Network Analysis Statistical Analysis of Social Network Data

Network Analysis Statistical Analysis of Social Network Data MICHAEL T. HEANEY UNIVERSITY OF GLASGOW APRIL 15, 2021 PART 1 -- MORNING INDIAN INSTITUTE OF MANAGEMENT KOZHIKODE

Inferential Network Statistics

The Problem of Network Dependence �Observations in a network are not independent of one another as required in classical statistical analysis. AB AC AD AE BC BD BE CD CE DE

Regression with Network Autocorrelation �We may want to use networked variables as dependent or independent variables in a typical regression. �For example, degree, centrality, and brokerage are common variables. �Follows models developed for spatial autocorrelation analysis, only the weighting matrix is determined by a network, rather than geographic contiguity. �Example: Y = b. X + g. NY + e, where Y is normally distributed and N is a network.

Regression on Ties in a Network � The network tie is the dependent variable. � Why do two nations form an alliance? Why do they break the alliance? � Chief problem: The independence assumption is severely violated. AB AC AD AE BC BD BE � There are multiple possible approaches to address this problem.

Simulating Independence �Many inferential statistics on networks involve some form of simulating independence. �We will learn three simulation approaches: Permutation tests The quadratic assignment procedure Exponential random graph models

Permutation Tests �Are sometimes referred to as “randomization tests”. �Permutation tests are generally performed with a correlation or a regression framework when network autocorrelation may be present. �An “exact” permutation test takes place by estimating the model with all possible orderings of the data. There are n! possibilities. n! = n x (n-1) x (n-2). . . 3 x 2 x 1.

Quadratic Assignment Procedure (QAP) �QAP is similar to a permutation test, but it is used in the case of an entire network, rather than just a regression analysis. �QAP scrambles the rows and the columns of a matrix in order to generate a new distribution against which the empirical observations can be compared. �An exact test is usually not possible, since the number of possibilities is too large. n 2! Is generally an enormous number for most real networks.

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