empirical_bayes {truelies}

Estimate proportions of liars in multiple samples using empirical Bayes

Description

This function creates a prior by fitting a Beta distribution to the heads/N vector, using MASS::fitdistr(). The prior is then updated using data from each individual sample to give the posterior distributions.

Usage

empirical_bayes(heads, ...)

## Default S3 method:
empirical_bayes(heads, N, P, ...)

## S3 method for class 'formula'
empirical_bayes(formula, data, P, subset, ...)

Arguments

heads

A vector of numbers of the good outcome reported

...

Ignored

N

A vector of sample sizes

P

Probability of bad outcome

formula

A two-sided formula of the form heads ~ group. heads is a logical vector specifying whether the "good" outcome was reported. group specifies the sample.

data

A data frame or matrix. Each row represents one individual.

subset

A logical or numeric vector specifying the subset of data to use

Details

The formula interface allows calling the function directly on experimental data.

Value

A list with two components:

• prior, the calculated empirical prior (of class densityFunction).

• posterior, a list of posterior distributions (objects of class densityFunction). If heads was named, the list will have the same names.

Examples

heads <- c(Baseline = 30, Treatment1 = 38, Treatment2 = 45)
N <- c(50, 52, 57)
res <- empirical_bayes(heads, N, P = 0.5)

compare_dists(res$posteriors$Baseline, res$posteriors$Treatment1)
plot(res$prior, ylim = c(0, 4), col = "grey", lty = 2)
plot(res$posteriors$Baseline, add = TRUE, col = "blue")
plot(res$posteriors$Treatment1, add = TRUE, col = "orange")
plot(res$posteriors$Treatment2, add = TRUE, col = "red")


# starting from raw data:
raw_data <- data.frame(
        report = sample(c("heads", "tails"),
          size = 300,
          replace = TRUE,
          prob = c(.8, .2)
        ),
        group = rep(LETTERS[1:10], each = 30)
    )
empirical_bayes(I(report == "heads") ~ group, data = raw_data, P = 0.5)