# [R] Help please with predict.lme from nlme with nested random effects

Tom Cameron T.C.Cameron at leeds.ac.uk
Wed Nov 7 19:19:06 CET 2007

```Apologies for long posting but with this one I thought you would want all the details.
I have tried all the usual books and searched internet and R pages but I cant find an example of an analysis with this problem and no examples of the predict function being used with lme models that have nested random terms.

I am trying to predict the average size at maturation of the average individual from a random family within a
random population that has matured at a random density. These predictions are based on a model that is tested against data from a an experiment looking at the age and size at maturation of individuals receiving different rearing food  (food = 1 or 2), from populations of different backgrounds (env = C(constant) or P(periodic), har = o (unharvested) or 1(harvested)). Data copied below.

To do this I have built the following model using the nlme library

lmeS<-lme(log(size)~log(age)+env*har*food, random=~1|pop/family/density)

with

pop<-as.factor(data1\$pop)
family<-as.factor(data1\$family)
har<-as.factor(data1\$har)
env<-as.factor(data1\$env)
age<-as.numeric(data1\$age)
food<-as.factor(data1\$food)
density<-as.numeric(data1\$density)

There are two replicate populations for each env/har/food combination, 7 randomaly chosen families from each and the density of the tube on the day that an individual matures is dependent on mortality and previous maturations( individuals are removed upon mauration).
This would appear to be the minimal and correct model
I then built a new data set as follows

envn<-rep(c("C","P"),1,each=560)
harn<-rep(c(0,1),2,each=280)
popn<-rep(c(5, 6, 11, 12, 41, 42, 47, 48),each=140)
repn<-rep(c(1,2,3,4,5,6,7),40,each=4)
foodn<-rep(c(2,1,1,1,1),8,each=28)
densn<-rep(c(5,10,15,20),280)
agen<-rep(c(5,10,15,20,25),8,each=28)

NB:food and age are not balanced as when food = 2(high), individuals mature early, when food = 1(low) they have a minimum maturation age of about 8-10 days)
I then used predict to try and capture what the expected size at maturity is for a given age in the two food groups, based on past evolutionary environment (i.e. env*har), when controlling for the random terms.

If I build a model with density as a fixed effect it is very significant, or if I just build a linear model then I get
different size predictions at the different densities.
However, I have tried predict.lme for the same aim (see below) but density makes no difference to the predictions
I can either get a single output that does not vary with densities from "lmeSpred" or two columns of output which give me the fitted fixed effects and separately the fitted effects of pop, but they are identcal with lmeSpred2 or 3.

