I am trying to run lme4
package in R. I have 10 Lines in total with four plants for each line in each of the two replications. But some of the plants died and there are some missing values. Weight
is the response variable. Here are some lines from the data:
Line Rep Weight PLANT
Line 1 1 NA 1
Line 1 1 NA 2
Line 1 1 NA 3
Line 1 1 NA 4
Line 2 1 26 1
Line 2 1 26 2
Line 2 1 26 3
Line 2 1 27 4
Line 1 2 26 1
Line 1 2 28 2
Line 1 2 26 3
Line 1 2 25 4
Line 2 2 24 1
Line 2 2 26 2
Line 2 2 25 3
Line 2 2 NA 4
I want to run linear mixed model using lme4
package so I tried running:
lme4 <- lmer(Weight ~ 1 + (1|Rep:Plant), data=Data)
But I got an error:
boundary (singular) fit: see ?isSingular
> dput(Data)
structure(list(Line = c("Line 1", "Line 1", "Line 1", "Line 1",
"Line 2", "Line 2", "Line 2", "Line 2", "Line 1", "Line 1", "Line 1",
"Line 1", "Line 2", "Line 2", "Line 2", "Line 2"), Rep = c(1,
1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2), Weight = c(NA,
NA, NA, NA, 26, 26, 26, 27, 26, 28, 26, 25, 24, 26, 25, NA),
PLANT = c(1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4)), row.names = c(NA,
-16L), class = c("tbl_df", "tbl", "data.frame"))
I am using it for the first time and I am not sure about the error. I will appreciate any help!
Your model did fit, but it generated that warning because your random effects are very small. You can read more about this in this post or the help page
Let us look at your data:
ggplot(Data,aes(x=PLANT,y=Weight,col=Rep)) + geom_jitter() + geom_boxplot(alpha=0.2) + facet_wrap(~Rep)
The effects of PLANT
and in combination with Rep is extremely small. Let's look at the fitted model:
fit = lmer(Weight ~ 1 + (1|PLANT:Rep),data=Data)
boundary (singular) fit: see ?isSingular
ranef(fit)
$`PLANT:Rep`
(Intercept)
1:1 0
1:2 0
2:1 0
2:2 0
3:1 0
3:2 0
4:1 0
4:2 0
This is exactly what happened. So we can try to account for some other effects and we still see very small coefficients:
fit = lmer(Weight ~ Line + (1|Rep:PLANT),data=Data)
ranef(fit)
$`Rep:PLANT`
(Intercept)
1:1 1.397563e-19
1:2 2.811371e-19
1:3 8.112169e-20
1:4 1.813251e-19
2:1 -1.725964e-19
2:2 -2.463986e-20
2:3 -2.027357e-19
2:4 -2.833681e-19
The takehome message is, there's no really systematic effect coming from PLANT, so you don't need to specify a highly complicated model, do something like:
fit = lmer(Weight ~ Line + (1|Rep),data=Data)
The data in case anyone is interested:
Data = structure(list(Line = structure(c(1L, 1L, 1L, 1L, 12L, 12L, 12L,
12L, 23L, 23L, 23L, 23L, 34L, 34L, 34L, 34L, 45L, 45L, 45L, 45L,
56L, 56L, 56L, 56L, 65L, 65L, 65L, 65L, 66L, 66L, 66L, 66L, 67L,
67L, 67L, 67L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L,
5L, 5L, 5L, 5L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, 7L, 8L, 8L, 8L, 8L,
9L, 9L, 9L, 9L, 10L, 10L, 10L, 10L, 11L, 11L, 11L, 11L, 13L,
13L, 13L, 13L, 14L, 14L, 14L, 14L, 15L, 15L, 15L, 15L, 16L, 16L,
16L, 16L, 8L, 8L, 8L, 8L, 66L, 66L, 66L, 66L, 17L, 17L, 17L,
17L, 18L, 18L, 18L, 18L, 9L, 9L, 9L, 9L, 19L, 19L, 19L, 19L,
20L, 20L, 20L, 20L, 21L, 21L, 21L, 21L, 22L, 22L, 22L, 22L, 24L,
24L, 24L, 24L, 25L, 25L, 25L, 25L, 2L, 2L, 2L, 2L, 26L, 26L,
26L, 26L, 27L, 27L, 27L, 27L, 10L, 10L, 10L, 10L, 28L, 28L, 28L,
28L, 29L, 29L, 29L, 29L, 30L, 30L, 30L, 30L, 31L, 31L, 31L, 31L,
67L, 67L, 67L, 67L, 32L, 32L, 32L, 32L, 32L, 32L, 32L, 32L, 33L,
33L, 33L, 33L, 35L, 35L, 35L, 35L, 36L, 36L, 36L, 36L, 37L, 37L,
37L, 37L, 38L, 38L, 38L, 38L, 39L, 39L, 39L, 39L, 40L, 40L, 40L,
40L, 25L, 25L, 25L, 25L, 19L, 19L, 19L, 19L, 24L, 24L, 24L, 24L,
41L, 41L, 41L, 41L, 42L, 42L, 42L, 42L, 30L, 30L, 30L, 30L, 43L,
43L, 43L, 43L, 44L, 44L, 44L, 44L, 22L, 22L, 22L, 22L, 46L, 46L,
