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

I am struggling with the formulation in lme of a generalize 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: 4years/2years- under crop rotation). The field divided to 4 strips: 2 strips- 4years rotation ; 2 strips- 2 year rotation. For each of those t_diversity treatments- 1 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!

Thanks

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

• Welcome Please indicate lme-4 output you obtained aftet executing your model. – Subhash C. Davar Sep 13 '17 at 14:53
• 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.. – Bents Sep 14 '17 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 ? – Subhash C. Davar Sep 14 '17 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). – Bents Sep 14 '17 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 ? – Subhash C. Davar Sep 15 '17 at 8:22