lmeSnew<-data.frame(env=factor(envn), har=factor(harn), pop=factor(popn),family=factor(repn),food=factor(foodn),density=densn, age=agen)

lmeSpred<-predict(lmeS,lmeSnew, level= 1:1,na.action=na.omit)
#or
lmeSpred2<-predict(lmeS,lmeSnew, level= 0:1,na.action=na.omit)
#or
lmeSpred3<-predict(lmeS,lmeSnew, level= 0:1/1/1,na.action=na.omit)
x<-data.frame(lmeSpred)
x

Can anyone tell me what I am doing wrong, and how I can get the predicts to tell me the effect of random density on size, or to give me the predicts for a specified control density?

data1
pop env har food family sex density size age
5 C 0 2 1 1 18 0.823 5
5 C 0 2 1 1 14 0.966 6
5 C 0 2 1 1 14 0.983 6
5 C 0 2 1 1 14 1.021 6
5 C 0 2 1 1 14 0.776 6
5 C 0 2 1 1 14 0.843 6
5 C 0 2 1 1 14 0.798 6
5 C 0 2 1 1 14 0.921 6
5 C 0 2 2 1 20 0.821 5
5 C 0 2 2 1 20 0.859 5
5 C 0 2 2 1 17 0.783 6
5 C 0 2 2 1 17 1.049 6
5 C 0 2 2 1 17 0.930 6
5 C 0 2 2 1 17 0.848 6
5 C 0 2 2 1 17 0.933 6
5 C 0 2 2 1 17 0.866 6
5 C 0 2 2 1 1 0.938 7
5 C 0 2 3 1 20 0.838 5
5 C 0 2 3 1 16 0.876 6
5 C 0 2 3 1 16 0.749 6
5 C 0 2 3 1 16 0.932 6
5 C 0 2 3 1 16 0.976 6
5 C 0 2 3 1 16 0.848 6
5 C 0 2 3 1 16 0.948 6
5 C 0 2 3 1 16 0.849 6
5 C 0 2 3 1 16 0.824 6
5 C 0 2 3 1 16 0.921 6
5 C 0 2 3 1 16 0.917 6
5 C 0 2 4 1 20 0.996 5
5 C 0 2 4 1 20 0.891 5
5 C 0 2 4 1 20 1.014 5
5 C 0 2 4 1 20 0.883 5
5 C 0 2 4 1 20 0.883 5
5 C 0 2 4 1 10 1.178 6
5 C 0 2 4 1 10 1.067 6
5 C 0 2 5 1 18 0.969 5
5 C 0 2 5 1 18 0.892 5
5 C 0 2 5 1 18 0.911 5
5 C 0 2 5 1 18 0.826 5
5 C 0 2 5 1 18 0.840 5
5 C 0 2 5 1 9 0.958 6
5 C 0 2 5 1 9 1.077 6
5 C 0 2 5 1 9 1.015 6
5 C 0 2 6 1 19 0.816 5
5 C 0 2 6 1 19 0.925 5
5 C 0 2 6 1 19 0.910 5
5 C 0 2 6 1 19 0.909 5
5 C 0 2 6 1 19 0.875 5
5 C 0 2 6 1 19 0.910 5
5 C 0 2 6 1 7 1.015 6
5 C 0 2 6 1 7 0.937 6
5 C 0 2 6 1 7 0.985 6
5 C 0 2 7 1 14 0.922 5
5 C 0 2 7 1 12 0.764 6
5 C 0 2 7 1 12 0.997 6
5 C 0 2 7 1 12 0.998 6
5 C 0 2 7 1 12 0.870 6
5 C 0 2 7 1 12 0.928 6
5 C 0 2 7 1 12 1.047 6
5 C 0 2 7 1 12 1.047 6
5 C 0 1 1 1 12 0.603 13
5 C 0 1 1 1 9 0.617 16
5 C 0 1 1 1 6 0.633 17
5 C 0 1 1 1 4 0.635 18
5 C 0 1 1 1 2 0.667 19
5 C 0 1 1 1 2 0.701 19
5 C 0 1 2 1 17 0.679 13
5 C 0 1 2 1 17 0.681 13
5 C 0 1 2 1 11 0.640 15
5 C 0 1 2 1 10 0.625 17
5 C 0 1 2 1 10 0.605 17
5 C 0 1 2 1 10 0.624 17
5 C 0 1 2 1 6 0.476 19
5 C 0 1 2 1 6 0.665 19
5 C 0 1 2 1 3 0.622 20
5 C 0 1 2 1 2 0.754 21
5 C 0 1 2 1 1 0.875 23
5 C 0 1 3 1 16 0.612 13
5 C 0 1 3 1 16 0.646 13
5 C 0 1 3 1 14 0.674 17
5 C 0 1 3 1 14 0.685 17
5 C 0 1 3 1 14 0.625 17
5 C 0 1 3 1 14 0.611 17
5 C 0 1 3 1 10 0.675 18
5 C 0 1 3 1 5 0.731 23
5 C 0 1 3 1 5 0.580 23
5 C 0 1 4 1 18 0.675 9
5 C 0 1 4 1 17 0.686 11
5 C 0 1 4 1 14 0.598 13
5 C 0 1 4 1 13 0.631 17
5 C 0 1 4 1 13 0.692 17
5 C 0 1 4 1 8 0.619 19
5 C 0 1 4 1 8 0.654 19
5 C 0 1 4 1 4 0.630 21
5 C 0 1 4 1 2 0.656 22
5 C 0 1 5 1 9 0.460 8
5 C 0 1 5 1 9 0.463 8
5 C 0 1 5 1 9 0.464 8
5 C 0 1 5 1 9 0.464 8
