MLE for multivariate discrete data {MLE}

MLE for multivariate discrete data

Description

MLE for multivariate discrete data.

Usage

mvdisc.mle(x, distr = "multinom", tol = 1e-07)

Arguments

x

A matrix with discrete valued non negative data.

distr

The distribution to fit. "multinom" stands for the multinomial distribution, "dirimultinom" stands for the Dirichlet-multinomial distribution. "bp.mle" and "bp.mle2" stand for the bivariate Poisson distribution. The The "bp.mle" returns a lot of information and is slower than "bp.mle2", which returns fewer information, but is faster.

tol

The tolerance level to terminate the Newton-Raphson algorithm for the Dirichlet multinomial distribution.

Value

A list including:

iters

The number of iterations required by the Newton-Raphson algortihm.

loglik

A vector with the value of the maximised log-likelihood.

param

A vector of the parameters.

prob

A vector with the estimated probabilities.

For the "bp.mle" a list including:

lambda

A vector with the estimated values of (\lambda_1, \lambda_2) and \lambda_3. Note that \hat{\lambda}_1=\bar{x}_1 - \lambda_3 and \hat{\lambda}_1=\bar{x}_1 - \lambda_3, where \bar{x}_1 and \bar{x}_2 are the two sample means.

rho

The estimated correlation coefficient, that is: \dfrac{\hat{\lambda}_3}{\sqrt{\left(\hat{\lambda}_1 + \hat{\lambda_3}\right)\left(\hat{\lambda}_2 + \hat{\lambda_3}\right)}}.

ci

The 95% Confidence intervals using the observed and the asymptotic information matrix.

loglik

The log-likelihood values assuming independence (\lambda_3=0) and assuming the bivariate Poisson distribution.

pvalue

Three p-values for testing \lambda_3=0. These are based on the log-likelihood ratio and two Wald tests using the observed and the asymptotic information matrix.

For the "bp.mle2" a list including:

lambda

A vector with the estimated values of (\lambda_1, \lambda_2) and \lambda_3. Note that \hat{\lambda}_1=\bar{x}_1 - \lambda_3 and \hat{\lambda}_1=\bar{x}_1 - \lambda_3, where \bar{x}_1 and \bar{x}_2 are the two sample means.

loglik

The log-likelihood values assuming independence (\lambda_3=0) and assuming the bivariate Poisson distribution.

Author(s)

Michail Tsagris and Sofia Piperaki.

R implementation and documentation: Michail Tsagris [e-mail] and Sofia Piperaki [e-mail].

References

Johnson Norman L., Kotz Samuel and Balakrishnan (1997). Discrete Multivariate Distributions. Wiley.

Kawamura K. (1984). Direct calculation of maximum likelihood estimator for the bivariate Poisson distribution. Kodai Mathematical Journal, 7(2): 211–221.

Kocherlakota S. and Kocherlakota K. (1992). Bivariate discrete distributions. CRC Press.

Karlis D. and Ntzoufras I. (2003). Analysis of sports data by using bivariate poisson models. Journal of the Royal Statistical Society: Series D (The Statistician), 52(3): 381–393.

See Also

disc.mle, coldisc.mle

Examples

x <- t( rmultinom(1000, 20, c(0.4, 0.5, 0.1) ) )
mvdisc.mle(x, distr = "multinom")