The simulated multivariate "simMV" dataset
simMV.RdThe simMV dataset was simulated from a multivariate DI model. It contains 192 plots
comprising of six species that vary in proportions (p1 - p6). Each plot was replicated once for testing a two-level factor treat, included at levels 0 and 1, resulting in a total
of 384 plots. There are four simulated responses (Y1 - Y4) recorded in a wide data format (one column per response). The data was simulated assuming that there were existing
covariances between the responses, an additive treatment effect, and both species identity and
species interaction effects were present.
Usage
data("simMV")Format
A data frame with 384 observations on the following twelve variables.
plotA numeric vector identifying each unique experimental unit
p1A numeric vector indicating the initial proportion of species 1
p2A numeric vector indicating the initial proportion of species 2
p3A numeric vector indicating the initial proportion of species 3
p4A numeric vector indicating the initial proportion of species 4
p5A numeric vector indicating the initial proportion of species 5
p6A numeric vector indicating the initial proportion of species 6
treatA two-level factor indicating whether a treatment was applied (1) or not (0)
Y1A numeric vector giving the simulated response for ecosystem function 1
Y2A numeric vector giving the simulated response for ecosystem function 2
Y3A numeric vector giving the simulated response for ecosystem function 3
Y4A numeric vector giving the simulated response for ecosystem function 4
Details
What are Diversity-Interactions (DI) models?
Diversity-Interactions (DI) models (Kirwan et al., 2009) are a set of tools for analysing and interpreting data from experiments that explore the effects of species diversity on community-level
responses. We strongly recommend that users read the short introduction to Diversity-Interactions
models (available at: DImodels). Further information on
Diversity-Interactions models is also available in Kirwan et al 2009 and Connolly et al 2013. The
multivariate DI model was developed by Dooley et al., 2015.
Parameter values for the simulation
Multivariate DI models take the general form of:
$${y}_{km} = {Identities}_{km} + {Interactions}_{km} + {Structures}_{k} + {\epsilon}_{km}$$
where \(y\) are the community-level responses, the \(Identities\) are the effects of species identities for each response and enter the model as individual species proportions at the beginning of the time period, the \(Interactions\) are the interactions among the species proportions, while \(Structures\) include other experimental structures such as blocks, treatments or density.
The dataset simMV was simulated with:
identity effects for the six species for response:
Y1 = 6.9, -0.3, 6.6, 1.7, -0.8, 4.3
Y2 = 4.9, 3.6, 4.4, 2.3, 4.3, 6.6
Y3 = -0.3, 4.6, 1.2, 6.8, 1.4, 6.9
Y4 = 4.1, 4.2, -0.5, 4.9, 6.7, -0.9, -1.0
an average pairwise interaction effect for response:
Y1 = 1.8
Y2 = 6.8
Y3 = 1.4
Y4 = 0.3
a teatment effect for response:
Y1 = 3.5
Y2 = -0.3
Y3 = 5.5
Y4 = -1.0
\(\epsilon\) assumed to have a multivaraite normal distribution with mean 0 and Sigma:
[1,] 3.87 -0.17 -0.23 0.31 [2,] -0.17 1.34 -0.11 0.49 [3,] -0.23 -0.11 2.95 -0.36 [4,] 0.31 0.49 -0.36 1.83
References
Dooley, A., Isbell, F., Kirwan, L., Connolly, J., Finn, J.A. and Brophy, C., 2015.
Testing the effects of diversity on ecosystem multifunctionality using a multivariate model.
Ecology Letters, 18(11), pp.1242-1251.
Finn, J.A., Kirwan, L., Connolly, J., Sebastia, M.T., Helgadottir, A., Baadshaug, O.H.,
Belanger, G., Black, A., Brophy, C., Collins, R.P., Cop, J., Dalmannsdóttir, S., Delgado, I.,
Elgersma, A., Fothergill, M., Frankow-Lindberg, B.E., Ghesquiere, A., Golinska, B., Golinski, P.,
Grieu, P., Gustavsson, A.M., Höglind, M., Huguenin-Elie, O., Jørgensen, M., Kadziuliene, Z.,
Kurki, P., Llurba, R., Lunnan, T., Porqueddu, C., Suter, M., Thumm, U., and Lüscher, A., 2013.
Ecosystem function enhanced by combining four functional types of plant species in intensively
managed grassland mixtures: a 3-year continental-scale field experiment.
Journal of Applied Ecology, 50(2), pp.365-375 .
Kirwan, L., Connolly, J., Finn, J.A., Brophy, C., Luscher, A., Nyfeler, D. and Sebastia, M.T.,
2009.
Diversity-interaction modeling: estimating contributions of species identities and interactions
to ecosystem function.
Ecology, 90(8), pp.2032-2038.
Examples
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#> <STYLE type='text/css' scoped>
#> PRE.fansi SPAN {padding-top: .25em; padding-bottom: .25em};
#> </STYLE>
## Modelling Example
# For a more thorough example of the workflow of this package, please see vignette
# DImulti_workflow using the following code:
# vignette("DImulti_workflow")
# We use head() to view the dataset
head(simMV)
#> plot p1 p2 p3 p4 p5 p6 treat Y1 Y2 Y3 Y4
#> 1 1 1 0 0 0 0 0 0 1.880817 5.108158 -1.9712356 4.8247704
#> 2 2 1 0 0 0 0 0 0 7.103477 5.183822 -4.0598298 3.1094539