5 C 0 1 5 1 7 0.607 11
5 C 0 1 5 1 7 0.611 11
5 C 0 1 5 1 7 0.674 11
5 C 0 1 5 1 2 0.609 13
5 C 0 1 6 1 15 0.624 11
5 C 0 1 6 1 14 0.617 17
5 C 0 1 6 1 14 0.643 17
5 C 0 1 6 1 11 0.604 18
5 C 0 1 6 1 11 0.610 18
5 C 0 1 6 1 11 0.649 18
5 C 0 1 6 1 11 0.594 18
5 C 0 1 6 1 3 0.790 20
5 C 0 1 7 1 16 0.648 10
5 C 0 1 7 1 9 0.733 11
5 C 0 1 7 1 9 0.675 11
5 C 0 1 7 1 9 0.648 11
5 C 0 1 7 1 3 0.804 17
5 C 0 1 7 1 3 0.757 17
5 C 0 1 7 1 1 0.763 19
6 C 0 2 1 1 20 0.832 6
6 C 0 2 1 1 20 1.007 6
6 C 0 2 1 1 20 0.903 6
6 C 0 2 1 1 13 0.976 7
6 C 0 2 1 1 13 0.902 7
6 C 0 2 1 1 13 0.895 7
6 C 0 2 2 1 20 0.791 6
6 C 0 2 2 1 20 0.784 6
6 C 0 2 2 1 20 0.861 6
6 C 0 2 2 1 9 0.976 7
6 C 0 2 2 1 9 0.891 7
6 C 0 2 2 1 9 0.995 7
6 C 0 2 2 1 9 0.947 7
6 C 0 2 3 1 15 0.864 7
6 C 0 2 3 1 15 0.922 7
6 C 0 2 3 1 15 0.849 7
6 C 0 2 3 1 15 0.944 7
6 C 0 2 3 1 15 0.975 7
6 C 0 2 3 1 15 1.040 7
6 C 0 2 3 1 15 0.885 7
6 C 0 2 3 1 15 0.928 7
6 C 0 2 3 1 15 0.849 7
6 C 0 2 3 1 4 0.872 8
6 C 0 2 3 1 4 0.898 8
6 C 0 2 4 1 20 0.840 6
6 C 0 2 4 1 12 0.884 7
6 C 0 2 4 1 12 0.855 7
6 C 0 2 4 1 12 0.853 7
6 C 0 2 4 1 12 0.857 7
6 C 0 2 4 1 12 0.812 7
6 C 0 2 4 1 12 0.834 7
6 C 0 2 4 1 12 0.797 7
6 C 0 2 4 1 12 0.904 7
6 C 0 2 5 1 19 0.823 7
6 C 0 2 5 1 19 0.895 7
6 C 0 2 5 1 19 0.875 7
6 C 0 2 5 1 19 0.822 7
6 C 0 2 5 1 19 0.899 7
6 C 0 2 5 1 19 0.971 7
6 C 0 2 5 1 19 0.944 7
6 C 0 2 5 1 19 0.926 7
6 C 0 2 5 1 19 0.933 7
6 C 0 2 5 1 19 0.913 7
6 C 0 2 5 1 1 0.928 8
6 C 0 2 6 1 21 0.925 6
6 C 0 2 6 1 21 0.884 6
6 C 0 2 6 1 21 0.887 6
6 C 0 2 6 1 10 0.919 7
6 C 0 2 6 1 10 0.979 7
6 C 0 2 6 1 10 1.106 7
6 C 0 2 6 1 10 0.989 7
6 C 0 2 7 1 20 1.020 6
6 C 0 2 7 1 18 1.084 7
6 C 0 2 7 1 18 1.050 7
6 C 0 2 7 1 18 0.989 7
6 C 0 2 7 1 18 0.909 7
6 C 0 2 7 1 18 0.878 7
6 C 0 2 7 1 18 0.994 7
6 C 0 1 1 1 17 0.683 10
6 C 0 1 1 1 15 0.642 13
6 C 0 1 1 1 15 0.622 13
6 C 0 1 1 1 13 0.646 17
6 C 0 1 1 1 9 0.686 19
6 C 0 1 1 1 9 0.648 19
6 C 0 1 1 1 6 0.610 20
6 C 0 1 1 1 5 0.742 21
6 C 0 1 1 1 5 0.734 21
6 C 0 1 1 1 1 0.698 22
6 C 0 1 2 1 20 0.585 19
6 C 0 1 2 1 17 0.599 20
6 C 0 1 2 1 15 0.557 21
6 C 0 1 2 1 14 0.596 22
6 C 0 1 2 1 7 0.712 23
6 C 0 1 2 1 7 0.629 23
6 C 0 1 2 1 7 0.641 23
6 C 0 1 3 1 12 0.746 10
6 C 0 1 3 1 8 0.672 12
6 C 0 1 3 1 8 0.753 12
6 C 0 1 3 1 3 0.692 17
6 C 0 1 3 1 3 0.638 17
6 C 0 1 4 1 10 0.699 13
6 C 0 1 4 1 10 0.675 13
6 C 0 1 4 1 8 0.632 15
6 C 0 1 4 1 7 0.724 16
6 C 0 1 4 1 5 0.858 17
6 C 0 1 4 1 5 0.790 17
6 C 0 1 4 1 5 0.770 17
6 C 0 1 4 1 5 0.800 17
6 C 0 1 5 1 12 0.704 11
6 C 0 1 5 1 8 0.648 18
6 C 0 1 5 1 6 0.719 19
6 C 0 1 5 1 6 0.603 19
6 C 0 1 5 1 6 0.661 19
6 C 0 1 5 1 2 0.837 23
6 C 0 1 5 1 2 0.741 23
6 C 0 1 6 1 16 0.594 11
6 C 0 1 6 1 16 0.617 11
6 C 0 1 6 1 16 0.572 11
6 C 0 1 6 1 16 0.672 11
6 C 0 1 6 1 10 0.614 12
6 C 0 1 6 1 10 0.682 12
6 C 0 1 6 1 8 0.582 13
6 C 0 1 6 1 8 0.620 13
6 C 0 1 6 1 2 0.770 17
6 C 0 1 7 1 13 0.708 11
