I am struggling with the formulation in lme
of a generalized randomized block design (GRBD's) with subsampling.
The experiment consists of 2 treatments:
Genetic diversity (g_diversity) with two levels: mix / nomix crops.
Temporal diversity (t_diversity) with two levels: 4-years / 2-years - under crop rotation).
The field divided to 4 strips:
- 2 strips — 4-years rotation;
- 2 strips — 2-year rotation.
For each of those t_diversity treatments - the 1st strip is crop A and the second is crop B (I want to eliminate crop effect, so I set it (strip) as random var).
Each strip consists of 3 blocks, in each block 4 experimental plots, 2 plots for each of g_diversity levels (mix/non-mix).
In each plot, I took 3 samples for decomposition rate, some samples are missing (NA's). Later on I want to compare between the treatments performance.
My initial model looks like this:
lme(decomposed_weight ~ g_diversity*t_diversity, random=
~1 | strip/block/plot/repetition, data=Dt, na.action=na.omit)
However, I'm not sure whether this model reflect correctly the GRBD's analysis and take in consideration correctly the experimental design. Any suggestions and explanations are welcome!
EDIT FOR ANSWERS
This is the summary of the model :
>summary(m3)
>
Linear mixed-effects model fit by REML
> Data: Dt
> AIC BIC logLik
> -463.1911 -437.1106 240.5956
>Random effects:
> Formula: ~1 | strip
> (Intercept)
>StdDev: 0.03953433
>Formula: ~1 | block %in% strip
> (Intercept)
>StdDev: 0.008416519
> Formula: ~1 | stt_plot %in% block %in% strip
> (Intercept)
>StdDev: 0.008113865
> Formula: ~1 | repetition %in% stt_plot %in% block %in% strip
> (Intercept) Residual
>StdDev: 1.725507e-06 0.03639066
>Fixed effects: decomposed_weight ~ g_diversity * t_diversity
> Value Std.Error DF t-value p-value
>(Intercept) 1.5211944 0.028968984 64 52.51114 0.0000
>g_diversityNo-Mix -0.0085286 0.009506106 17 -0.89717 0.3822
>t_diversity4 years -0.0314160 0.008853077 64 -3.54860 0.0007
>g_diversityNo-Mix:t_diversity4 years 0.0534725 0.012414291 64 4.30733 0.0001
>Correlation:
> (Intr) g_dN-M t_dv4y
>g_diversityNo-Mix -0.167
>t_diversity4 years -0.158 0.480
>g_diversityNo-Mix:t_diversity4 years 0.112 -0.673 -0.713
>Standardized Within-Group Residuals:
> Min Q1 Med Q3 Max
>-2.49720166 -0.53862596 -0.01131197 0.67967649 3.39422115
>Number of Observations: 138
>Number of Groups:
> strip
>block %in% strip
2 >6
> stt_plot %in% block %in% strip repetition %in% stt_plot %in% block %in% strip
> 24 >72
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