#> 3 3 0 1 0 0 0 0 0 -1.444736 6.900983 6.3342200 4.9055054
#> 4 4 0 1 0 0 0 0 0 -1.756776 4.784160 5.2155726 5.3583856
#> 5 5 0 0 1 0 0 0 0 5.311257 4.258924 -0.4694982 -2.3078377
#> 6 6 0 0 1 0 0 0 0 5.975319 3.148215 1.9509040 -0.6064387
# We can use the function DImulti() to fit a multivariate DI model, with an intercept for "treat"
# for each ecosystem function. The dataset is wide, so the Y columns are all entered through 'y'
# and the first index of eco_func is "NA". We fit the average interaction structure and use "ML"
# so that we can perform model comparisons with varying fixed effects
MVmodel <- DImulti(y = paste0("Y", 1:4), eco_func = c("NA", "UN"), unit_IDs = 1,
prop = paste0("p", 1:6), data = simMV, DImodel = "AV", extra_fixed = ~ treat,
method = "ML")
print(MVmodel)
#> Note:
#> Method Used = ML
#> Correlation Structure Used = UN
#> Average Term Model
#> Theta value(s) = 1
#>
#> Generalized least squares fit by maximum likelihood
#> Model: value ~ 0 + func:((p1_ID + p2_ID + p3_ID + p4_ID + p5_ID + p6_ID + AV) + treat)
#> AIC BIC logLik
#> 5602.953 5827.104 -2759.476
#>
#> Multivariate Correlation Structure: General
#> Formula: ~0 | plot
#> Parameter estimate(s):
#> Correlation:
#> 1 2 3
#> 2 -0.108
#> 3 -0.019 -0.033
#> 4 0.041 0.241 -0.104
#>
#>
#> Table: Fixed Effect Coefficients
#>
#> Beta Std. Error t-value p-value Signif
#> -------------- ------- ----------- -------- ----------- -------
#> funcY1:p1_ID +6.659 0.554 12.025 7.253e-32 ***
#> funcY2:p1_ID +5.023 0.299 16.784 4.393e-58 ***
#> funcY3:p1_ID -1.110 0.434 -2.557 0.01065 *
#> funcY4:p1_ID +4.637 0.331 14.015 4.946e-42 ***
#> funcY1:p2_ID -0.007 0.558 -0.013 0.9897
#> funcY2:p2_ID +4.288 0.301 14.229 3.382e-43 ***
#> funcY3:p2_ID +4.405 0.437 10.082 3.539e-23 ***
#> funcY4:p2_ID +5.353 0.333 16.070 9.468e-54 ***
#> funcY1:p3_ID +6.948 0.597 11.640 4.808e-30 ***
#> funcY2:p3_ID +4.395 0.323 13.624 6.109e-40 ***
#> funcY3:p3_ID +1.325 0.468 2.831 0.004695 **
#> funcY4:p3_ID -0.614 0.357 -1.722 0.08536 +
#> funcY1:p4_ID +2.581 0.545 4.733 2.422e-06 ***
#> funcY2:p4_ID +1.993 0.295 6.763 1.93e-11 ***
#> funcY3:p4_ID +5.873 0.427 13.745 1.384e-40 ***
#> funcY4:p4_ID +5.400 0.326 16.577 8.141e-57 ***
#> funcY1:p5_ID -1.034 0.581 -1.779 0.07552 +
#> funcY2:p5_ID +4.733 0.314 15.070 6.646e-48 ***
#> funcY3:p5_ID +1.448 0.455 3.180 0.001505 **
#> funcY4:p5_ID +7.225 0.347 20.810 9.933e-85 ***
#> funcY1:p6_ID +4.374 0.533 8.203 4.99e-16 ***
#> funcY2:p6_ID +7.332 0.288 25.441 4.79e-119 ***
#> funcY3:p6_ID +6.508 0.418 15.571 8.463e-51 ***
#> funcY4:p6_ID -0.146 0.319 -0.458 0.6471
#> funcY1:AV +2.215 1.085 2.041 0.04144 *
#> funcY2:AV +7.502 0.586 12.791 1.228e-35 ***
#> funcY3:AV +2.470 0.850 2.905 0.003727 **
#> funcY4:AV +0.037 0.648 0.058 0.9541
#> funcY1:treat1 +3.368 0.214 15.702 1.447e-51 ***
#> funcY2:treat1 -0.449 0.116 -3.875 0.0001113 ***
#> funcY3:treat1 +5.602 0.168 33.329 7.422e-183 ***
#> funcY4:treat1 -1.002 0.128 -7.821 9.78e-15 ***
#>
#> Signif codes: 0-0.001 '***', 0.001-0.01 '**', 0.01-0.05 '*', 0.05-0.1 '+', 0.1-1.0 ' '
#>
#> Degrees of freedom: 1536 total; 1504 residual
#> Residual standard error: 2.079496
#>
#> Marginal variance covariance matrix
#> Y1 Y2 Y3 Y4
#> Y1 4.324300 -0.253190 -0.063976 0.10660
#> Y2 -0.253190 1.263000 -0.059597 0.33650
#> Y3 -0.063976 -0.059597 2.655800 -0.21084
#> Y4 0.106600 0.336500 -0.210840 1.54340
#> Standard Deviations: 2.0795 1.1238 1.6297 1.2423
# We can adjust the previous model to now cross "treat" with each other ID effect. We also specify
# different values of theta for each ecosystem function and use the "REML" method to get unbiased
# estimates.
# \donttest{
MVmodel_theta <- DImulti(y = paste0("Y", 1:4), eco_func = c("NA", "UN"), unit_IDs = 1,
prop = paste0("p", 1:6), data = simMV, DImodel = "AV", extra_fixed = ~ 1:treat,
theta = c(1, 0.5, 0.8, 0.6), method = "REML")
summary(MVmodel_theta)
#> Generalized least squares fit by REML
#> Model: value ~ 0 + func:((p1_ID + p2_ID + p3_ID + p4_ID + p5_ID + p6_ID + AV):treat)
#> Data: data
#> AIC BIC logLik
#> 5656.549 6006.336 -2762.275
#>
#> Correlation Structure: General
#> Formula: ~0 | plot
#> Parameter estimate(s):
#> Correlation:
#> 1 2 3
#> 2 -0.093
#> 3 -0.015 -0.026
#> 4 0.043 0.241 -0.109
#> Variance function:
#> Structure: Different standard deviations per stratum
#> Formula: ~0 | func
#> Parameter estimates:
#> Y1 Y2 Y3 Y4
#> 1.0000000 0.5658241 0.7829125 0.5930811
#>
#> Coefficients:
#> Value Std.Error t-value p-value
#> funcY1:p1_ID:treat0 6.074314 0.7699716 7.889010 0.0000
#> funcY2:p1_ID:treat0 6.281537 0.3739749 16.796678 0.0000
#> funcY3:p1_ID:treat0 -0.887469 0.5551350 -1.598654 0.1101
#> funcY4:p1_ID:treat0 4.824526 0.3988368 12.096491 0.0000
#> funcY1:p1_ID:treat1 10.435051 0.7699716 13.552514 0.0000
#> funcY2:p1_ID:treat1 5.879588 0.3739749 15.721876 0.0000
#> funcY3:p1_ID:treat1 4.650491 0.5551350 8.377225 0.0000
#> funcY4:p1_ID:treat1 3.602901 0.3988368 9.033523 0.0000
#> funcY1:p2_ID:treat0 -0.546413 0.7755777 -0.704524 0.4812