6 C 0 1 7 1 9 0.617 13
6 C 0 1 7 1 8 0.649 17
6 C 0 1 7 1 6 0.687 18
6 C 0 1 7 1 6 0.635 18
6 C 0 1 7 1 4 0.700 20
6 C 0 1 7 1 4 0.715 20
6 C 0 1 7 1 4 0.673 20
6 C 0 1 7 1 4 0.528 20
11 C 1 2 1 1 20 0.856 6
11 C 1 2 1 1 20 0.812 6
11 C 1 2 1 1 20 0.792 6
11 C 1 2 1 1 20 0.807 6
11 C 1 2 1 1 11 0.954 7
11 C 1 2 1 1 11 0.997 7
11 C 1 2 1 1 11 0.936 7
11 C 1 2 1 1 11 0.890 7
11 C 1 2 1 1 11 1.005 7
11 C 1 2 1 1 11 1.036 7
11 C 1 2 2 1 18 0.847 5
11 C 1 2 2 1 18 0.956 5
11 C 1 2 2 1 16 0.951 6
11 C 1 2 2 1 16 0.836 6
11 C 1 2 2 1 10 1.073 7
11 C 1 2 2 1 10 0.919 7
11 C 1 2 2 1 10 0.885 7
11 C 1 2 2 1 10 1.034 7
11 C 1 1 2 1 2 1.032 9
11 C 1 1 2 1 2 1.016 9
11 C 1 2 3 1 18 0.801 6
11 C 1 2 3 1 18 0.831 6
11 C 1 2 3 1 18 0.830 6
11 C 1 2 3 1 18 0.758 6
11 C 1 2 3 1 12 0.990 7
11 C 1 2 3 1 12 0.981 7
11 C 1 2 3 1 12 1.032 7
11 C 1 2 3 1 12 0.995 7
11 C 1 2 3 1 12 1.016 7
11 C 1 2 3 1 12 1.010 7
11 C 1 2 3 1 12 0.967 7
11 C 1 2 3 1 12 0.999 7
11 C 1 2 4 1 16 0.806 5
11 C 1 2 4 1 15 1.045 6
11 C 1 2 4 1 15 1.008 6
11 C 1 2 4 1 15 0.974 6
11 C 1 2 4 1 15 0.869 6
11 C 1 2 4 1 15 0.801 6
11 C 1 2 4 1 15 0.952 6
11 C 1 2 4 1 15 0.879 6
11 C 1 2 4 1 15 0.953 6
11 C 1 2 4 1 15 0.792 6
11 C 1 2 4 1 2 0.927 7
11 C 1 2 5 1 20 0.795 5
11 C 1 2 5 1 20 1.027 5
11 C 1 2 5 1 20 0.737 5
11 C 1 2 5 1 20 0.814 5
11 C 1 2 5 1 20 0.895 5
11 C 1 2 5 1 20 0.886 5
11 C 1 2 5 1 20 0.933 5
11 C 1 2 5 1 20 0.765 5
11 C 1 2 5 1 20 0.781 5
11 C 1 2 5 1 3 0.847 6
11 C 1 1 1 1 16 0.868 9
11 C 1 1 1 1 14 0.650 12
11 C 1 1 1 1 14 0.670 12
11 C 1 1 1 1 11 0.631 13
11 C 1 1 1 1 8 0.638 14
11 C 1 1 1 1 8 0.677 14
11 C 1 1 1 1 5 0.568 15
11 C 1 1 1 1 4 0.653 16
11 C 1 1 1 1 2 0.795 19
11 C 1 1 3 1 8 0.776 7
11 C 1 1 3 1 6 0.659 9
11 C 1 1 3 1 2 0.684 12
11 C 1 1 3 1 2 0.688 12
11 C 1 1 3 1 2 0.762 13
11 C 1 1 3 1 2 0.769 13
11 C 1 1 4 1 15 0.651 7
11 C 1 1 4 1 14 0.588 9
11 C 1 1 4 1 12 0.629 10
11 C 1 1 4 1 11 0.672 11
11 C 1 1 4 1 11 0.623 11
11 C 1 1 4 1 9 0.638 12
11 C 1 1 4 1 2 0.662 14
11 C 1 1 6 1 13 0.694 9
11 C 1 1 6 1 6 0.789 13
11 C 1 1 6 1 3 0.735 15
11 C 1 1 6 1 1 0.787 18
11 C 1 1 7 1 20 0.631 8
11 C 1 1 7 1 17 0.609 11
11 C 1 1 7 1 12 0.678 14
11 C 1 1 7 1 10 0.677 15
11 C 1 1 7 1 8 0.578 16
11 C 1 1 7 1 4 0.634 18
11 C 1 1 7 1 2 0.681 19
12 C 1 2 2 1 20 0.960 5
12 C 1 2 2 1 16 0.909 6
12 C 1 2 2 1 16 0.822 6
12 C 1 2 2 1 16 0.895 6
12 C 1 2 2 1 16 0.962 6
12 C 1 2 2 1 16 0.812 6
12 C 1 2 2 1 3 0.929 7
12 C 1 2 3 1 18 0.614 5
12 C 1 2 3 1 18 0.715 5
12 C 1 2 3 1 18 0.693 5
12 C 1 2 3 1 14 0.933 8
12 C 1 2 3 1 14 0.904 8
12 C 1 2 3 1 14 0.896 8
12 C 1 2 3 1 14 0.921 8
12 C 1 2 3 1 14 0.953 8
12 C 1 2 3 1 14 0.907 8
12 C 1 2 3 1 14 0.830 8
12 C 1 2 4 1 17 0.799 8
12 C 1 2 4 1 17 0.798 8
12 C 1 2 4 1 17 0.901 8
12 C 1 2 4 1 17 0.865 8
12 C 1 2 4 1 17 0.726 8
12 C 1 2 4 1 17 0.744 8
12 C 1 2 4 1 17 0.866 8
12 C 1 2 4 1 6 0.981 9
