permPower {GraphAT} R Documentation

## Function to compute estimated probability of detecting preferential connection of intracluster nodes

### Description

This function simulates graphs from the alternative hypothesis of preferential connection of intracluster nodes. For each graph, it runs a node and edge permutation test. The estimated ``power'' of each test is the proportion of graphs that the test rejects the null hypothesis of no preferential connection of intracluster edges.

### Usage

```permPower(psi=1,clsizes, nedge, nhyper=100, nperms=1000)
```

### Arguments

 `psi` The non-centrality parameter for the noncentral hypergeometric distribution used to simulate the graphs. `clsizes` A vector of cluster sizes. `nedge` The number of edges in each graph. `nhyper` The number of noncentral hypergeometric graphs simulated to estimate "power". `nperms` The number of permutations used for each run of the edge and node permutation tests.

### Details

The function first generates nhyper realizations of a noncentral hypergeometric(nedge,n,k,psi) random variable, where n is the number of node pairs and k is the number of intracluster node pairs. For each realization x, a graph with n edges, x of which are intracluster, is generated. The edge and node permutation tests (with nperms permutations each) are performed on each graph. The estimated ``power'' of each test is the proportion of graphs for which the test rejects the null hypothesis of no preferential connection of intracluster nodes (at the 5% level). The 95% confidence intervals for the power levels are also computed.

### Value

A list with four components:

 `power.permedge` Estimated ``power'' for edge permutation test. `power.permnode` Estimated ``power'' for node permutation test. `CI.permedge` Vector giving 95% confidence interval for edge permutation test power. `CI.permnode` Vector giving 95% confidence interval for node permutation test power.

### Author(s)

Tom LaFramboise tlaframb@hsph.harvard.edu

`permEdgesM2M`, `permNodesM2M`, `makeClustM`
```permPower(psi=5,clsizes=c(1,2,3,4),nedge=10,nhyper=100,nperms=100)