46L, 46L, 47L, 47L, 47L, 47L, 17L, 17L, 17L, 17L, 48L, 48L, 48L,
48L, 49L, 49L, 49L, 49L, 27L, 27L, 27L, 27L, 23L, 23L, 23L, 23L,
50L, 50L, 50L, 50L, 51L, 51L, 51L, 51L, 52L, 52L, 52L, 52L, 41L,
41L, 41L, 41L, 7L, 7L, 7L, 7L, 46L, 46L, 46L, 46L, 11L, 11L,
11L, 11L, 33L, 33L, 33L, 33L, 53L, 53L, 53L, 53L, 54L, 54L, 54L,
54L, 13L, 13L, 13L, 13L, 38L, 38L, 38L, 38L, 4L, 4L, 4L, 4L,
37L, 37L, 37L, 37L, 55L, 55L, 55L, 55L, 57L, 57L, 57L, 57L, 44L,
44L, 44L, 44L, 58L, 58L, 58L, 58L, 59L, 59L, 59L, 59L, 12L, 12L,
12L, 12L, 47L, 47L, 47L, 47L, 48L, 48L, 48L, 48L, 60L, 60L, 60L,
60L, 21L, 21L, 21L, 21L, 18L, 18L, 18L, 18L, 28L, 28L, 28L, 28L,
26L, 26L, 26L, 26L, 61L, 61L, 61L, 61L, 31L, 31L, 31L, 31L, 59L,
59L, 59L, 59L, 52L, 52L, 52L, 52L, 29L, 29L, 29L, 29L, 62L, 62L,
62L, 62L, 63L, 63L, 63L, 63L, 54L, 54L, 54L, 54L, 55L, 55L, 55L,
55L, 53L, 53L, 53L, 53L, 51L, 51L, 51L, 51L, 50L, 50L, 50L, 50L,
64L, 64L, 64L, 64L, 20L, 20L, 20L, 20L, 58L, 58L, 58L, 58L, 16L,
16L, 16L, 16L, 57L, 57L, 57L, 57L, 14L, 14L, 14L, 14L, 63L, 63L,
63L, 63L, 64L, 64L, 64L, 64L, 61L, 61L, 61L, 61L, 36L, 36L, 36L,
36L, 40L, 40L, 40L, 40L, 6L, 6L, 6L, 6L, 39L, 39L, 39L, 39L,
45L, 45L, 45L, 45L, 15L, 15L, 15L, 15L, 1L, 1L, 1L, 1L, 42L,
42L, 42L, 42L, 43L, 43L, 43L, 43L, 65L, 65L, 65L, 65L, 49L, 49L,
49L, 49L, 56L, 56L, 56L, 56L, 3L, 3L, 3L, 3L, 62L, 62L, 62L,
62L, 35L, 35L, 35L, 35L, 5L, 5L, 5L, 5L, 60L, 60L, 60L, 60L,
34L, 34L, 34L, 34L), .Label = c("Line1", "Line10", "Line11",
"Line12", "Line13", "Line14", "Line15", "Line16", "Line17", "Line18",
"Line19", "Line2", "Line20", "Line21", "Line22", "Line23", "Line24",
"Line25", "Line26", "Line27", "Line28", "Line29", "Line3", "Line30",
"Line31", "Line32", "Line33", "Line34", "Line35", "Line36", "Line37",
"Line38", "Line39", "Line4", "Line40", "Line41", "Line42", "Line43",
"Line44", "Line45", "Line46", "Line47", "Line48", "Line49", "Line5",
"Line50", "Line51", "Line52", "Line53", "Line54", "Line55", "Line56",
"Line57", "Line58", "Line59", "Line6", "Line60", "Line61", "Line62",
"Line63", "Line64", "Line65", "Line66", "Line67", "Line7", "Line8",
"Line9"), class = "factor"), Rep = structure(c(1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L), .Label = c("1", "2"), class = "factor"), Weight = c(NA,
NA, NA, NA, 26L, 26L, 26L, 27L, NA, NA, NA, NA, 26L, 28L, 26L,
25L, 22L, 17L, 20L, 20L, 28L, 20L, 27L, 26L, 22L, 25L, 21L, 25L,
18L, 18L, 19L, 18L, 24L, 28L, 23L, 30L, 29L, 25L, 26L, 27L, NA,
NA, NA, NA, 29L, 30L, 29L, 30L, NA, NA, NA, NA, 33L, NA, NA,
NA, 21L, 23L, 18L, 23L, 32L, 29L, 30L, 30L, 18L, 19L, 21L, 21L,
25L, 25L, 25L, 26L, 26L, 27L, NA, NA, 29L, 29L, 27L, 29L, 26L,
NA, NA, NA, 26L, 20L, 23L, 27L, NA, NA, NA, NA, 32L, 32L, 30L,
30L, 20L, 20L, 20L, 19L, 22L, 21L, 22L, 22L, 24L, 23L, 23L, 25L,
20L, 25L, NA, NA, 27L, 26L, NA, NA, NA, NA, NA, NA, 30L, 28L,
NA, NA, 25L, 26L, 27L, 26L, NA, NA, NA, NA, 20L, 19L, NA, NA,
19L, 27L, 26L, 29L, 26L, 29L, 31L, 29L, 25L, 25L, 24L, 25L, 26L,
25L, 26L, 26L, 25L, 24L, 24L, 28L, 22L, 26L, 24L, 28L, 29L, 30L,
26L, NA, NA, NA, NA, NA, 26L, 24L, 24L, 24L, NA, NA, NA, NA,
NA, NA, NA, NA, 30L, 30L, 30L, 31L, 24L, 25L, 28L, 22L, 28L,
31L, 30L, NA, 31L, 30L, 29L, 25L, 25L, 22L, 24L, 20L, 30L, 30L,
30L, 29L, 26L, 32L, 28L, 29L, 20L, 15L, 15L, 11L, 25L, 24L, 24L,
24L, 26L, 29L, 31L, 30L, 24L, 28L, 20L, 22L, 29L, 26L, 26L, 28L,
27L, 27L, 27L, 26L, 21L, 22L, 21L, NA, 28L, 29L, 24L, 24L, 28L,
29L, 28L, 27L, 28L, 29L, 27L, 29L, NA, NA, NA, NA, 22L, 26L,
21L, 21L, 26L, 30L, 28L, 30L, 27L, 26L, 28L, 26L, 25L, 25L, 26L,
26L, 27L, 26L, 23L, 29L, NA, NA, NA, NA, 27L, 23L, 29L, 23L,
28L, 29L, 28L, 26L, 20L, NA, NA, NA, 28L, 23L, 26L, 21L, 28L,