12 C 1 2 4 1 6 0.789 9
12 C 1 2 4 1 6 1.033 9
12 C 1 2 5 1 19 0.764 6
12 C 1 2 5 1 19 0.752 6
12 C 1 2 5 1 19 0.744 6
12 C 1 2 5 1 19 0.801 6
12 C 1 2 5 1 19 0.769 6
12 C 1 2 5 1 19 0.783 6
12 C 1 2 5 1 10 0.980 7
12 C 1 2 5 1 10 0.962 7
12 C 1 2 5 1 10 0.965 7
12 C 1 2 5 1 10 0.946 7
12 C 1 2 6 1 2 0.997 7
12 C 1 1 1 1 11 0.644 8
12 C 1 1 1 1 10 0.735 9
12 C 1 1 1 1 8 0.608 10
12 C 1 1 1 1 6 0.681 11
12 C 1 1 1 1 3 0.726 12
12 C 1 1 3 1 18 0.591 8
12 C 1 1 3 1 14 0.767 9
12 C 1 1 3 1 12 0.724 10
12 C 1 1 3 1 12 0.686 10
12 C 1 1 3 1 10 0.853 11
12 C 1 1 3 1 10 0.743 11
12 C 1 1 3 1 10 0.780 11
12 C 1 1 3 1 10 0.654 11
12 C 1 1 3 1 10 0.781 11
12 C 1 1 3 1 3 0.675 12
12 C 1 1 3 1 3 0.639 12
12 C 1 1 3 1 4 0.746 13
12 C 1 1 3 1 4 0.723 13
12 C 1 1 3 1 1 0.771 14
12 C 1 1 4 1 11 0.708 9
12 C 1 1 4 1 7 0.681 12
12 C 1 1 4 1 3 0.576 14
41 P 0 2 1 1 20 0.824 7
41 P 0 2 1 1 20 0.892 7
41 P 0 2 1 1 14 0.872 8
41 P 0 2 1 1 14 0.764 8
41 P 0 2 1 1 14 0.783 8
41 P 0 2 1 1 14 0.782 8
41 P 0 2 1 1 14 0.754 8
41 P 0 2 2 1 17 0.789 6
41 P 0 2 2 1 16 0.984 7
41 P 0 2 2 1 16 0.913 7
41 P 0 2 2 1 16 0.831 7
41 P 0 2 2 1 16 0.943 7
41 P 0 2 2 1 16 0.966 7
41 P 0 2 2 1 16 1.017 7
41 P 0 2 2 1 16 0.934 7
41 P 0 2 2 1 16 0.962 7
41 P 0 2 2 1 3 0.689 8
41 P 0 2 2 1 3 0.773 8
41 P 0 2 3 1 18 0.649 7
41 P 0 2 3 1 18 0.742 7
41 P 0 2 3 1 18 0.809 7
41 P 0 2 3 1 18 0.773 7
41 P 0 2 3 1 18 0.855 7
41 P 0 2 3 1 18 0.747 7
41 P 0 2 3 1 18 0.816 7
41 P 0 2 3 1 6 0.828 8
41 P 0 2 3 1 6 0.798 8
41 P 0 2 3 1 6 0.837 8
41 P 0 2 3 1 6 0.761 8
41 P 0 2 3 1 6 0.834 8
41 P 0 2 4 1 17 0.875 7
41 P 0 2 4 1 17 0.789 7
41 P 0 2 4 1 17 0.912 7
41 P 0 2 4 1 7 0.809 8
41 P 0 2 4 1 7 0.739 8
41 P 0 2 4 1 2 0.745 9
41 P 0 2 5 1 14 0.868 5
41 P 0 2 5 1 14 0.802 5
41 P 0 2 5 1 14 0.828 5
41 P 0 2 5 1 14 0.863 5
41 P 0 2 5 1 7 0.894 6
41 P 0 2 5 1 7 0.872 6
41 P 0 2 5 1 7 1.029 6
41 P 0 2 5 1 7 0.871 6
41 P 0 2 6 1 2 1.200 7
41 P 0 2 7 1 15 0.899 5
41 P 0 2 7 1 15 0.935 5
41 P 0 2 7 1 15 0.994 5
41 P 0 2 7 1 15 0.879 5
41 P 0 2 7 1 15 1.052 5
41 P 0 2 7 1 15 1.066 5
41 P 0 2 7 1 5 1.002 6
41 P 0 2 7 1 1 0.952 9
41 P 0 1 1 1 17 0.686 12
41 P 0 1 1 1 13 0.690 15
41 P 0 1 1 1 9 0.743 17
41 P 0 1 1 1 9 0.826 17
41 P 0 1 2 1 14 0.625 12
41 P 0 1 2 1 14 0.671 12
41 P 0 1 2 1 14 0.771 12
41 P 0 1 2 1 5 0.632 14
41 P 0 1 2 1 5 0.612 14
41 P 0 1 2 1 5 0.695 14
41 P 0 1 2 1 1 0.874 17
41 P 0 1 3 1 16 0.604 12
41 P 0 1 3 1 11 0.591 14
41 P 0 1 3 1 10 0.666 16
41 P 0 1 3 1 6 0.748 17
41 P 0 1 3 1 6 0.722 17
41 P 0 1 4 1 16 0.615 12
41 P 0 1 4 1 8 0.607 14
41 P 0 1 4 1 8 0.574 14
41 P 0 1 4 1 5 0.677 16
41 P 0 1 4 1 4 0.804 17
41 P 0 1 5 1 19 0.762 9
41 P 0 1 5 1 9 0.642 17
41 P 0 1 5 1 9 0.775 17
41 P 0 1 5 1 3 0.606 18
41 P 0 1 5 1 3 0.675 19
41 P 0 1 5 1 3 0.637 19
41 P 0 1 5 1 1 0.735 21
41 P 0 1 6 1 14 0.629 12
41 P 0 1 6 1 14 0.576 12
41 P 0 1 6 1 10 0.633 14
