EMbinom: Fit mixture of two binomial distributions using EM.

In NeuroStat/NeuRRoStat: A rare collection of R functions used at the NeuroStat lab (Ghent University)

Description

Function to estimate the parameters of a mixture of two binomial distributions using the Expectation-Maximization algorithm (EM). Can be used in a setting where the data contains V independent observations. Each of these is a realization of a binomial data generating process with the probability of success (out of N trials) being either π 1 or π 2.

Usage

EMbinom(Y, N, iniL, iniPI1, iniPI2, max.iter = 500, tolerance = 0.001)

Arguments

Y	vector of length V with the observed data (number of successes)
N	the amount of trials
iniL	initial value for λ
iniPI1	initial value for π 1
iniPI2	initial value for π 2
max.iter	maximum iterations (optional)
tolerance	level of tolerance when comparing the likelihood of previous and current step in the algorithm (optional). Convergence is assumed when the absolute difference between both log likelihoods is smaller than the tolerance level.

Details

Assume Y is i.i.d. from

λ P1(Y;k, π 1) + (1 - λ) P2(Y;k,π 2)

The complete log-likelihood of the data over all observations (V) is then given as:

cst + ∑_{v = 1}^V log(λ(π 1)^Y(v) (1 - π 1)^(N - Y(v)) + (1 - λ)(π 2)^Y(v) (1 - π 2)^(N - Y(v)))

The EM algorithm is then used to estimate λ, π 1 and π 2.

Note on starting values: it is not advised to use the same values for the starting values of π 1 and π 2 as the algorithm does not seem to handle this setting very well. Starting values far away from the true value do converge to the true value most of the time, but take more iterations.

Value

Data frame with the parameter estimates and the number of iterations after convergence

NeuroStat/NeuRRoStat documentation built on May 15, 2019, 1:26 p.m.