BetaMixture: Class "BetaMixture"

In BetaModels: Bayesian Analysis of Different Rates in Different Groups

Class "BetaMixture"

Description

Model data on the interval [0,1] as a mixture of an arbitrary number of beta distributions.

Usage

BetaMixture(datavec, K = 2, forever = 100, epsilon = 0.001,
            relative = 0.001, debug = FALSE)
## S4 method for signature 'BetaMixture'
summary(object, ...)
## S4 method for signature 'BetaMixture'
hist(x, mixcols = 1:7, ...)

Arguments

datavec	The observed vector of data points (between 0 and 1).
K	The number of mixture components to fit.
forever	The maximum number of iterations of the algorithm.
epsilon	The minimum change of parameters that must be observed in order to continue iterating.
relative	The minimum relative change of parameters that must be observed in order to continue iterating.
debug	A local valuecontrolling whethe to print out intermediate steps.
x	In the hist method, an object of class BetaMixture.
mixcols	A vector of colors used to show differnt components. Recycled as necessary.
object	Object of class BetaMixture.
...	Extra arguments for generic routines.

Details

Given a data set consisting of values in the interval [0,1], we want to model it as a mixture of K beta distributions:

f(x) = \sum_{i=1}^K \phi_i B(\nu_i, \omega_i)

f(X) = sum phi[u] B(nu[i], omega[i]) where the non-negative frequencies or weights of the components sum to 1 (that is, \sum_{i=1}^K \phi_i = 1).

We fit such a model using en Expectation-Maximation (EM) algorithm. To accomplish this goal, we must introduce a matrix 431Z of latent assignments of each of the $N$ observation to the $K$ components. In the current implementation, we intialize teh assignments by dividing the range of the observed data into $K$ subintervals of equal width, and assign the elemnts in the Kth subinterval to component $K$. (Warning: This may change in later versions.) We then alternate between the M-step (finding a maximum likelihood estimate of the parameters of the beta distributions given Z), and the E-step (estimating the weights \phi by averaging the columns of Z). Iterations continue up to the number specified by forever times, or until the log likelihood changes by less than the amount specified by epsilon.

Value

The BetaMixture constructor returns an object of the indicated class.

The graphical method hist and the summary method invisibly return the object on which it was invoked.

Creating Objects

Although objects can be created directly using new, the most common usage will be to pass a vector of unit interval values to the BetaMixture function.

Slots

datavec:

input data vector of values between 0 and 1.

phi:

vector of non-negative component frequencies; will sum to 1.

mle:

2\times K matrix of parameters of the $K$ beta mixture components.

Z:

N\times K matrix of the probability for each of the $N$ observations to arise from beta mixture component $K$. Each row will sum to 1.

loglike:

The log likelihood of the fitted model.

converged:

A logical value indicating where the EM algorithm converged.

Methods

summary(object, ...)

Prints a summary of the BetaMixture object. This includes (1) the frequency/weight of each component, (2) the parameters of each beta distribution, (3) an indicator of convergence, and (4) the log-likelihood of the fimal model.

Author(s)

Kevin R. Coombes [e-mail]

Examples

showClass("BetaMixture")
set.seed(73892)
datavec <- c(rbeta(130, 1, 4),
             rbeta(170, 7, 4))
model <- BetaMixture(datavec)
summary(model)
hist(model, breaks=35)

BetaModels documentation built on Feb. 9, 2024, 3:01 a.m.