41 P 0 1 6 1 8 0.606 17
41 P 0 1 6 1 8 0.559 17
41 P 0 1 6 1 3 0.627 18
41 P 0 1 6 1 3 0.642 18
41 P 0 1 7 1 4 0.713 14
42 P 0 2 1 1 19 1.018 6
42 P 0 2 1 1 19 0.986 6
42 P 0 2 1 1 19 1.025 6
42 P 0 2 1 1 19 0.916 6
42 P 0 2 1 1 19 0.838 6
42 P 0 2 1 1 5 1.141 7
42 P 0 2 1 1 5 0.987 7
42 P 0 2 1 1 5 1.074 7
42 P 0 2 1 1 5 1.067 7
42 P 0 2 2 1 18 0.937 6
42 P 0 2 2 1 11 1.040 7
42 P 0 2 2 1 11 1.075 7
42 P 0 2 2 1 11 0.922 7
42 P 0 2 2 1 11 1.123 7
42 P 0 2 2 1 11 1.163 7
42 P 0 2 2 1 11 1.079 7
42 P 0 2 3 1 18 0.907 6
42 P 0 2 3 1 18 0.909 6
42 P 0 2 3 1 18 0.857 6
42 P 0 2 3 1 18 0.931 6
42 P 0 2 3 1 18 0.797 6
42 P 0 2 3 1 18 0.748 6
42 P 0 2 3 1 18 0.893 6
42 P 0 2 3 1 18 0.836 6
42 P 0 2 3 1 2 0.816 7
42 P 0 2 4 1 16 1.007 6
42 P 0 2 4 1 16 0.890 6
42 P 0 2 4 1 16 0.798 6
42 P 0 2 4 1 16 0.867 6
42 P 0 2 4 1 16 0.865 6
42 P 0 2 4 1 8 0.986 7
42 P 0 2 4 1 8 0.911 7
42 P 0 2 4 1 8 0.892 7
42 P 0 2 5 1 20 0.770 6
42 P 0 2 5 1 20 0.937 6
42 P 0 2 5 1 20 0.768 6
42 P 0 2 5 1 20 0.775 6
42 P 0 2 5 1 20 0.828 6
42 P 0 2 5 1 20 0.731 6
42 P 0 2 5 1 5 0.849 7
42 P 0 2 5 1 5 0.923 7
42 P 0 2 6 1 20 0.872 5
42 P 0 2 6 1 20 0.926 5
42 P 0 2 6 1 20 0.820 5
42 P 0 2 6 1 16 0.986 6
42 P 0 2 6 1 16 0.889 6
42 P 0 2 6 1 16 0.875 6
42 P 0 2 6 1 16 0.962 6
42 P 0 2 6 1 16 0.932 6
42 P 0 2 6 1 16 0.904 6
42 P 0 2 6 1 16 0.955 6
42 P 0 2 6 1 16 0.877 6
42 P 0 2 6 1 16 0.936 6
42 P 0 2 6 1 16 0.961 6
42 P 0 2 6 1 3 1.152 7
42 P 0 2 6 1 2 0.927 8
42 P 0 2 7 1 15 0.773 7
42 P 0 2 7 1 15 0.917 7
42 P 0 2 7 1 15 0.692 7
42 P 0 2 7 1 15 0.811 7
42 P 0 2 7 1 7 0.918 8
42 P 0 2 7 1 7 0.814 8
42 P 0 2 7 1 7 0.938 8
42 P 0 2 7 1 7 0.885 8
42 P 0 2 7 1 7 0.873 8
42 P 0 1 1 1 18 0.691 10
42 P 0 1 1 1 17 0.688 11
42 P 0 1 1 1 17 0.681 11
42 P 0 1 1 1 12 0.698 13
42 P 0 1 1 1 9 0.722 17
42 P 0 1 1 1 9 0.771 17
42 P 0 1 1 1 5 0.850 18
42 P 0 1 1 1 5 0.669 18
42 P 0 1 1 1 5 0.667 18
42 P 0 1 1 1 1 0.840 20
42 P 0 1 2 1 10 0.630 9
42 P 0 1 2 1 8 0.659 11
42 P 0 1 2 1 8 0.640 11
42 P 0 1 2 1 4 0.722 13
42 P 0 1 2 1 3 0.625 14
42 P 0 1 2 1 3 0.624 14
42 P 0 1 2 1 1 0.751 22
42 P 0 1 3 1 14 0.683 11
42 P 0 1 3 1 14 0.666 11
42 P 0 1 3 1 14 0.623 11
42 P 0 1 3 1 8 0.689 14
42 P 0 1 3 1 2 0.831 17
42 P 0 1 3 1 2 0.853 17
42 P 0 1 4 1 10 0.684 8
42 P 0 1 4 1 10 0.684 8
42 P 0 1 4 1 6 0.648 9
42 P 0 1 4 1 6 0.697 12
42 P 0 1 4 1 6 0.680 12
42 P 0 1 4 1 6 0.834 12
42 P 0 1 4 1 6 0.753 12
42 P 0 1 4 1 1 0.791 13
42 P 0 1 5 1 16 0.685 11
42 P 0 1 5 1 14 0.678 12
42 P 0 1 5 1 14 0.629 13
42 P 0 1 5 1 13 0.681 13
42 P 0 1 5 1 13 0.632 13
42 P 0 1 5 1 13 0.701 13
42 P 0 1 5 1 8 0.687 17
42 P 0 1 5 1 8 0.609 17
42 P 0 1 5 1 8 0.696 17
42 P 0 1 5 1 4 0.679 18
42 P 0 1 5 1 3 0.667 19
42 P 0 1 5 1 2 0.840 20
42 P 0 1 5 1 2 0.717 20
42 P 0 1 6 1 13 0.682 9
42 P 0 1 6 1 13 0.688 11
42 P 0 1 6 1 9 0.648 13
42 P 0 1 6 1 9 0.758 13
42 P 0 1 6 1 7 0.754 14
