lme4 error: boundary (singular) fit: see ?isSingular

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,

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