#> funcY2:p2_ID:treat0 4.871846 0.4089567 11.912865 0.0000
#> funcY3:p2_ID:treat0 4.884123 0.5869862 8.320676 0.0000
#> funcY4:p2_ID:treat0 5.533862 0.4329721 12.781106 0.0000
#> funcY1:p2_ID:treat1 3.753696 0.7755777 4.839872 0.0000
#> funcY2:p2_ID:treat1 4.809390 0.4089567 11.760146 0.0000
#> funcY3:p2_ID:treat1 9.723044 0.5869862 16.564347 0.0000
#> funcY4:p2_ID:treat1 4.332442 0.4329721 10.006285 0.0000
#> funcY1:p3_ID:treat0 6.523914 0.8321763 7.839582 0.0000
#> funcY2:p3_ID:treat0 5.022780 0.4179306 12.018214 0.0000
#> funcY3:p3_ID:treat0 1.035904 0.6149437 1.684551 0.0923
#> funcY4:p3_ID:treat0 -1.169494 0.4454722 -2.625291 0.0087
#> funcY1:p3_ID:treat1 10.544432 0.8321763 12.670911 0.0000
#> funcY2:p3_ID:treat1 5.470532 0.4179306 13.089569 0.0000
#> funcY3:p3_ID:treat1 7.494440 0.6149437 12.187196 0.0000
#> funcY4:p3_ID:treat1 -0.847901 0.4454722 -1.903375 0.0572
#> funcY1:p4_ID:treat0 2.921773 0.7576065 3.856584 0.0001
#> funcY2:p4_ID:treat0 2.954543 0.3715477 7.951988 0.0000
#> funcY3:p4_ID:treat0 5.602123 0.5527220 10.135517 0.0000
#> funcY4:p4_ID:treat0 5.373394 0.3970943 13.531782 0.0000
#> funcY1:p4_ID:treat1 5.423992 0.7576065 7.159379 0.0000
#> funcY2:p4_ID:treat1 2.802422 0.3715477 7.542563 0.0000
#> funcY3:p4_ID:treat1 12.046152 0.5527220 21.794232 0.0000
#> funcY4:p4_ID:treat1 4.612772 0.3970943 11.616312 0.0000
#> funcY1:p5_ID:treat0 -1.577562 0.8094772 -1.948865 0.0515
#> funcY2:p5_ID:treat0 5.984675 0.4092022 14.625227 0.0000
#> funcY3:p5_ID:treat0 1.199457 0.5986821 2.003496 0.0453
#> funcY4:p5_ID:treat0 7.751561 0.4352873 17.807918 0.0000
#> funcY1:p5_ID:treat1 2.695421 0.8094772 3.329829 0.0009
#> funcY2:p5_ID:treat1 5.097724 0.4092022 12.457714 0.0000
#> funcY3:p5_ID:treat1 7.577898 0.5986821 12.657633 0.0000
#> funcY4:p5_ID:treat1 5.891723 0.4352873 13.535251 0.0000
#> funcY1:p6_ID:treat0 3.895051 0.7403994 5.260743 0.0000
#> funcY2:p6_ID:treat0 8.300093 0.3688007 22.505633 0.0000
#> funcY3:p6_ID:treat0 6.201641 0.5409894 11.463517 0.0000
#> funcY4:p6_ID:treat0 -0.335013 0.3921846 -0.854224 0.3931
#> funcY1:p6_ID:treat1 8.061220 0.7403994 10.887664 0.0000
#> funcY2:p6_ID:treat1 8.125028 0.3688007 22.030947 0.0000
#> funcY3:p6_ID:treat1 12.741699 0.5409894 23.552587 0.0000
#> funcY4:p6_ID:treat1 -0.810038 0.3921846 -2.065452 0.0391
#> funcY1:AV:treat0 3.458425 1.5363658 2.251043 0.0245
#> funcY2:AV:treat0 1.228740 0.1473665 8.337984 0.0000
#> funcY3:AV:treat0 1.689570 0.5974726 2.827861 0.0047
#> funcY4:AV:treat0 -0.021516 0.2209063 -0.097399 0.9224
#> funcY1:AV:treat1 1.573802 1.5363658 1.024367 0.3058
#> funcY2:AV:treat1 0.993603 0.1473665 6.742389 0.0000
#> funcY3:AV:treat1 0.741279 0.5974726 1.240691 0.2149
#> funcY4:AV:treat1 -0.181836 0.2209063 -0.823135 0.4106
#>
#> Theta values: Y1:1, Y2:0.5, Y3:0.8, Y4:0.6
#>
#>
#> Correlation:
#> fY1:1_ID:0 fY2:1_ID:0 fY3:1_ID:0 fY4:1_ID:0 fY1:1_ID:1
#> funcY2:p1_ID:treat0 -0.086
#> funcY3:p1_ID:treat0 -0.015 -0.025
#> funcY4:p1_ID:treat0 0.041 0.241 -0.108
#> funcY1:p1_ID:treat1 0.000 0.000 0.000 0.000
#> funcY2:p1_ID:treat1 0.000 0.000 0.000 0.000 -0.086
#> funcY3:p1_ID:treat1 0.000 0.000 0.000 0.000 -0.015
#> funcY4:p1_ID:treat1 0.000 0.000 0.000 0.000 0.041
#> funcY1:p2_ID:treat0 0.177 -0.001 -0.002 0.002 0.000
#> funcY2:p2_ID:treat0 -0.005 -0.020 -0.001 -0.001 0.000
#> funcY3:p2_ID:treat0 -0.002 0.000 0.082 -0.003 0.000
#> funcY4:p2_ID:treat0 0.004 -0.003 -0.005 0.008 0.000
#> funcY1:p2_ID:treat1 0.000 0.000 0.000 0.000 0.177
#> funcY2:p2_ID:treat1 0.000 0.000 0.000 0.000 -0.005
#> funcY3:p2_ID:treat1 0.000 0.000 0.000 0.000 -0.002
#> funcY4:p2_ID:treat1 0.000 0.000 0.000 0.000 0.004
#> funcY1:p3_ID:treat0 0.256 -0.005 -0.003 0.004 0.000
#> funcY2:p3_ID:treat0 -0.010 0.018 -0.002 0.009 0.000
#> funcY3:p3_ID:treat0 -0.003 -0.001 0.142 -0.009 0.000
#> funcY4:p3_ID:treat0 0.006 0.007 -0.011 0.052 0.000
#> funcY1:p3_ID:treat1 0.000 0.000 0.000 0.000 0.256
#> funcY2:p3_ID:treat1 0.000 0.000 0.000 0.000 -0.010
#> funcY3:p3_ID:treat1 0.000 0.000 0.000 0.000 -0.003
#> funcY4:p3_ID:treat1 0.000 0.000 0.000 0.000 0.006
#> funcY1:p4_ID:treat0 0.342 -0.014 -0.004 0.008 0.000
#> funcY2:p4_ID:treat0 -0.018 0.112 -0.004 0.032 0.000
#> funcY3:p4_ID:treat0 -0.004 -0.004 0.232 -0.019 0.000
#> funcY4:p4_ID:treat0 0.010 0.030 -0.021 0.145 0.000
#> funcY1:p4_ID:treat1 0.000 0.000 0.000 0.000 0.342
#> funcY2:p4_ID:treat1 0.000 0.000 0.000 0.000 -0.018
#> funcY3:p4_ID:treat1 0.000 0.000 0.000 0.000 -0.004
#> funcY4:p4_ID:treat1 0.000 0.000 0.000 0.000 0.010
#> funcY1:p5_ID:treat0 0.159 0.004 -0.001 0.000 0.000
#> funcY2:p5_ID:treat0 0.000 -0.100 0.001 -0.019 0.000
#> funcY3:p5_ID:treat0 -0.001 0.001 0.033 0.004 0.000
#> funcY4:p5_ID:treat0 0.002 -0.021 0.001 -0.064 0.000
#> funcY1:p5_ID:treat1 0.000 0.000 0.000 0.000 0.159
#> funcY2:p5_ID:treat1 0.000 0.000 0.000 0.000 0.000
#> funcY3:p5_ID:treat1 0.000 0.000 0.000 0.000 -0.001
#> funcY4:p5_ID:treat1 0.000 0.000 0.000 0.000 0.002
#> funcY1:p6_ID:treat0 0.215 -0.003 -0.002 0.003 0.000