42 P 0 1 6 1 7 0.725 14
42 P 0 1 6 1 7 0.655 14
42 P 0 1 6 1 7 0.736 14
42 P 0 1 6 1 7 0.683 14
42 P 0 1 6 1 7 0.701 14
42 P 0 1 7 1 11 0.675 11
42 P 0 1 7 1 11 0.661 11
42 P 0 1 7 1 11 0.633 11
42 P 0 1 7 1 8 0.726 12
42 P 0 1 7 1 6 0.662 14
47 P 1 2 1 1 18 0.717 6
47 P 1 2 1 1 18 0.763 6
47 P 1 2 1 1 18 0.822 6
47 P 1 2 1 1 18 0.732 6
47 P 1 2 1 1 18 0.765 6
47 P 1 2 1 1 10 0.852 7
47 P 1 2 1 1 10 0.838 7
47 P 1 2 1 1 10 0.867 7
47 P 1 2 1 1 10 0.777 7
47 P 1 2 1 1 10 0.829 7
47 P 1 2 2 1 11 0.960 6
47 P 1 2 2 1 11 1.057 6
47 P 1 2 2 1 11 1.120 6
47 P 1 2 2 1 11 1.040 6
47 P 1 2 2 1 2 0.929 7
47 P 1 2 3 1 19 0.838 6
47 P 1 2 3 1 19 0.926 6
47 P 1 2 3 1 19 0.824 6
47 P 1 2 3 1 19 0.874 6
47 P 1 2 3 1 19 0.781 6
47 P 1 2 3 1 19 0.775 6
47 P 1 2 3 1 19 0.952 6
47 P 1 2 3 1 19 0.816 6
47 P 1 2 3 1 19 0.809 6
47 P 1 2 3 1 5 0.735 7
47 P 1 2 3 1 5 0.874 7
47 P 1 2 3 1 5 0.744 7
47 P 1 2 3 1 1 0.948 8
47 P 1 2 4 1 20 0.924 6
47 P 1 2 4 1 20 0.789 6
47 P 1 2 4 1 20 0.957 6
47 P 1 2 4 1 20 0.922 6
47 P 1 2 4 1 20 0.891 6
47 P 1 2 4 1 20 0.972 6
47 P 1 2 4 1 20 0.862 6
47 P 1 2 4 1 20 0.899 6
47 P 1 2 4 1 7 0.927 7
47 P 1 2 4 1 7 0.863 7
47 P 1 2 4 1 7 0.968 7
47 P 1 2 4 1 7 0.931 7
47 P 1 2 5 1 20 0.835 6
47 P 1 2 5 1 20 0.851 6
47 P 1 2 5 1 20 0.835 6
47 P 1 2 5 1 20 0.808 6
47 P 1 2 5 1 20 0.849 6
47 P 1 2 5 1 20 0.763 6
47 P 1 2 5 1 20 0.759 6
47 P 1 2 5 1 20 0.765 6
47 P 1 2 5 1 20 0.903 6
47 P 1 2 5 1 7 0.786 7
47 P 1 2 6 1 19 0.792 6
47 P 1 2 6 1 19 0.885 6
47 P 1 2 6 1 19 0.816 6
47 P 1 2 6 1 19 0.769 6
47 P 1 2 6 1 19 0.865 6
47 P 1 2 6 1 19 0.874 6
47 P 1 2 6 1 7 0.777 7
47 P 1 2 6 1 7 0.878 7
47 P 1 2 6 1 7 0.808 7
47 P 1 2 6 1 7 0.877 7
47 P 1 2 7 1 14 0.944 6
47 P 1 2 7 1 14 0.936 6
47 P 1 2 7 1 14 0.999 6
47 P 1 2 7 1 14 0.877 6
47 P 1 2 7 1 14 0.820 6
47 P 1 2 7 1 14 0.844 6
47 P 1 2 7 1 4 0.882 7
47 P 1 2 7 1 4 0.911 7
47 P 1 2 7 1 4 0.962 7
47 P 1 1 1 1 18 0.775 9
47 P 1 1 1 1 18 0.738 10
47 P 1 1 1 1 18 0.720 10
47 P 1 1 1 1 12 0.639 16
47 P 1 1 1 1 4 0.662 18
47 P 1 1 1 1 3 0.744 20
47 P 1 1 1 1 2 0.807 21
47 P 1 1 2 1 19 0.735 6
47 P 1 1 2 1 18 0.759 9
47 P 1 1 2 1 18 0.765 9
47 P 1 1 2 1 18 0.717 9
47 P 1 1 2 1 10 0.724 12
47 P 1 1 2 1 10 0.711 12
47 P 1 1 2 1 8 0.768 13
47 P 1 1 2 1 2 0.735 18
47 P 1 1 3 1 10 0.599 13
47 P 1 1 3 1 9 0.637 14
47 P 1 1 3 1 8 0.635 15
47 P 1 1 3 1 4 0.671 18
47 P 1 1 3 1 3 0.658 20
47 P 1 1 3 1 1 0.743 22
47 P 1 1 4 1 13 0.761 11
47 P 1 1 4 1 12 0.679 13
47 P 1 1 4 1 9 0.592 14
47 P 1 1 4 1 9 0.596 14
47 P 1 1 4 1 6 0.631 15
47 P 1 1 4 1 6 0.705 15
47 P 1 1 4 1 1 0.647 17
47 P 1 1 5 1 14 0.7 11
47 P 1 1 5 1 11 0.663 12
47 P 1 1 5 1 7 0.673 13
47 P 1 1 5 1 5 0.665 14
47 P 1 1 5 1 5 0.616 14
47 P 1 1 5 1 3 0.713 15
47 P 1 1 6 1 15 0.785 9
47 P 1 1 6 1 15 0.665 11
47 P 1 1 6 1 5 0.752 18
47 P 1 1 6 1 5 0.74 18
47 P 1 1 6 1 3 0.712 19
47 P 1 1 6 1 3 0.903 19
