# Sim.MultiRR: Simulate data setes to be analyzed by a multi-level random... In MultiRR: Bias, Precision, and Power for Multi-Level Random Regressions

## Description

Simulate n data sets to be analyzed with a multi-level random regression.

## Usage

 ```1 2 3``` ```Sim.MultiRR(n.ind, SeriesPerInd, ObsPerLevel, EnvGradient, PopInt, PopSlope, VCVInd, VCVSeries, ResVar, n.sim, unbalanced = FALSE, prop.ind, complete.observations = TRUE, n.obs) ```

## Arguments

 `n.ind` A vector consisting of the total individuals sampled. `SeriesPerInd` A vector consisting of the number of series sampled for each individual. `ObsPerLevel` The number of observations per series in each level of the environment. `EnvGradient` A vector consisting of the levels in the environmental gradient. `PopInt` Population level intercept. `PopSlope` Population level slope. `VCVInd` A positive definite variance covariance matrix of dimensions 2 X 2, defining the among-individual variance in intercepts and slopes in the diagonals and their covariance in the off diagonals. `VCVSeries` A positive definite variance covariance matrix of dimensions 2 X 2, defining the among-series variance in intercepts and slopes in the diagonals and their covariance in the off diagonals. `ResVar` Residual variance `n.sim` Number of data sets to simulate. `unbalanced` Optional argument determining whether not all the individuals were assayed the same number of series. The default is "FALSE". `prop.ind` When unbalanced = "TRUE", A vector that has the same length as the number of series per individual, with the proportion of individuals measured n times. All individuals should have been measured once (1,.,.,.). `complete.observations` Optional argument determining whether all the levels were assayed the same number of times. The default is "TRUE". `n.obs` The total number of observations, if complete.observartions = "FALSE".

## Value

A list of data sets to be analyzed by Anal.MultiRR.

Yimen Araya

## References

Araya-Ajoy Y.G., Mathot, K. J., Dingemanse N. J. (2015) An approach to estimate short-term, long-term, and reaction norm repeatability. Methods in Ecology and Evolution.

`Anal.MultiRR`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98``` ```#Example 1: Balanced sampling design. #Define sample sizes. n.ind <-c(40, 50) ##Numbers of individuals to simulate. SeriesPerInd <- c(4, 5) ##Number of series per individual to simulate. ObsPerLevel <- 2 ##Number of observations per level in the environmental gradient. #Number of simulated data sets, use at least 10. n.sim=3 #Define the environmetal gradient. EnvGradient <- c(-0.5, 0.5) #Define the population level parameters. PopInt <- 0 ##Population level intercept. PopSlope <- -0.5 ##Population level slope. #Define individual level parameters VCVInd <-matrix(c(0.3, 0.15, 0.15, 0.3),2,2) ##Creates a variance-covariance matrix. #Define series level parameters VCVSeries <-matrix(c(0.3, 0.15, 0.15, 0.3),2,2) ##Creates a variance-covariance matrix. #Define the residual variance. ResVar <- 0.4 #Simulate the data sets. sim.data <- Sim.MultiRR(n.ind=n.ind, SeriesPerInd=SeriesPerInd, ObsPerLevel=ObsPerLevel, EnvGradient=EnvGradient, PopInt=PopInt, PopSlope=PopSlope, VCVInd=VCVInd, VCVSeries=VCVSeries, ResVar=ResVar, n.sim=3) #Analyze the simulated data sets. This may take a while. ressim <- Anal.MultiRR(sim.data) #Summarize the results of the multi-level random regressions. Summary(ressim) #Estimate bias. Bias(ressim) #Estiamte imprecision. Imprecision(ressim) #Estimate power. Power(ressim) #Example 2: Unbalanced sampling desing. #Define sample sizes. n.ind <-40 ##Numbers of individuals to simulate. SeriesPerInd <- 4 ##Number of series per individual to simulate. ObsPerLevel <- 2 ##Number of observations per level in the environmental gradient. #Define the proportion of individuals that were sampled in all the series. #All individuals were assayed at least once, 0.9 of individuals twice... prop.ind<-c(1, 0.9, 0.8, 0.7) #Define the total number of observations n.obs=300 #Number of simulated data sets, use at least 10. n.sim=3 #Define the environmetal gradient. EnvGradient <- c(-0.5, 0.5) #Define the population level parameters. PopInt <- 0 ##Population level intercept. PopSlope <- -0.5 ##Population level slope. #Define the individual level parameters. VCVInd <-matrix(c(0.3, 0.15, 0.15, 0.3),2,2) ##Creates a variance-covariance matrix. #Define the series level parameters. VCVSeries <-matrix(c(0.3, 0.15, 0.15, 0.3),2,2) ##Creates a variance-covariance matrix. #Define the residual variance. ResVar <- 0.4 #Simulate the data. sim.data <- Sim.MultiRR(n.ind=n.ind, SeriesPerInd=SeriesPerInd, ObsPerLevel=ObsPerLevel, EnvGradient=EnvGradient, PopInt=PopInt, PopSlope=PopSlope, VCVInd= VCVInd, VCVSeries=VCVSeries, ResVar=ResVar, n.sim=n.sim, unbalanced=TRUE, prop.ind=c(1, 0.9, 0.8, 0.7), complete.observations=FALSE, n.obs=n.obs) #Analyze simulated data sets. This may take a while. ressim <- Anal.MultiRR(sim.data) #Summarize the results of the multi-level random regressions. Summary(ressim) #Estimate bias. Bias(ressim) #Estiamte imprecision. Imprecision(ressim) #Estimate power. Power(ressim) ```