Package netdep. July 10, 2018

Transcription

1 Type Package Title Testing for Network Dependence Version Maintainer oujin Lee Imports stats, igraph, igraphdata, MSS, mvrtn Suggests knitr, testthat Package netdep July 10, 2018 When network dependence is present, that is when social relations can engender dependence in the outcome of interest, treating such observations as independent results in invalid, anti-conservative statistical inference. We propose a test of independence among observations sampled from a single network <arxiv: >. License GPL (>= 3) file LICENSE Encoding UTF-8 LazyData true RoxygenNote VignetteBuilder knitr NeedsCompilation no uthor oujin Lee [aut, cre], Elizabeth Ogburn [aut] Repository CRN Date/Publication :00:07 UTC R topics documented: latent.netdep make.permute.moran make.permute.phi MoranI peer.process phi.moment phi.stat snowball.sampling

2 2 latent.netdep Index 9 latent.netdep Generate latent variable dependent network. Generate latent variable dependent network. latent.netdep(n.node, rho = 0.3, dep.factor = 1, dep.range = c(-5, 5)) n.node The number of nodes in network. rho correlation coefficient between continuous observations and latent factor. dep.factor multiplicative factor applied to. If dep.factor < 0 Then i j Bern (logistic ( dep.factor* X_i - X_j )) If dep.factor 0Then i j Bern (logistic ( dep.factor / X_i - X_j )) dep.range a vector specifying lower bound and upper bound for dep.factor* X_i - X_j. Defaults to c(-5, 5). an undirected and binary igraph object G having both and U as nodal attributes. V(G)$outcome V(G)$latent one-dimensional continuous observations. one-dimensional continuous latent variable dependent on V(G)$ through rho. library(mss) library(mvrtn) G = latent.netdep(n.node = 100, rho = 0.5, dep.factor = 1)

3 make.permute.moran 3 make.permute.moran Permutation Test of Moran s I Permutation Test of Moran s I make.permute.moran(,, np = 100) np [n x n] adjacency matrix or general relational weight matrix of which i j a vector of n continuous or binary, one-dimensional observations. the number of permutation samples. moran pval.z pval.permute a standardized Moran s I statistic. p-value of a standardized Moran s I statistic assuming asymptotic normality. p-value of a standardized Moran s I statistic using np independent permutation samples. uthor(s) oujin Lee library(igraphdata) data(karate) = as.matrix(get.adjacency(karate, attr= "weight", sparse = TRUE)) # weighted adjacency matrix = V(karate)$Faction result = make.permute.moran(,, np = 100)

4 4 make.permute.phi make.permute.phi Permutation Test of Φ This function prints out the network dependence test results for categorical observations. make.permute.phi(,, np) np [n x n] adjacency matrix or general relational weight matrix of which i j a vector of n continuous or binary, one-dimensional observations. the number of permutation samples. phi pval.z pval.permute a standardized Φ statistic. p-value of a standardized Φ statistic assuming asymptotic normality. p-value of a standardized Φ statistic using np independent permutation samples. uthor(s) oujin Lee library(igraphdata) data(ukfaculty) = as.matrix(get.adjacency(ukfaculty, attr= "weight", sparse = TRUE)) # weighted adjacency matrix = V(UKfaculty)$Group result = make.permute.phi(,, np = 50)

5 MoranI 5 MoranI Moran s I statistic This function calculates Moran s I statistic given adjacency matrix and outcome. The statistic can be used for testing network dependence. MoranI(, ) [n x n] adjacency matrix or general relational weight matrix of which i j a vector of n continuous or binary, one-dimensional observations. moran a standardized Moran s I statistic. uthor(s) oujin Lee peer.process Generate direct transmission process Generate time-evolving outcomes where outcomes at time t of i depends on outcomes of i s adjacent peers at time t 1. peer.process(, max.time = 3, mprob = 0.5, epsilon = 0.3)

6 6 phi.moment max.time mprob epsilon [n x n] adjacency matrix. the maximum discrete time that direct transmission occurs. the maximum susceptibility probability, i.e. maximum probability that i s outcome at time t depends on i s peers at time t 1. standard deviation of error process. This adds uncertainties in outcomes. For t=1,2,... max.time : p Unif(0, mprob) t i = t i = (1 p) t 1 i + p j ij t 1 j / j ij + N(0, ɛ) a list of time-evolving outcomes from time0 to time(max.time). library(stats) G = latent.netdep(n.node = 100, rho = 0.2) = as.matrix(get.adjacency(g)) outcomes = peer.process(, max.time = 3, mprob = 0.3, epsilon = 0.5) phi.moment Calculate Φ statistic This is an auxiliary function to calculate non-standardized Φ statistic and its first and second moment. phi.moment(, ) [n x n] adjacency matrix or general relational weight matrix of which i j a vector of n nominal or binary, one-dimensional observations.

7 phi.stat 7 rawphi m1.rawphi m2.rawphi Non-standardized Φ statistic. the first (permutation) moment of rawphi. the second (permutation) moment of rawphi. uthor(s) oujin Lee phi.stat Standardized Φ statistic test statistic of Φ is to test network dependence in categorical observations. phi.stat(, ) [n x n] adjacency matrix or general relational weight matrix of which i j a vector of n nominal or binary, one-dimensional observations. phi a standardized Φ statistic. uthor(s) oujin Lee

8 8 snowball.sampling snowball.sampling Snowball sampling Sampling from one graph to its induced subgraph depending on network structure. snowball.sampling(g, samn) G an igraph object. samn is a size of snowball sample that will be samples from G. subg ind an induced subgraph of G sampled using snowball sampling. a set of index of samples. G = latent.netdep(n.node = 200, rho = 0.2, dep.factor = -3, dep.range = c(-10, 0)) subg = snowball.sampling(g, 100)

9 Index latent.netdep, 2 make.permute.moran, 3 make.permute.phi, 4 MoranI, 5 peer.process, 5 phi.moment, 6 phi.stat, 7 snowball.sampling, 8 9