#> funcY2:p6_ID:treat0 -0.004 -0.038 0.000 -0.005 0.000
#> funcY3:p6_ID:treat0 -0.002 0.000 0.087 -0.003 0.000
#> funcY4:p6_ID:treat0 0.003 -0.006 -0.004 -0.006 0.000
#> funcY1:p6_ID:treat1 0.000 0.000 0.000 0.000 0.215
#> funcY2:p6_ID:treat1 0.000 0.000 0.000 0.000 -0.004
#> funcY3:p6_ID:treat1 0.000 0.000 0.000 0.000 -0.002
#> funcY4:p6_ID:treat1 0.000 0.000 0.000 0.000 0.003
#> funcY1:AV:treat0 -0.583 0.026 0.007 -0.015 0.000
#> funcY2:AV:treat0 0.047 -0.323 0.012 -0.089 0.000
#> funcY3:AV:treat0 0.008 0.008 -0.471 0.039 0.000
#> funcY4:AV:treat0 -0.023 -0.078 0.051 -0.367 0.000
#> funcY1:AV:treat1 0.000 0.000 0.000 0.000 -0.583
#> funcY2:AV:treat1 0.000 0.000 0.000 0.000 0.047
#> funcY3:AV:treat1 0.000 0.000 0.000 0.000 0.008
#> funcY4:AV:treat1 0.000 0.000 0.000 0.000 -0.023
#> fY2:1_ID:1 fY3:1_ID:1 fY4:1_ID:1 fY1:2_ID:0 fY2:2_ID:0
#> funcY2:p1_ID:treat0
#> funcY3:p1_ID:treat0
#> funcY4:p1_ID:treat0
#> funcY1:p1_ID:treat1
#> funcY2:p1_ID:treat1
#> funcY3:p1_ID:treat1 -0.025
#> funcY4:p1_ID:treat1 0.241 -0.108
#> funcY1:p2_ID:treat0 0.000 0.000 0.000
#> funcY2:p2_ID:treat0 0.000 0.000 0.000 -0.089
#> funcY3:p2_ID:treat0 0.000 0.000 0.000 -0.015 -0.026
#> funcY4:p2_ID:treat0 0.000 0.000 0.000 0.042 0.241
#> funcY1:p2_ID:treat1 -0.001 -0.002 0.002 0.000 0.000
#> funcY2:p2_ID:treat1 -0.020 -0.001 -0.001 0.000 0.000
#> funcY3:p2_ID:treat1 0.000 0.082 -0.003 0.000 0.000
#> funcY4:p2_ID:treat1 -0.003 -0.005 0.008 0.000 0.000
#> funcY1:p3_ID:treat0 0.000 0.000 0.000 0.139 -0.001
#> funcY2:p3_ID:treat0 0.000 0.000 0.000 -0.001 -0.035
#> funcY3:p3_ID:treat0 0.000 0.000 0.000 -0.001 0.000
#> funcY4:p3_ID:treat0 0.000 0.000 0.000 0.002 -0.005
#> funcY1:p3_ID:treat1 -0.005 -0.003 0.004 0.000 0.000
#> funcY2:p3_ID:treat1 0.018 -0.002 0.009 0.000 0.000
#> funcY3:p3_ID:treat1 -0.001 0.142 -0.009 0.000 0.000
#> funcY4:p3_ID:treat1 0.007 -0.011 0.052 0.000 0.000
#> funcY1:p4_ID:treat0 0.000 0.000 0.000 0.201 -0.007
#> funcY2:p4_ID:treat0 0.000 0.000 0.000 -0.006 0.024
#> funcY3:p4_ID:treat0 0.000 0.000 0.000 -0.002 -0.002
#> funcY4:p4_ID:treat0 0.000 0.000 0.000 0.004 0.009
#> funcY1:p4_ID:treat1 -0.014 -0.004 0.008 0.000 0.000
#> funcY2:p4_ID:treat1 0.112 -0.004 0.032 0.000 0.000
#> funcY3:p4_ID:treat1 -0.004 0.232 -0.019 0.000 0.000
#> funcY4:p4_ID:treat1 0.030 -0.021 0.145 0.000 0.000
#> funcY1:p5_ID:treat0 0.000 0.000 0.000 0.231 -0.011
#> funcY2:p5_ID:treat0 0.000 0.000 0.000 -0.011 0.081
#> funcY3:p5_ID:treat0 0.000 0.000 0.000 -0.003 -0.003
#> funcY4:p5_ID:treat0 0.000 0.000 0.000 0.006 0.022
#> funcY1:p5_ID:treat1 0.004 -0.001 0.000 0.000 0.000
#> funcY2:p5_ID:treat1 -0.100 0.001 -0.019 0.000 0.000
#> funcY3:p5_ID:treat1 0.001 0.033 0.004 0.000 0.000
#> funcY4:p5_ID:treat1 -0.021 0.001 -0.064 0.000 0.000
#> funcY1:p6_ID:treat0 0.000 0.000 0.000 0.194 -0.008
#> funcY2:p6_ID:treat0 0.000 0.000 0.000 -0.005 0.022
#> funcY3:p6_ID:treat0 0.000 0.000 0.000 -0.002 -0.002
#> funcY4:p6_ID:treat0 0.000 0.000 0.000 0.003 0.009
#> funcY1:p6_ID:treat1 -0.003 -0.002 0.003 0.000 0.000
#> funcY2:p6_ID:treat1 -0.038 0.000 -0.005 0.000 0.000
#> funcY3:p6_ID:treat1 0.000 0.087 -0.003 0.000 0.000
#> funcY4:p6_ID:treat1 -0.006 -0.004 -0.006 0.000 0.000
#> funcY1:AV:treat0 0.000 0.000 0.000 -0.480 0.027
#> funcY2:AV:treat0 0.000 0.000 0.000 0.038 -0.337
#> funcY3:AV:treat0 0.000 0.000 0.000 0.007 0.009
#> funcY4:AV:treat0 0.000 0.000 0.000 -0.019 -0.081
#> funcY1:AV:treat1 0.026 0.007 -0.015 0.000 0.000
#> funcY2:AV:treat1 -0.323 0.012 -0.089 0.000 0.000
#> funcY3:AV:treat1 0.008 -0.471 0.039 0.000 0.000
#> funcY4:AV:treat1 -0.078 0.051 -0.367 0.000 0.000
#> fY3:2_ID:0 fY4:2_ID:0 fY1:2_ID:1 fY2:2_ID:1 fY3:2_ID:1
#> funcY2:p1_ID:treat0
#> funcY3:p1_ID:treat0
#> funcY4:p1_ID:treat0
#> funcY1:p1_ID:treat1
#> funcY2:p1_ID:treat1
#> funcY3:p1_ID:treat1
#> funcY4:p1_ID:treat1
#> funcY1:p2_ID:treat0
#> funcY2:p2_ID:treat0
#> funcY3:p2_ID:treat0
#> funcY4:p2_ID:treat0 -0.109
#> funcY1:p2_ID:treat1 0.000 0.000
#> funcY2:p2_ID:treat1 0.000 0.000 -0.089
#> funcY3:p2_ID:treat1 0.000 0.000 -0.015 -0.026
#> funcY4:p2_ID:treat1 0.000 0.000 0.042 0.241 -0.109
#> funcY1:p3_ID:treat0 -0.001 0.002 0.000 0.000 0.000
#> funcY2:p3_ID:treat0 0.000 -0.005 0.000 0.000 0.000
#> funcY3:p3_ID:treat0 0.059 -0.002 0.000 0.000 0.000
#> funcY4:p3_ID:treat0 -0.002 -0.008 0.000 0.000 0.000
#> funcY1:p3_ID:treat1 0.000 0.000 0.139 -0.001 -0.001
#> funcY2:p3_ID:treat1 0.000 0.000 -0.001 -0.035 0.000
#> funcY3:p3_ID:treat1 0.000 0.000 -0.001 0.000 0.059
#> funcY4:p3_ID:treat1 0.000 0.000 0.002 -0.005 -0.002
#> funcY1:p4_ID:treat0 -0.002 0.005 0.000 0.000 0.000
#> funcY2:p4_ID:treat0 -0.002 0.009 0.000 0.000 0.000
#> funcY3:p4_ID:treat0 0.119 -0.009 0.000 0.000 0.000
#> funcY4:p4_ID:treat0 -0.008 0.051 0.000 0.000 0.000
#> funcY1:p4_ID:treat1 0.000 0.000 0.201 -0.007 -0.002
#> funcY2:p4_ID:treat1 0.000 0.000 -0.006 0.024 -0.002
#> funcY3:p4_ID:treat1 0.000 0.000 -0.002 -0.002 0.119
#> funcY4:p4_ID:treat1 0.000 0.000 0.004 0.009 -0.008
#> funcY1:p5_ID:treat0 -0.003 0.006 0.000 0.000 0.000
