P J 3 L 10 0 2
52 P J 3 L 10 0 2
52 P J 4 L 10 0 3
52 P J 7 L 10 0 1
52 P J 1 L 11 1 2
52 P J 3 L 11 1 2
52 P J 3 L 11 1 2
52 P J 4 L 11 1 2
52 P J 5 L 11 1 4
52 P J 5 L 11 1 4
52 P J 5 L 11 1 4
52 P J 5 L 11 1 4
52 P J 6 L 11 1 2
52 P J 6 L 11 1 2
52 P J 7 L 11 1 2
52 P J 2 L 12 0 1
52 P J 3 L 12 0 2
52 P J 3 L 12 0 2
52 P J 5 L 12 0 1
52 P J 6 L 12 0 1
52 P J 1 L 13 1 2
52 P J 2 L 13 1 1
52 P J 4 L 13 1 1
52 P J 5 L 13 1 6
52 P J 5 L 13 1 6
52 P J 6 L 13 1 2
52 P J 6 L 13 1 2
52 P J 1 L 14 0 3
52 P J 2 L 14 0 3
52 P J 4 L 14 0 1
52 P J 1 L 15 1 1
52 P J 2 L 15 1 2
52 P J 2 L 15 1 2
52 P J 3 L 15 1 1
52 P J 6 L 15 1 4
52 P J 6 L 15 1 4
52 P J 6 L 15 1 4
52 P J 1 L 16 0 1
52 P J 4 L 16 0 1
52 P J 2 L 17 1 1
53 P J 7 H 5 1 1
53 P J 1 H 6 1 11
53 P J 1 H 6 1 11
53 P J 1 H 6 1 11
53 P J 1 H 6 1 11
53 P J 1 H 6 1 11
53 P J 1 H 6 1 11
53 P J 1 H 6 1 11
53 P J 2 H 6 1 10
53 P J 2 H 6 1 10
53 P J 2 H 6 1 10
53 P J 2 H 6 1 10
53 P J 2 H 6 1 10
53 P J 2 H 6 1 10
53 P J 2 H 6 1 10
53 P J 3 H 6 1 14
53 P J 3 H 6 1 14
53 P J 3 H 6 1 14
53 P J 3 H 6 1 14
53 P J 3 H 6 1 14
53 P J 3 H 6 1 14
53 P J 4 H 6 1 18
53 P J 4 H 6 1 18
53 P J 4 H 6 1 18
53 P J 4 H 6 1 18
53 P J 4 H 6 1 18
53 P J 4 H 6 1 18
53 P J 4 H 6 1 18
53 P J 4 H 6 1 18
53 P J 4 H 6 1 18
53 P J 5 H 6 1 17
53 P J 5 H 6 1 17
53 P J 5 H 6 1 17
53 P J 5 H 6 1 17
53 P J 6 H 6 1 11
53 P J 6 H 6 1 11
53 P J 6 H 6 1 11
53 P J 6 H 6 1 11
53 P J 6 H 6 1 11
53 P J 6 H 6 1 11
53 P J 7 H 6 1 9
53 P J 7 H 6 1 9
53 P J 7 H 6 1 9
53 P J 7 H 6 1 9
53 P J 7 H 6 1 9
53 P J 7 H 6 1 9
53 P J 1 H 7 1 2
53 P J 2 H 7 1 4
53 P J 2 H 7 1 4
53 P J 3 H 7 1 1
53 P J 4 H 7 1 1
53 P J 1 L 7 1 4
53 P J 1 L 7 1 4
53 P J 2 L 7 1 1
53 P J 1 L 9 1 2
53 P J 2 L 9 1 3
53 P J 2 L 9 1 3
53 P J 2 L 9 1 3
53 P J 4 L 9 1 2
53 P J 7 L 9 1 4
53 P J 7 L 9 1 4
53 P J 7 L 9 1 4
53 P J 2 L 10 0 2
53 P J 3 L 10 0 1
53 P J 1 L 11 1 4
53 P J 3 L 11 1 6
53 P J 3 L 11 1 6
53 P J 5 L 11 1 2
53 P J 7 L 11 1 6
53 P J 7 L 11 1 6
53 P J 7 L 11 1 6
53 P J 4 L 12 0 3
53 P J 5 L 12 0 4
53 P J 5 L 12 0 4
53 P J 1 L 13 1 3
53 P J 3 L 13 1 1
53 P J 4 L 13 1 3
53 P J 4 L 13 1 3
53 P J 1 L 14 0 2
53 P J 3 L 14 0 5
53 P J 3 L 14 0 5
53 P J 3 L 14 0 5
53 P J 3 L 14 0 5
53 P J 5 L 14 0 4
53 P J 5 L 14 0 4
53 P J 5 L 14 0 4
53 P J 6 L 14 0 4
53 P J 6 L 14 0 4
53 P J 6 L 14 0 4
53 P J 6 L 14 0 4
53 P J 3 L 15 1 1
53 P J 5 L 15 1 3
53 P J 5 L 15 1 3
53 P J 6 L 15 1 4
53 P J 6 L 17 1 6
53 P J 6 L 18 0 1
library(MASS)
library(repeated)
library(rmutil)
library(lme4)
test<-read.table("...........\\test.txt",header=T)
attach(test)
names(test)
sapply(test, class)
test$pop <- factor(test$pop)
test$rep <- factor(test$rep)
m3<-lmer(dev~env*har*treat+dens + (1|pop/rep), family = Gamma)
summary(m3)
anova(m3)
m3.means<-colMeans(mcmcsamp(m3,10000,trans=FALSE))
m3.mcmc<-mcmcsamp(m3,10000,trans=FALSE)
qqmath(m3.mcmc)
library(coda)
summary(m3.mcmc)
........................................................................
............
Dr Tom C Cameron
Genetics, Ecology and Evolution
IICB, University of Leeds
Leeds, UK
Office: +44 (0)113 343 2837
Lab: +44 (0)113 343 2854
Fax: +44 (0)113 343 2835
Email: t.c.cameron at leeds.ac.uk
Webpage: click here
<http://www.fbs.leeds.ac.uk/staff/profile.php?tag=Cameron_TC>
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