B2mix {REBayes}

Bivariate Binomial mixture estimation via Kiefer Wolfowitz MLE

Description

Interior point solution of Kiefer-Wolfowitz NPMLE for mixture of bivariate binomials

Usage

B2mix(x, k, u = 40, v = 40, weights = NULL, ...)

Arguments

x

n by 2 matrix of counts of "successes" for binomial observations

k

n by 2 matrix of Number of trials for binomial observations

u

Grid Values for the mixing distribution defaults to equal spacing of length u on [eps, 1- eps], if u is scalar.

v

Grid Values for the mixing distribution defaults to equal spacing of length v on [eps, 1- eps], if v is scalar.

weights

replicate weights for x obervations, should sum to 1

...

Other arguments to be passed to KWDual to control optimization

Details

This function was inspired by a paper by Kline and Walters (2019) on evaluation of audit experiments for employment discrimination. An example of its usage is available with 'demo(B2mix1)'. There can be identification issues particularly when the numbers of trials are modest as described in Koenker and Gu (2024). Caveat emptor! The predict method for B2mix objects will compute posterior means,

Value

An object of class density with components:

u

grid of evaluation points of the mixing density

v

grid of evaluation points of the mixing density

y

function values of the mixing density at x

g

estimates of the mixture density at the distinct data values

logLik

Log Likelihood value at the estimate

dy

Bayes rule estimates of binomial probabilities for distinct data values

status

exit code from the optimizer

Author(s)

R. Koenker

References

Kiefer, J. and J. Wolfowitz Consistency of the Maximum Likelihood Estimator in the Presence of Infinitely Many Incidental Parameters Ann. Math. Statist. 27, (1956), 887-906.

Kline, P. and C. Walters, (2019) Audits as Evidence: Experiments, Ensembles and Enforcement, preprint.

Koenker, R. and Gu, J. (2024) Empirical Bayes: Some Tools, Rules and Duals, Cambridge University Press.

See Also

'Bmix' for univariate binomial mixtures.