#> funcY2:p5_ID:treat0 -0.003 0.022 0.000 0.000 0.000
#> funcY3:p5_ID:treat0 0.161 -0.014 0.000 0.000 0.000
#> funcY4:p5_ID:treat0 -0.014 0.103 0.000 0.000 0.000
#> funcY1:p5_ID:treat1 0.000 0.000 0.231 -0.011 -0.003
#> funcY2:p5_ID:treat1 0.000 0.000 -0.011 0.081 -0.003
#> funcY3:p5_ID:treat1 0.000 0.000 -0.003 -0.003 0.161
#> funcY4:p5_ID:treat1 0.000 0.000 0.006 0.022 -0.014
#> funcY1:p6_ID:treat0 -0.002 0.005 0.000 0.000 0.000
#> funcY2:p6_ID:treat0 -0.001 0.007 0.000 0.000 0.000
#> funcY3:p6_ID:treat0 0.110 -0.009 0.000 0.000 0.000
#> funcY4:p6_ID:treat0 -0.007 0.045 0.000 0.000 0.000
#> funcY1:p6_ID:treat1 0.000 0.000 0.194 -0.008 -0.002
#> funcY2:p6_ID:treat1 0.000 0.000 -0.005 0.022 -0.001
#> funcY3:p6_ID:treat1 0.000 0.000 -0.002 -0.002 0.110
#> funcY4:p6_ID:treat1 0.000 0.000 0.003 0.009 -0.007
#> funcY1:AV:treat0 0.006 -0.014 0.000 0.000 0.000
#> funcY2:AV:treat0 0.011 -0.087 0.000 0.000 0.000
#> funcY3:AV:treat0 -0.420 0.039 0.000 0.000 0.000
#> funcY4:AV:treat0 0.045 -0.362 0.000 0.000 0.000
#> funcY1:AV:treat1 0.000 0.000 -0.480 0.027 0.006
#> funcY2:AV:treat1 0.000 0.000 0.038 -0.337 0.011
#> funcY3:AV:treat1 0.000 0.000 0.007 0.009 -0.420
#> funcY4:AV:treat1 0.000 0.000 -0.019 -0.081 0.045
#> fY4:2_ID:1 fY1:3_ID:0 fY2:3_ID:0 fY3:3_ID:0 fY4:3_ID:0
#> funcY2:p1_ID:treat0
#> funcY3:p1_ID:treat0
#> funcY4:p1_ID:treat0
#> funcY1:p1_ID:treat1
#> funcY2:p1_ID:treat1
#> funcY3:p1_ID:treat1
#> funcY4:p1_ID:treat1
#> funcY1:p2_ID:treat0
#> funcY2:p2_ID:treat0
#> funcY3:p2_ID:treat0
#> funcY4:p2_ID:treat0
#> funcY1:p2_ID:treat1
#> funcY2:p2_ID:treat1
#> funcY3:p2_ID:treat1
#> funcY4:p2_ID:treat1
#> funcY1:p3_ID:treat0 0.000
#> funcY2:p3_ID:treat0 0.000 -0.087
#> funcY3:p3_ID:treat0 0.000 -0.015 -0.026
#> funcY4:p3_ID:treat0 0.000 0.042 0.241 -0.109
#> funcY1:p3_ID:treat1 0.002 0.000 0.000 0.000 0.000
#> funcY2:p3_ID:treat1 -0.005 0.000 0.000 0.000 0.000
#> funcY3:p3_ID:treat1 -0.002 0.000 0.000 0.000 0.000
#> funcY4:p3_ID:treat1 -0.008 0.000 0.000 0.000 0.000
#> funcY1:p4_ID:treat0 0.000 0.307 -0.015 -0.004 0.008
#> funcY2:p4_ID:treat0 0.000 -0.013 0.100 -0.004 0.028
#> funcY3:p4_ID:treat0 0.000 -0.004 -0.004 0.213 -0.018
#> funcY4:p4_ID:treat0 0.000 0.008 0.028 -0.018 0.132
#> funcY1:p4_ID:treat1 0.005 0.000 0.000 0.000 0.000
#> funcY2:p4_ID:treat1 0.009 0.000 0.000 0.000 0.000
#> funcY3:p4_ID:treat1 -0.009 0.000 0.000 0.000 0.000
#> funcY4:p4_ID:treat1 0.051 0.000 0.000 0.000 0.000
#> funcY1:p5_ID:treat0 0.000 0.332 -0.019 -0.004 0.010
#> funcY2:p5_ID:treat0 0.000 -0.018 0.158 -0.005 0.041
#> funcY3:p5_ID:treat0 0.000 -0.004 -0.005 0.251 -0.023
#> funcY4:p5_ID:treat0 0.000 0.010 0.041 -0.023 0.184
#> funcY1:p5_ID:treat1 0.006 0.000 0.000 0.000 0.000
#> funcY2:p5_ID:treat1 0.022 0.000 0.000 0.000 0.000
#> funcY3:p5_ID:treat1 -0.014 0.000 0.000 0.000 0.000
#> funcY4:p5_ID:treat1 0.103 0.000 0.000 0.000 0.000
#> funcY1:p6_ID:treat0 0.000 0.237 -0.009 -0.003 0.006
#> funcY2:p6_ID:treat0 0.000 -0.006 0.019 -0.001 0.008
#> funcY3:p6_ID:treat0 0.000 -0.002 -0.002 0.132 -0.010
#> funcY4:p6_ID:treat0 0.000 0.004 0.009 -0.008 0.050
#> funcY1:p6_ID:treat1 0.005 0.000 0.000 0.000 0.000
#> funcY2:p6_ID:treat1 0.007 0.000 0.000 0.000 0.000
#> funcY3:p6_ID:treat1 -0.009 0.000 0.000 0.000 0.000
#> funcY4:p6_ID:treat1 0.045 0.000 0.000 0.000 0.000
#> funcY1:AV:treat0 0.000 -0.598 0.034 0.008 -0.018
#> funcY2:AV:treat0 0.000 0.048 -0.429 0.014 -0.111
#> funcY3:AV:treat0 0.000 0.009 0.011 -0.528 0.049
#> funcY4:AV:treat0 0.000 -0.024 -0.104 0.057 -0.460
#> funcY1:AV:treat1 -0.014 0.000 0.000 0.000 0.000
#> funcY2:AV:treat1 -0.087 0.000 0.000 0.000 0.000
#> funcY3:AV:treat1 0.039 0.000 0.000 0.000 0.000
#> funcY4:AV:treat1 -0.362 0.000 0.000 0.000 0.000
#> fY1:3_ID:1 fY2:3_ID:1 fY3:3_ID:1 fY4:3_ID:1 fY1:4_ID:0
#> funcY2:p1_ID:treat0
#> funcY3:p1_ID:treat0
#> funcY4:p1_ID:treat0
#> funcY1:p1_ID:treat1
#> funcY2:p1_ID:treat1
#> funcY3:p1_ID:treat1
#> funcY4:p1_ID:treat1
#> funcY1:p2_ID:treat0
#> funcY2:p2_ID:treat0
#> funcY3:p2_ID:treat0
#> funcY4:p2_ID:treat0
#> funcY1:p2_ID:treat1
#> funcY2:p2_ID:treat1
#> funcY3:p2_ID:treat1
#> funcY4:p2_ID:treat1
#> funcY1:p3_ID:treat0
#> funcY2:p3_ID:treat0
#> funcY3:p3_ID:treat0
#> funcY4:p3_ID:treat0
#> funcY1:p3_ID:treat1
#> funcY2:p3_ID:treat1 -0.087
#> funcY3:p3_ID:treat1 -0.015 -0.026
#> funcY4:p3_ID:treat1 0.042 0.241 -0.109
#> funcY1:p4_ID:treat0 0.000 0.000 0.000 0.000
#> funcY2:p4_ID:treat0 0.000 0.000 0.000 0.000 -0.087
#> funcY3:p4_ID:treat0 0.000 0.000 0.000 0.000 -0.015
#> funcY4:p4_ID:treat0 0.000 0.000 0.000 0.000 0.042
#> funcY1:p4_ID:treat1 0.307 -0.015 -0.004 0.008 0.000
#> funcY2:p4_ID:treat1 -0.013 0.100 -0.004 0.028 0.000
#> funcY3:p4_ID:treat1 -0.004 -0.004 0.213 -0.018 0.000
#> funcY4:p4_ID:treat1 0.008 0.028 -0.018 0.132 0.000
#> funcY1:p5_ID:treat0 0.000 0.000 0.000 0.000 0.197
#> funcY2:p5_ID:treat0 0.000 0.000 0.000 0.000 -0.003
#> funcY3:p5_ID:treat0 0.000 0.000 0.000 0.000 -0.002
#> funcY4:p5_ID:treat0 0.000 0.000 0.000 0.000 0.003
