power.test: performs a simulation based analysis of statistical power
In EvoRAG: Evolutionary Rates Across Gradients

Description Usage Arguments Details Value Author(s) See Also Examples

performs a simulation based analysis of statistical power

1 2	power.test(TIME, GRAD, parameters, test.model, threshold_deltaAICc, REP=1, N, write = "FALSE", wd = "")

`TIME`	vector of evolutionary ages (i.e. node ages ) for sister pair dataset
`GRAD`	vector of gradient values (i.e. any continuous variable) for sister pair dataset
`parameters`	A vector listing the model parameters under which to simulate. Model parameters must be in the same order as described in sisterContinuous.
`test.model`	Any one of the following models are currently supported ("BM_linear", "OU_linear_beta", "OU_linear")
`threshold_deltaAICc`	A single threshold deltaAICc or a list of such values
`REP`	How many replicated datasets of TIME and GRAD to use. Default = 1. Example: REP=3 generates a dataset with each element in TIME and GRAD repeated 3 times. This option will be used primarily for calculating statistical power as a function of increasing number of sister pairs
`N`	The number of simulations to perform
`write`	If true, writes output to several files
`wd`	directory to write files to if other than the current working directory. (Windows example, "D:/SIMS/"

Performs an analysis of statistical power (e.g. the probability of supporting a true alternative hypothesis) for a given dataset under a given model and set of model parameters. The threshold_deltaAICc should be set at a level that will maintain a type I error (probability of rejecting a true null model) of 0.05. Appropriate threshold_deltaAICc values can be determined using the function TypeI.error. The null hypothesis here tested is that rates of evolution do not vary as a function of gradient (e.g. "BM_null", and "OU_null"). The alternative, is rates do vary as a linear function of a gradient (e.g. "BM_linear", "OU_linear_beta", "OU_linear"). Several hundred or more replicates should be performed. Currently, only "BM_linear", "OU_linear_beta", "OU_linear" are included in the candidate set of gradient models.

Returns a list with the following elements: test.model The model for which power was calculated parameters The parameters under which power was calculated N_sisters The number of sister pairs in the dataset N_sims The number of simulations performed power_test_hypothesis Statistical power calculated for the alternative hypothesis that rates of evolution vary as a linear function of a gradient. Power is returned for each threshold value in threshold_deltaAIC. Where appropriate, power to reject BM_null and OU_null is returned for three comparisons: 1) BMlinear_and_OUlinear_beta_vs_2null: power when simulating data either under BM_linear or OU_linear_beta, but when the OU_linear model is not included in the analysis; 2) BMlinear_and_OUlinear_vs_2null: power when OU_linear_beta is not included; 3) 3gradient_vs_2null: power when all three gradient models are included.

power_test_hypothesis The probability of the test model correctly rejecting each of the other null and gradient models on an individual basis.

Jason T. Weir

TypeI.error

## Not run: 

 ###simulate data
  set.seed(seed = 3)
  TIME = runif(n=300, min = 0, max = 10)
  GRAD = runif(n=300, min = 0, max = 60)
  DATA1 <- sim.sisters(TIME = TIME, GRAD=GRAD, parameters = c(2, -0.03), 
     model=c("BM_linear"))

  ###run power.test
  model = c("BM_linear")
  power.test(TIME=TIME, GRAD=GRAD, parameters = c(2, -0.03), test.model="BM_linear", 
     threshold_deltaAICc = c((1:20)*0.5), REP=1, N=2, write = "FALSE", wd = "")
 
## End(Not run)#end dontrun