em_link {zoomerjoin}

Fit a Probabilistic Matching Model using Naive Bayes + E.M.

Description

A Rust implementation of the Naive Bayes / Fellegi-Sunter model of record linkage as detailed in the article "Using a Probabilistic Model to Assist Merging of Large-Scale Administrative Records" by Enamorado, Fifield and Imai (2019). Takes an integer matrix describing the similarities between each possible pair of observations, and a vector of initial guesses of the probability each pair is a match (these can either be set from domain knowledge, or one can hand-label a subset of the data and leave the rest as p=.5). Iteratively refines these guesses using the Expectation Maximization algorithm until an optima is reached. for more details, see doi:10.1017/S0003055418000783.

Usage

em_link(X, g, tol = 10^-6, max_iter = 10^3)

Arguments

X

an integer matrix of similarities. Must go from 0 (the most disagreement) to the maximum without any "gaps" or unused levels. As an example, a column with values 0,1,2,3 is a valid column, but 0,1,2,4 is not as three is omitted

g

a vector of initial guesses that are iteratively improved using the EM algorithm (my personal approach is to guess at logistic regression coefficients and use them to create the intitial probability guesses). This is chosen to avoid the model getting stuck in a local optimum, and to avoid the problem of label-switching, where the labels for matches and non-matches are reversed.

tol

tolerance in the sense of the infinity norm. i.e. how close the parameters have to be between iterations before the EM algorithm terminates.

max_iter

iterations after which the algorithm will error out if it has not converged.

Value

a vector of probabilities representing the posterior probability each record pair is a match.

Examples

inv_logit <- function (x) {
   exp(x)/(1+exp(x))
}
n <- 10^6
d <- 1:n %% 5 == 0
X <- cbind(
        as.integer(ifelse(d, runif(n)<.8, runif(n)<.2)),
        as.integer(ifelse(d, runif(n)<.9, runif(n)<.2)),
        as.integer(ifelse(d, runif(n)<.7, runif(n)<.2)),
        as.integer(ifelse(d, runif(n)<.6, runif(n)<.2)),
        as.integer(ifelse(d, runif(n)<.5, runif(n)<.2)),
        as.integer(ifelse(d, runif(n)<.1, runif(n)<.9)),
        as.integer(ifelse(d, runif(n)<.1, runif(n)<.9)),
        as.integer(ifelse(d, runif(n)<.8, runif(n)<.01))
        )

# inital guess at class assignments based on # a hypothetical logistic
# regression. Should be based on domain knowledge, or a handful of hand-coded
# observations.

x_sum <- rowSums(X)
g <- inv_logit((x_sum - mean(x_sum))/sd(x_sum))

out <- em_link(X, g,tol=.0001, max_iter = 100)