#> funcY1:p5_ID:treat1 0.332 -0.019 -0.004 0.010 0.000
#> funcY2:p5_ID:treat1 -0.018 0.158 -0.005 0.041 0.000
#> funcY3:p5_ID:treat1 -0.004 -0.005 0.251 -0.023 0.000
#> funcY4:p5_ID:treat1 0.010 0.041 -0.023 0.184 0.000
#> funcY1:p6_ID:treat0 0.000 0.000 0.000 0.000 0.228
#> funcY2:p6_ID:treat0 0.000 0.000 0.000 0.000 -0.004
#> funcY3:p6_ID:treat0 0.000 0.000 0.000 0.000 -0.002
#> funcY4:p6_ID:treat0 0.000 0.000 0.000 0.000 0.003
#> funcY1:p6_ID:treat1 0.237 -0.009 -0.003 0.006 0.000
#> funcY2:p6_ID:treat1 -0.006 0.019 -0.001 0.008 0.000
#> funcY3:p6_ID:treat1 -0.002 -0.002 0.132 -0.010 0.000
#> funcY4:p6_ID:treat1 0.004 0.009 -0.008 0.050 0.000
#> funcY1:AV:treat0 0.000 0.000 0.000 0.000 -0.616
#> funcY2:AV:treat0 0.000 0.000 0.000 0.000 0.049
#> funcY3:AV:treat0 0.000 0.000 0.000 0.000 0.009
#> funcY4:AV:treat0 0.000 0.000 0.000 0.000 -0.025
#> funcY1:AV:treat1 -0.598 0.034 0.008 -0.018 0.000
#> funcY2:AV:treat1 0.048 -0.429 0.014 -0.111 0.000
#> funcY3:AV:treat1 0.009 0.011 -0.528 0.049 0.000
#> funcY4:AV:treat1 -0.024 -0.104 0.057 -0.460 0.000
#> fY2:4_ID:0 fY3:4_ID:0 fY4:4_ID:0 fY1:4_ID:1 fY2:4_ID:1
#> funcY2:p1_ID:treat0
#> funcY3:p1_ID:treat0
#> funcY4:p1_ID:treat0
#> funcY1:p1_ID:treat1
#> funcY2:p1_ID:treat1
#> funcY3:p1_ID:treat1
#> funcY4:p1_ID:treat1
#> funcY1:p2_ID:treat0
#> funcY2:p2_ID:treat0
#> funcY3:p2_ID:treat0
#> funcY4:p2_ID:treat0
#> funcY1:p2_ID:treat1
#> funcY2:p2_ID:treat1
#> funcY3:p2_ID:treat1
#> funcY4:p2_ID:treat1
#> funcY1:p3_ID:treat0
#> funcY2:p3_ID:treat0
#> funcY3:p3_ID:treat0
#> funcY4:p3_ID:treat0
#> funcY1:p3_ID:treat1
#> funcY2:p3_ID:treat1
#> funcY3:p3_ID:treat1
#> funcY4:p3_ID:treat1
#> funcY1:p4_ID:treat0
#> funcY2:p4_ID:treat0
#> funcY3:p4_ID:treat0 -0.026
#> funcY4:p4_ID:treat0 0.241 -0.108
#> funcY1:p4_ID:treat1 0.000 0.000 0.000
#> funcY2:p4_ID:treat1 0.000 0.000 0.000 -0.087
#> funcY3:p4_ID:treat1 0.000 0.000 0.000 -0.015 -0.026
#> funcY4:p4_ID:treat1 0.000 0.000 0.000 0.042 0.241
#> funcY1:p5_ID:treat0 -0.002 -0.002 0.003 0.000 0.000
#> funcY2:p5_ID:treat0 -0.036 -0.001 -0.004 0.000 0.000
#> funcY3:p5_ID:treat0 0.000 0.088 -0.004 0.000 0.000
#> funcY4:p5_ID:treat0 -0.005 -0.004 -0.001 0.000 0.000
#> funcY1:p5_ID:treat1 0.000 0.000 0.000 0.197 -0.002
#> funcY2:p5_ID:treat1 0.000 0.000 0.000 -0.003 -0.036
#> funcY3:p5_ID:treat1 0.000 0.000 0.000 -0.002 0.000
#> funcY4:p5_ID:treat1 0.000 0.000 0.000 0.003 -0.005
#> funcY1:p6_ID:treat0 -0.006 -0.002 0.005 0.000 0.000
#> funcY2:p6_ID:treat0 -0.013 -0.001 0.000 0.000 0.000
#> funcY3:p6_ID:treat0 -0.001 0.111 -0.007 0.000 0.000
#> funcY4:p6_ID:treat0 0.001 -0.006 0.021 0.000 0.000
#> funcY1:p6_ID:treat1 0.000 0.000 0.000 0.228 -0.006
#> funcY2:p6_ID:treat1 0.000 0.000 0.000 -0.004 -0.013
#> funcY3:p6_ID:treat1 0.000 0.000 0.000 -0.002 -0.001
#> funcY4:p6_ID:treat1 0.000 0.000 0.000 0.003 0.001
#> funcY1:AV:treat0 0.033 0.008 -0.018 0.000 0.000
#> funcY2:AV:treat0 -0.417 0.014 -0.109 0.000 0.000
#> funcY3:AV:treat0 0.011 -0.534 0.049 0.000 0.000
#> funcY4:AV:treat0 -0.101 0.057 -0.453 0.000 0.000
#> funcY1:AV:treat1 0.000 0.000 0.000 -0.616 0.033
#> funcY2:AV:treat1 0.000 0.000 0.000 0.049 -0.417
#> funcY3:AV:treat1 0.000 0.000 0.000 0.009 0.011
#> funcY4:AV:treat1 0.000 0.000 0.000 -0.025 -0.101
#> fY3:4_ID:1 fY4:4_ID:1 fY1:5_ID:0 fY2:5_ID:0 fY3:5_ID:0
#> funcY2:p1_ID:treat0
#> funcY3:p1_ID:treat0
#> funcY4:p1_ID:treat0
#> funcY1:p1_ID:treat1
#> funcY2:p1_ID:treat1
#> funcY3:p1_ID:treat1
#> funcY4:p1_ID:treat1
#> funcY1:p2_ID:treat0
#> funcY2:p2_ID:treat0
#> funcY3:p2_ID:treat0
#> funcY4:p2_ID:treat0
#> funcY1:p2_ID:treat1
#> funcY2:p2_ID:treat1
#> funcY3:p2_ID:treat1
#> funcY4:p2_ID:treat1
#> funcY1:p3_ID:treat0
#> funcY2:p3_ID:treat0
#> funcY3:p3_ID:treat0
#> funcY4:p3_ID:treat0
#> funcY1:p3_ID:treat1
#> funcY2:p3_ID:treat1
#> funcY3:p3_ID:treat1
#> funcY4:p3_ID:treat1
#> funcY1:p4_ID:treat0
#> funcY2:p4_ID:treat0
#> funcY3:p4_ID:treat0
#> funcY4:p4_ID:treat0
#> funcY1:p4_ID:treat1
#> funcY2:p4_ID:treat1
#> funcY3:p4_ID:treat1
#> funcY4:p4_ID:treat1 -0.108
#> funcY1:p5_ID:treat0 0.000 0.000
#> funcY2:p5_ID:treat0 0.000 0.000 -0.088
#> funcY3:p5_ID:treat0 0.000 0.000 -0.015 -0.026
#> funcY4:p5_ID:treat0 0.000 0.000 0.042 0.241 -0.109
#> funcY1:p5_ID:treat1 -0.002 0.003 0.000 0.000 0.000
#> funcY2:p5_ID:treat1 -0.001 -0.004 0.000 0.000 0.000
#> funcY3:p5_ID:treat1 0.088 -0.004 0.000 0.000 0.000
#> funcY4:p5_ID:treat1 -0.004 -0.001 0.000 0.000 0.000
#> funcY1:p6_ID:treat0 0.000 0.000 0.270 -0.013 -0.003
#> funcY2:p6_ID:treat0 0.000 0.000 -0.010 0.068 -0.003
#> funcY3:p6_ID:treat0 0.000 0.000 -0.003 -0.003 0.170
#> funcY4:p6_ID:treat0 0.000 0.000 0.006 0.020 -0.013
#> funcY1:p6_ID:treat1 -0.002 0.005 0.000 0.000 0.000
#> funcY2:p6_ID:treat1 -0.001 0.000 0.000 0.000 0.000
#> funcY3:p6_ID:treat1 0.111 -0.007 0.000 0.000 0.000
#> funcY4:p6_ID:treat1 -0.006 0.021 0.000 0.000 0.000
#> funcY1:AV:treat0 0.000 0.000 -0.575 0.032 0.007
#> funcY2:AV:treat0 0.000 0.000 0.046 -0.402 0.013
#> funcY3:AV:treat0 0.000 0.000 0.008 0.010 -0.500
