I have a field experiment looking at the effect of a seed-mix treatment on insect abundance and I am struggling to define the correct random effects structure. My experiment is structured like this:

I have 16 Blocks, each split into 3 Sections, with each Section having a different seed mix (Treatment). Each night, I sample insects in 4 Blocks then the next night move on to the next 4 Blocks. This continues on a rotation Monday - Thursday (see image). So the whole experiment is sampled fully once in each week. I repeated this over 8 weeks (32 nights), and then repeated the whole thing again the next year, resulting in 16 weeks and 64 sample nights.

Originally, I thought that this was a partially crossed design as each Block is sampled on multiple nights and each Night is associated with multiple Blocks. I was originally coding my model (in R - lme4) as so:

Mod1 <- glm.nb(Abundance ~ Treatment + (1|Night) + (1|Block), data = data)

Mod2 <- glm.nb(Abundance ~ Treatment + (1|Big_block/Block/Site/Week), data = data)

This includes a random intercept for each Week, nested in each Site, nested in each Block, nested in each Big_block. As each Big_block is only sampled once in each week, this implicitly includes a Night effect... I think.

I am still not convinced by this structure though as I feel like it should be partially crossed, not fully nested. As I see it, the Night happens to 4 Blocks all at the same time, so I don't see how the temporal effect can be nested within Site, rather than 'above' it, as I am visualising it. I think It should be more like this:

Mod3 <- glm.nb(Abundance ~ Treatment + (1|Night) + (1|Block/Site), data = data)

Which is almost the same as my original formulation. In fact, I don't know whether (1|Block/Site) is any different to (1|Block) considering it's always the same Site in the same block.

Abundance: Continuous response
Treatment: Factor (3 levels)
Big_block: Factor (4 levels). Each Big_block contains 4 Blocks Block: Factor (16 levels). Each Block contains 3 Sites Site: Factor (48 levels). Each Site contains 1 Treatment
Night: Factor with 64 levels
Week: Factor with 16 levels.

I have a field experiment looking at the effect of a seed-mix treatment on moth abundance and I am struggling to define the correct random effects structure. My experiment is structured like this:

I have 16 Blocks, each split into 3 Sections, with each Section having a different seed mix (Treatment). Each night, I sample insects in 4 Blocks then the next night move on to the next 4 Blocks. This continues on a rotation Monday - Thursday (see image). So the whole experiment is sampled fully once in each week. I repeated this over 16 weeks over 2 years, amounting to 64 sample nights.

The data look like this:

str(Moths)

'data.frame':   768 obs. of  8 variables:
 $ Section  : Factor w/ 48 levels "10BC","10GR",..: 22 23 24 25 26 27 28 29 30 31 ...
 $ Week     : Factor w/ 16 levels "1_2018","1_2019",..: 1 1 1 1 1 1 1 1 1 1 ...
 $ Treatment: Factor w/ 3 levels "BC","GR","WF": 1 2 3 1 2 3 1 2 3 1 ...
 $ Abundance: int  5 3 5 7 3 16 6 6 14 8 ...
 $ Year     : Factor w/ 2 levels "2018","2019": 1 1 1 1 1 1 1 1 1 1 ...
 $ Big_block: Factor w/ 4 levels "B_1","B_2","B_3",..: 1 1 1 1 1 1 1 1 1 1 ...
 $ Night    : Factor w/ 64 levels "1_2019","10_2018",..: 58 58 58 58 58 58 58 58 58 58 ...
 $ Block    : Factor w/ 16 levels "1","2","3","4",..: 1 1 1 2 2 2 3 3 3 4 ...

head(Moths, 10)

   Section   Week Treatment Abundance Year Big_block  Night Block
1      1BC 1_2018        BC         5 2018       B_1 6_2018     1
2      1GR 1_2018        GR         3 2018       B_1 6_2018     1
3      1WF 1_2018        WF         5 2018       B_1 6_2018     1
4      2BC 1_2018        BC         7 2018       B_1 6_2018     2
5      2GR 1_2018        GR         3 2018       B_1 6_2018     2
6      2WF 1_2018        WF        16 2018       B_1 6_2018     2
7      3BC 1_2018        BC         6 2018       B_1 6_2018     3
8      3GR 1_2018        GR         6 2018       B_1 6_2018     3
9      3WF 1_2018        WF        14 2018       B_1 6_2018     3
10     4BC 1_2018        BC         8 2018       B_1 6_2018     4
> 

Originally, I thought that this was a partially crossed design as each Block is sampled on multiple Nights and each Night is associated with multiple Blocks. I was originally coding my model (in R - lme4) as so:

Mod1 <- glm.nb(Abundance ~ Treatment + (1|Night) + (1|Block), data = Moths)

Mod2 <- glm.nb(Abundance ~ Treatment + (1|Big_block/Block/Section/Week), data = Moths)

This includes a random intercept for each Week, nested in each Section, nested in each Block, nested in each Big_block. As each Big_block is only sampled once in each week, this implicitly includes a Night effect... I think.

I am still not convinced by this structure though as I feel like it should be partially crossed, not fully nested. As I see it, the Night happens to 4 Blocks all at the same time, so I don't see how the temporal effect can be nested within Section, rather than 'above' it, as I am visualising it. I think It should be more like this:

Mod3 <- glm.nb(Abundance ~ Treatment + (1|Night) + (1|Block/Section), data = Moths)

Which is almost the same as my original formulation. In fact, I don't know whether (1|Block/Section) is any different to (1|Block) considering it's always the same Section in the same Block.

Abundance: Continuous response
Treatment: Factor (3 levels)
Big_block: Factor (4 levels). Each Big_block contains 4 Blocks 
Block: Factor (16 levels). Each Block contains 3 Sections
Section: Factor (48 levels). Each Section contains 1 Treatment
Night: Factor with 64 levels
Week: Factor with 16 levels (Each Week contains 4 Nights).