bbnam.mix

Code to Fit a Multi-informant Bayesian Network Accuracy Model (BNAM) with Graph Mixture Priors

This simple R script contains the core function needed to reproduce the graph mixture prior BNAM of Butts (2014), along with the separate estimation of self-report and proxy reporting errors employed by Lee and Butts (2018,2020). This function is based on the bbnam.actor function of the sna package for R, with which it will eventually be integrated. (However, this stand-alone version may be useful in the interim.)

Installation

Simply put the mixture.code.R file in a convenient location, and use source("/path/to/mixture.code.R") within R to load. (Note that the sna package for R is required.)

Usage

bbnam.mix(dat, nprior = NULL, emprior = c(1, 11), epprior = c(1, 11), 
    diag = FALSE, mode = "digraph", reps = 5, draws = 1500, 
    burntime = 500, quiet = TRUE, anames = NULL, onames = NULL, 
    compute.sqrtrhat = TRUE) 

Arguments:

• dat: Input networks to be analyzed. This may be supplied in any reasonable form, but must be reducible to an array of dimension m x n x n, where n is |V(G)|, the first dimension indexes the observer (or information source), the second indexes the sender of the relation, and the third dimension indexes the recipient of the relation. (E.g., dat[i,j,k]==1 implies that i observed j sending the relation in question to k.) Note that only dichotomous data is supported at present, and missing values are permitted; the data collection pattern, however, is assumed to be ignorable, and hence the posterior draws are implicitly conditional on the observation pattern. (Note: to estimate self-report and proxy report error rates separately, provide two entries for each informant, one in which the informant's own row and column are set as missing, and another in which every entry other than those in the informant's own row and column are set as missing. This will both treat self and proxy reports separately and estimate distinct false positive and false negative rates for the self and proxy reports produced by each informant.)

• nprior: Network prior hyperparameters. This should be a vector of length 2 (for beta-Bernoulli graphs) or length 3 (for Dirichlet-categorical graphs) containing the hyperparameters for the graph mixture distribution. For the beta-Binomial model, these can be thought of as the alpha and beta parameters for a beta hyperprior distribution on the expected graph density. For the Dirichlet-categorical model, these can be thought as the three concentration parameters governing a three-dimensional Dirichlet distribution over the expected rates of incidence for mutual, asymmetric, and null dyads (respectively) in the network prior. In particular, note that choosing c(0.5,0.5) or c(0.5,0.5,0.5) will employ the Jeffreys hyperprior for each respective case; this is the default.

• emprior: Parameters for the (Beta) false negative prior; these should be in the form of an n x 2 matrix of (alpha,beta) pairs (or something which can be converted to this form). If no emprior is given, a weakly informative prior (1,11) will be assumed. Missing values are not allowed.

• epprior: Parameters for the (Beta) false positive prior; these should be in the form of an n x 2 matrix of (alpha,beta) pairs (or something which can be converted to this form). If no epprior is given, a weakly informative prior (1,11) will be assumed. Missing values are not allowed.

• diag: Boolean indicating whether loops (matrix diagonals) should be counted as data.

• mode: A string indicating whether the data in question forms a "graph" or a "digraph".

• reps: Number of replicate chains for the Gibbs sampler.

• draws: Integer indicating the total number of draws to take from the posterior distribution. Draws are taken evenly from each replication (thus, the number of draws from a given chain is draws/reps).

• burntime: Integer indicating the burn-in time for the Markov Chain. Each replication is iterated burntime times before taking draws (with these initial iterations being discarded); hence, one should realize that each increment to burntime increases execution time by a quantity proportional to reps.

• quiet: Boolean indicating whether MCMC diagnostics should be displayed.

• anames: A vector of names for the actors (vertices) in the graph.

• onames: A vector of names for the observers (possibly the actors themselves) whose reports are contained in the input data.

• compute.sqrtrhat: A boolean indicating whether or not Gelman et al.'s potential scale reduction measure (an MCMC convergence diagnostic) should be computed.

Return value:

An object of class bbnam.actor. (See the sna package.)

References

Butts, C. T. (2014). Baseline mixture models for social networks. arXiv:1710.7402773.

Lee, F., and Butts, C. T. (2020). On the validity of perceived social structure. Journal of Mathematical Psychology, forthcoming.

Lee, F., and Butts, C. T. (2018). Mutual assent or unilateral nomination? A performance comparison of intersection and union rules for integrating self-reports of social relationships. Social Networks, 55, 55–62.

Other

This work was supported by NSF award SES-1826589.