#> funcY4:AV:treat0 0.000 0.000 -0.023 -0.097 0.054
#> funcY1:AV:treat1 0.008 -0.018 0.000 0.000 0.000
#> funcY2:AV:treat1 0.014 -0.109 0.000 0.000 0.000
#> funcY3:AV:treat1 -0.534 0.049 0.000 0.000 0.000
#> funcY4:AV:treat1 0.057 -0.453 0.000 0.000 0.000
#> fY4:5_ID:0 fY1:5_ID:1 fY2:5_ID:1 fY3:5_ID:1 fY4:5_ID:1
#> funcY2:p1_ID:treat0
#> funcY3:p1_ID:treat0
#> funcY4:p1_ID:treat0
#> funcY1:p1_ID:treat1
#> funcY2:p1_ID:treat1
#> funcY3:p1_ID:treat1
#> funcY4:p1_ID:treat1
#> funcY1:p2_ID:treat0
#> funcY2:p2_ID:treat0
#> funcY3:p2_ID:treat0
#> funcY4:p2_ID:treat0
#> funcY1:p2_ID:treat1
#> funcY2:p2_ID:treat1
#> funcY3:p2_ID:treat1
#> funcY4:p2_ID:treat1
#> funcY1:p3_ID:treat0
#> funcY2:p3_ID:treat0
#> funcY3:p3_ID:treat0
#> funcY4:p3_ID:treat0
#> funcY1:p3_ID:treat1
#> funcY2:p3_ID:treat1
#> funcY3:p3_ID:treat1
#> funcY4:p3_ID:treat1
#> funcY1:p4_ID:treat0
#> funcY2:p4_ID:treat0
#> funcY3:p4_ID:treat0
#> funcY4:p4_ID:treat0
#> funcY1:p4_ID:treat1
#> funcY2:p4_ID:treat1
#> funcY3:p4_ID:treat1
#> funcY4:p4_ID:treat1
#> funcY1:p5_ID:treat0
#> funcY2:p5_ID:treat0
#> funcY3:p5_ID:treat0
#> funcY4:p5_ID:treat0
#> funcY1:p5_ID:treat1 0.000
#> funcY2:p5_ID:treat1 0.000 -0.088
#> funcY3:p5_ID:treat1 0.000 -0.015 -0.026
#> funcY4:p5_ID:treat1 0.000 0.042 0.241 -0.109
#> funcY1:p6_ID:treat0 0.007 0.000 0.000 0.000 0.000
#> funcY2:p6_ID:treat0 0.019 0.000 0.000 0.000 0.000
#> funcY3:p6_ID:treat0 -0.015 0.000 0.000 0.000 0.000
#> funcY4:p6_ID:treat0 0.095 0.000 0.000 0.000 0.000
#> funcY1:p6_ID:treat1 0.000 0.270 -0.013 -0.003 0.007
#> funcY2:p6_ID:treat1 0.000 -0.010 0.068 -0.003 0.019
#> funcY3:p6_ID:treat1 0.000 -0.003 -0.003 0.170 -0.015
#> funcY4:p6_ID:treat1 0.000 0.006 0.020 -0.013 0.095
#> funcY1:AV:treat0 -0.017 0.000 0.000 0.000 0.000
#> funcY2:AV:treat0 -0.104 0.000 0.000 0.000 0.000
#> funcY3:AV:treat0 0.046 0.000 0.000 0.000 0.000
#> funcY4:AV:treat0 -0.431 0.000 0.000 0.000 0.000
#> funcY1:AV:treat1 0.000 -0.575 0.032 0.007 -0.017
#> funcY2:AV:treat1 0.000 0.046 -0.402 0.013 -0.104
#> funcY3:AV:treat1 0.000 0.008 0.010 -0.500 0.046
#> funcY4:AV:treat1 0.000 -0.023 -0.097 0.054 -0.431
#> fY1:6_ID:0 fY2:6_ID:0 fY3:6_ID:0 fY4:6_ID:0 fY1:6_ID:1
#> funcY2:p1_ID:treat0
#> funcY3:p1_ID:treat0
#> funcY4:p1_ID:treat0
#> funcY1:p1_ID:treat1
#> funcY2:p1_ID:treat1
#> funcY3:p1_ID:treat1
#> funcY4:p1_ID:treat1
#> funcY1:p2_ID:treat0
#> funcY2:p2_ID:treat0
#> funcY3:p2_ID:treat0
#> funcY4:p2_ID:treat0
#> funcY1:p2_ID:treat1
#> funcY2:p2_ID:treat1
#> funcY3:p2_ID:treat1
#> funcY4:p2_ID:treat1
#> funcY1:p3_ID:treat0
#> funcY2:p3_ID:treat0
#> funcY3:p3_ID:treat0
#> funcY4:p3_ID:treat0
#> funcY1:p3_ID:treat1
#> funcY2:p3_ID:treat1
#> funcY3:p3_ID:treat1
#> funcY4:p3_ID:treat1
#> funcY1:p4_ID:treat0
#> funcY2:p4_ID:treat0
#> funcY3:p4_ID:treat0
#> funcY4:p4_ID:treat0
#> funcY1:p4_ID:treat1
#> funcY2:p4_ID:treat1
#> funcY3:p4_ID:treat1
#> funcY4:p4_ID:treat1
#> funcY1:p5_ID:treat0
#> funcY2:p5_ID:treat0
#> funcY3:p5_ID:treat0
#> funcY4:p5_ID:treat0
#> funcY1:p5_ID:treat1
#> funcY2:p5_ID:treat1
#> funcY3:p5_ID:treat1
#> funcY4:p5_ID:treat1
#> funcY1:p6_ID:treat0
#> funcY2:p6_ID:treat0 -0.087
#> funcY3:p6_ID:treat0 -0.015 -0.026
#> funcY4:p6_ID:treat0 0.042 0.241 -0.108
#> funcY1:p6_ID:treat1 0.000 0.000 0.000 0.000
#> funcY2:p6_ID:treat1 0.000 0.000 0.000 0.000 -0.087
#> funcY3:p6_ID:treat1 0.000 0.000 0.000 0.000 -0.015
#> funcY4:p6_ID:treat1 0.000 0.000 0.000 0.000 0.042
#> funcY1:AV:treat0 -0.552 0.026 0.006 -0.014 0.000
#> funcY2:AV:treat0 0.044 -0.320 0.011 -0.086 0.000
#> funcY3:AV:treat0 0.008 0.008 -0.449 0.038 0.000
#> funcY4:AV:treat0 -0.022 -0.077 0.048 -0.358 0.000
#> funcY1:AV:treat1 0.000 0.000 0.000 0.000 -0.552
#> funcY2:AV:treat1 0.000 0.000 0.000 0.000 0.044
#> funcY3:AV:treat1 0.000 0.000 0.000 0.000 0.008
#> funcY4:AV:treat1 0.000 0.000 0.000 0.000 -0.022
#> fY2:6_ID:1 fY3:6_ID:1 fY4:6_ID:1 fY1:AV:0 fY2:AV:0 fY3:AV:0
#> funcY2:p1_ID:treat0
#> funcY3:p1_ID:treat0
#> funcY4:p1_ID:treat0
#> funcY1:p1_ID:treat1
#> funcY2:p1_ID:treat1
#> funcY3:p1_ID:treat1
#> funcY4:p1_ID:treat1
#> funcY1:p2_ID:treat0
#> funcY2:p2_ID:treat0
#> funcY3:p2_ID:treat0
#> funcY4:p2_ID:treat0
#> funcY1:p2_ID:treat1
#> funcY2:p2_ID:treat1
#> funcY3:p2_ID:treat1
#> funcY4:p2_ID:treat1
#> funcY1:p3_ID:treat0
#> funcY2:p3_ID:treat0
#> funcY3:p3_ID:treat0
#> funcY4:p3_ID:treat0
#> funcY1:p3_ID:treat1
#> funcY2:p3_ID:treat1
#> funcY3:p3_ID:treat1
#> funcY4:p3_ID:treat1
#> funcY1:p4_ID:treat0
#> funcY2:p4_ID:treat0
#> funcY3:p4_ID:treat0
#> funcY4:p4_ID:treat0
#> funcY1:p4_ID:treat1
#> funcY2:p4_ID:treat1
#> funcY3:p4_ID:treat1
#> funcY4:p4_ID:treat1
#> funcY1:p5_ID:treat0
#> funcY2:p5_ID:treat0
#> funcY3:p5_ID:treat0
#> funcY4:p5_ID:treat0
#> funcY1:p5_ID:treat1
#> funcY2:p5_ID:treat1
#> funcY3:p5_ID:treat1
#> funcY4:p5_ID:treat1
#> funcY1:p6_ID:treat0
#> funcY2:p6_ID:treat0
#> funcY3:p6_ID:treat0
#> funcY4:p6_ID:treat0
#> funcY1:p6_ID:treat1
#> funcY2:p6_ID:treat1
#> funcY3:p6_ID:treat1 -0.026
#> funcY4:p6_ID:treat1 0.241 -0.108