26L, 26L, 29L, 20L, 27L, 20L, 26L, 29L, 26L, 28L, 28L, 30L, 27L,
NA, NA, 26L, 21L, 26L, 25L, 27L, 26L, 27L, 24L, 25L, 20L, 21L,
20L, 25L, 25L, 31L, 24L, 29L, 28L, 31L, 27L, 25L, 28L, 26L, 26L,
NA, NA, NA, NA, 24L, 25L, 23L, 27L, 20L, 26L, 25L, 25L, 29L,
28L, 29L, 29L, 26L, 27L, 25L, 28L, NA, NA, NA, NA, 26L, 28L,
NA, NA, 21L, 20L, 31L, 25L, 31L, 28L, 30L, 29L, 23L, 25L, 24L,
28L, 25L, 22L, 25L, 25L, 28L, 29L, 28L, 29L, 26L, 24L, 25L, 26L,
29L, 27L, NA, NA, 26L, 29L, 29L, 30L, 25L, 24L, 25L, 24L, 28L,
25L, 29L, 28L, 24L, 24L, 24L, 24L, 28L, 30L, 27L, 27L, 26L, 25L,
25L, 25L, 25L, 25L, 28L, 25L, 25L, 30L, 28L, 25L, 22L, 24L, 25L,
24L, NA, NA, NA, NA, 5L, 7L, 4L, 5L, 21L, 20L, 22L, 24L, 25L,
27L, 25L, 28L, 32L, 31L, NA, NA, 19L, 26L, 20L, NA, 26L, 26L,
30L, 25L, 28L, 31L, 30L, 26L, 5L, 8L, 4L, 8L, 25L, 25L, 28L,
25L, 28L, 28L, 27L, 26L, 30L, 27L, 27L, 24L, 32L, 29L, 31L, 25L,
30L, 30L, 27L, 28L, 16L, 20L, 16L, 21L, 25L, 22L, 25L, 20L, 24L,
25L, 18L, 25L, 25L, 26L, 29L, 29L, 21L, 20L, 22L, 21L, 19L, 22L,
19L, 21L, 28L, 25L, 26L, 24L, 28L, 26L, 24L, 25L, NA, NA, NA,
NA, 25L, NA, NA, NA, 23L, 21L, 19L, 23L, 25L, 24L, 25L, NA, 22L,
30L, 29L, 26L, 25L, 25L, 24L, 24L), PLANT = structure(c(1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L,
3L, 4L, 1L, 2L, 3L, 4L), .Label = c("1", "2", "3", "4"), class = "factor"),
X = structure(c(4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L,
6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L,
5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L,
2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L,
4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L,
6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L,
5L, 6L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L,
7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L,
3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L,
1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L,
8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L,
7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L,
4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L,
6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L,
5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L,
2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L,
4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L,
6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L,
5L, 6L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L,
7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L,
3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L,
1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L,
8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L,
7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L,
3L, 7L, 8L, 1L, 4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L,
6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L,
5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L,
2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L,
4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L,
6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L, 5L, 6L, 4L, 2L,
5L, 6L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L,
7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L,
3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L,
1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L,
8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L,
7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L, 3L, 7L, 8L, 1L
), .Label = c("24", "12", "21", "11", "13", "14", "22", "23"
), class = "factor")), row.names = c(NA, -536L), class = "data.frame")
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