# Help with modeling GRBDs experimental design analysis (Generalized randomized block design)

I am struggling with the formulation in lme of a generalized randomized block design (GRBD's) with subsampling.

The experiment consists of 2 treatments:

1. Genetic diversity (g_diversity) with two levels: mix / nomix crops.

2. 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!

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
$$$$

• One more question about this model- while I'm running ANOVA on the model including the plot factor (random- nested) the g_diversity p.value is higher in comparison to ANOVA without the plot factor. The plot factor is in direct relations with the g_diversity (levels:mix/nomix) means that the plot represent a repetition of g_diversity treatment inside the blocks, in each block 2 plots are mix and 2 plots nomix. This is the reason for the higher p.value? Because I would expect lower p.value after considering plot as a random factor.. Sep 14, 2017 at 10:15
• I am not in a position to understand what exactly you want me to respond ? Try to be more specific in terms of hypothesis or your goals . T values in output ? P- value in comments ? Plot factor, between treatments what are exact goals ?
– user10619
Sep 14, 2017 at 10:50
• firstly, I want to write a model that reflect my experimental design (that mentioned above) in a proper way ( GRBD's). later on, I would like to compere between the treatments (g_diversity & t_diversity) effects on the response variable (decomposed_weight). Sep 14, 2017 at 11:56
• Do you want an interpretation of output you have incorporated as part of your question ? And - What do you mean by comparisons between treatments ?
– user10619
Sep 15, 2017 at 8:22