47 P 1 1 7 1 12 0.639 15
47 P 1 1 7 1 5 0.742 16
47 P 1 1 7 1 4 0.627 17
47 P 1 1 7 1 3 0.555 18
47 P 1 1 7 1 2 0.707 19
48 P 1 2 1 1 20 0.785 6
48 P 1 2 1 1 15 0.927 7
48 P 1 2 1 1 15 0.696 7
48 P 1 2 1 1 15 0.917 7
48 P 1 2 1 1 15 0.883 7
48 P 1 2 1 1 15 0.882 7
48 P 1 2 1 1 15 0.728 7
48 P 1 2 1 1 15 0.799 7
48 P 1 2 1 1 15 0.822 7
48 P 1 2 1 1 2 0.935 8
48 P 1 2 1 1 2 0.926 8
48 P 1 2 2 1 17 0.777 6
48 P 1 2 2 1 17 0.868 6
48 P 1 2 2 1 17 0.771 6
48 P 1 2 2 1 17 0.772 6
48 P 1 2 2 1 17 0.852 6
48 P 1 2 2 1 17 0.825 6
48 P 1 2 2 1 17 0.856 6
48 P 1 2 2 1 17 0.823 6
48 P 1 2 2 1 6 0.915 7
48 P 1 2 2 1 6 0.967 7
48 P 1 2 2 1 6 0.843 7
48 P 1 2 2 1 6 0.913 7
48 P 1 2 3 1 20 0.904 6
48 P 1 2 3 1 17 0.923 7
48 P 1 2 3 1 17 0.885 7
48 P 1 2 3 1 17 0.873 7
48 P 1 2 3 1 17 0.886 7
48 P 1 2 3 1 17 0.899 7
48 P 1 2 3 1 17 0.861 7
48 P 1 2 3 1 17 0.857 7
48 P 1 2 3 1 17 0.821 7
48 P 1 2 3 1 17 0.872 7
48 P 1 2 3 1 2 0.935 8
48 P 1 2 4 1 19 0.914 5
48 P 1 2 4 1 19 1.035 5
48 P 1 2 4 1 19 0.830 5
48 P 1 2 4 1 13 0.961 6
48 P 1 2 4 1 13 1.100 6
48 P 1 2 4 1 13 0.921 6
48 P 1 2 4 1 13 0.941 6
48 P 1 2 4 1 13 0.929 6
48 P 1 2 4 1 2 0.779 7
48 P 1 2 5 1 18 0.826 6
48 P 1 2 5 1 18 0.979 6
48 P 1 2 5 1 18 0.922 6
48 P 1 2 5 1 18 0.888 6
48 P 1 2 5 1 18 0.975 6
48 P 1 2 5 1 18 0.859 6
48 P 1 2 5 1 18 0.991 6
48 P 1 2 5 1 18 0.858 6
48 P 1 2 5 1 18 0.853 6
48 P 1 2 5 1 18 1.098 6
48 P 1 2 5 1 18 0.904 6
48 P 1 2 6 1 17 0.670 6
48 P 1 2 6 1 17 0.749 6
48 P 1 2 6 1 17 0.720 6
48 P 1 2 6 1 17 0.798 6
48 P 1 2 6 1 17 0.776 6
48 P 1 2 6 1 10 0.837 7
48 P 1 2 6 1 10 0.842 7
48 P 1 2 6 1 10 0.801 7
48 P 1 2 6 1 1 0.948 8
48 P 1 2 7 1 17 0.914 7
48 P 1 2 7 1 17 0.838 7
48 P 1 2 7 1 17 0.974 7
48 P 1 2 7 1 17 0.835 7
48 P 1 2 7 1 17 0.807 7
48 P 1 2 7 1 17 0.852 7
48 P 1 2 7 1 17 0.888 7
48 P 1 2 7 1 17 0.874 7
48 P 1 2 7 1 17 0.834 7
48 P 1 2 7 1 17 0.756 7
48 P 1 1 1 1 13 0.634 10
48 P 1 1 1 1 12 0.791 11
48 P 1 1 1 1 11 0.767 13
48 P 1 1 1 1 8 0.617 14
48 P 1 1 1 1 6 0.889 15
48 P 1 1 1 1 6 0.763 15
48 P 1 1 1 1 2 0.738 18
48 P 1 1 1 1 2 0.744 18
48 P 1 1 2 1 18 0.637 12
48 P 1 1 2 1 18 0.611 13
48 P 1 1 2 1 10 0.614 14
48 P 1 1 2 1 9 0.639 15
48 P 1 1 2 1 9 0.808 15
48 P 1 1 2 1 9 0.686 15
48 P 1 1 3 1 12 0.799 8
48 P 1 1 3 1 7 0.749 9
48 P 1 1 3 1 7 0.882 9
48 P 1 1 3 1 1 0.739 12
48 P 1 1 4 1 18 0.626 9
48 P 1 1 4 1 17 0.643 10
48 P 1 1 4 1 12 0.626 11
48 P 1 1 4 1 10 0.706 13
48 P 1 1 4 1 8 0.689 14
48 P 1 1 4 1 7 0.641 15
48 P 1 1 4 1 7 0.751 15
48 P 1 1 4 1 7 0.769 15
48 P 1 1 5 1 18 0.718 9
48 P 1 1 5 1 18 0.745 9
48 P 1 1 5 1 15 0.608 11
48 P 1 1 5 1 14 0.667 12
48 P 1 1 5 1 11 0.652 14
48 P 1 1 5 1 10 0.611 15
48 P 1 1 5 1 4 0.676 18
48 P 1 1 6 1 9 0.814 9
48 P 1 1 6 1 9 0.666 9
48 P 1 1 6 1 7 0.642 11
48 P 1 1 7 1 19 0.659 9
48 P 1 1 7 1 18 0.765 11
48 P 1 1 7 1 6 0.699 18

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