#> funcY1:AV:treat0 0.000 0.000 0.000
#> funcY2:AV:treat0 0.000 0.000 0.000 -0.080
#> funcY3:AV:treat0 0.000 0.000 0.000 -0.014 -0.026
#> funcY4:AV:treat0 0.000 0.000 0.000 0.040 0.242 -0.107
#> funcY1:AV:treat1 0.026 0.006 -0.014 0.000 0.000 0.000
#> funcY2:AV:treat1 -0.320 0.011 -0.086 0.000 0.000 0.000
#> funcY3:AV:treat1 0.008 -0.449 0.038 0.000 0.000 0.000
#> funcY4:AV:treat1 -0.077 0.048 -0.358 0.000 0.000 0.000
#> fY4:AV:0 fY1:AV:1 fY2:AV:1 fY3:AV:1
#> funcY2:p1_ID:treat0
#> funcY3:p1_ID:treat0
#> funcY4:p1_ID:treat0
#> funcY1:p1_ID:treat1
#> funcY2:p1_ID:treat1
#> funcY3:p1_ID:treat1
#> funcY4:p1_ID:treat1
#> funcY1:p2_ID:treat0
#> funcY2:p2_ID:treat0
#> funcY3:p2_ID:treat0
#> funcY4:p2_ID:treat0
#> funcY1:p2_ID:treat1
#> funcY2:p2_ID:treat1
#> funcY3:p2_ID:treat1
#> funcY4:p2_ID:treat1
#> funcY1:p3_ID:treat0
#> funcY2:p3_ID:treat0
#> funcY3:p3_ID:treat0
#> funcY4:p3_ID:treat0
#> funcY1:p3_ID:treat1
#> funcY2:p3_ID:treat1
#> funcY3:p3_ID:treat1
#> funcY4:p3_ID:treat1
#> funcY1:p4_ID:treat0
#> funcY2:p4_ID:treat0
#> funcY3:p4_ID:treat0
#> funcY4:p4_ID:treat0
#> funcY1:p4_ID:treat1
#> funcY2:p4_ID:treat1
#> funcY3:p4_ID:treat1
#> funcY4:p4_ID:treat1
#> funcY1:p5_ID:treat0
#> funcY2:p5_ID:treat0
#> funcY3:p5_ID:treat0
#> funcY4:p5_ID:treat0
#> funcY1:p5_ID:treat1
#> funcY2:p5_ID:treat1
#> funcY3:p5_ID:treat1
#> funcY4:p5_ID:treat1
#> funcY1:p6_ID:treat0
#> funcY2:p6_ID:treat0
#> funcY3:p6_ID:treat0
#> funcY4:p6_ID:treat0
#> funcY1:p6_ID:treat1
#> funcY2:p6_ID:treat1
#> funcY3:p6_ID:treat1
#> funcY4:p6_ID:treat1
#> funcY1:AV:treat0
#> funcY2:AV:treat0
#> funcY3:AV:treat0
#> funcY4:AV:treat0
#> funcY1:AV:treat1 0.000
#> funcY2:AV:treat1 0.000 -0.080
#> funcY3:AV:treat1 0.000 -0.014 -0.026
#> funcY4:AV:treat1 0.000 0.040 0.242 -0.107
#>
#> Standardized residuals:
#> Min Q1 Med Q3 Max
#> -2.94493716 -0.65287965 -0.01437135 0.67321174 3.86323102
#>
#> Residual standard error: 2.1071
#> Degrees of freedom: 1536 total; 1480 residual
# We can now use any S3 method compatible with a gls object, for example, predict()
predict(MVmodel_theta, newdata = simMV[which(simMV$plot == 1), ])
#> plot Yvalue func
#> 1 1 6.0743137 Y1
#> 2 1 6.2815368 Y2
#> 3 1 -0.8874687 Y3
#> 4 1 4.8245259 Y4
# }
##################################################################################################
#
##################################################################################################
## Code to simulate data
#
#
# \donttest{
set.seed(412)
props <- data.frame(plot = integer(),
p1 = integer(),
p2 = integer(),
p3 = integer(),
p4 = integer(),
p5 = integer(),
p6 = integer())
index <- 1 #row number
#Monocultures
for(i in 1:6) #6 species
{
for(j in 1:2) #2 technical reps
{
props[index, i+1] <- 1
index <- index + 1
}
}
#Equal Mixtures
for(rich in sort(rep(2:6, 3))) #3 reps at each richness level
{
sp <- sample(1:6, rich) #randomly pick species from pool
for(j in 1:2) #2 technical reps
{
for(i in sp)
{
props[index, i+1] <- 1/rich #equal proportions
}
index <- index + 1
}
}
#Unequal Mixtures
for(rich in sort(rep(c(2, 3, 4, 5, 6), 15))) #15 reps at each richness level
{
sp <- sample(1:6, rich, replace = TRUE) #randomly pick species from pool
for(j in 1:2) #2 technical reps
{
for(i in 1:6)
{
props[index, i+1] <- sum(sp==i)/rich #equal proportions
}
index <- index + 1
}
}
props[is.na(props)] <- 0
mySimData <- props
mySimData$treat <- 0
mySimDataDupe <- mySimData
mySimDataDupe$treat <- 1
mySimData <- rbind(mySimData, mySimDataDupe)
mySimData$plot <- 1:nrow(mySimData)
mySimData$Y1 <- NA
mySimData$Y2 <- NA
mySimData$Y3 <- NA
mySimData$Y4 <- NA
ADDs <- DImodels::DI_data(prop=2:7, what=c("ADD"), data=mySimData)
mySimData <- cbind(mySimData, ADDs)
E_AV <- DImodels::DI_data(prop=2:7, what=c("E", "AV"), data=mySimData)
mySimData <- cbind(mySimData, E_AV)
n <- 4 #Number of Ys
p <- qr.Q(qr(matrix(stats::rnorm(n^2), n))) #Principal Components (make sure it's positive definite)
S <- crossprod(p, p*(n:1)) #Sigma
m <- stats::runif(n, -0.25, 1.5)
#runif(8, -1, 7) #decide on betas randomly
for(i in 1:nrow(mySimData))
{
#Within subject error
error <- MASS::mvrnorm(n=1, mu=m, Sigma=S)
mySimData$Y1[i] <- 6.9*mySimData$p1[i] + -0.3*mySimData$p2[i] + 6.6*mySimData$p3[i] +
1.7*mySimData$p4[i] + -0.8*mySimData$p5[i] + 4.3*mySimData$p6[i] + 3.5*mySimData$treat[i] +
1.8*mySimData$AV[i] + error[1]
mySimData$Y2[i] <- 4.9*mySimData$p1[i] + 3.6*mySimData$p2[i] + 4.4*mySimData$p3[i] +
2.3*mySimData$p4[i] + 4.3*mySimData$p5[i] + 6.6*mySimData$p6[i] + -0.3*mySimData$treat[i] +
6.8*mySimData$AV[i] + error[2]
mySimData$Y3[i] <- -0.3*mySimData$p1[i] + 4.6*mySimData$p2[i] + 1.2*mySimData$p3[i] +
6.8*mySimData$p4[i] + 1.4*mySimData$p5[i] + 6.9*mySimData$p6[i] + 5.5*mySimData$treat[i] +
1.4*mySimData$AV[i] + error[3]
mySimData$Y4[i] <- 4.1*mySimData$p1[i] + 4.2*mySimData$p2[i] + -0.5*mySimData$p3[i] +
4.9*mySimData$p4[i] + 6.7*mySimData$p5[i] + -0.9*mySimData$p6[i] + -1.0*mySimData$treat[i] +
0.3*mySimData$AV[i] + error[4]
}
mySimData$treat <- as.factor(mySimData$treat)
# }