A mixture model-based approach to the clustering of exponential repeated data

The analysis of finite mixture models for exponential repeated data is considered. The mixture components correspond to different unknown groups of the statistical units. Dependency and variability of repeated data are taken into account through random effects. For each component, an exponential mixed model is thus defined. When considering parameter estimation in this mixture of exponential mixed models, the EM-algorithm cannot be directly used since the marginal distribution of each mixture component cannot be analytically derived. In this paper, we propose two parameter estimation methods. The first one uses a linearisation specific to the exponential distribution hypothesis within each component. The second approach uses a Metropolis–Hastings algorithm as a building block of a general MCEM-algorithm.     

Mixture normal models in which the proportions of susceptibility are related to dose levels

A problem that frequently occurs in biological experiments with laboratory animals is that some subjects are less susceptible to the treatment group than others. Finite mixture models have traditionally been used to describe the distribution of responses in treated subjects for such studies. In this paper, we first study the mixture normal model with multi-levels and multiple mixture sub-populations under each level, with particular attention being given to the model in which the proportions of susceptibility are related to dose levels, then we use EM-algorithm to find the maximum likelihood estimators of model parameters. Our results are generalizations of the existing results. Finally, we illustrate realistic significance of the above extension based on a set of real dose-response data.     

An Akaike information criterion for multiple event mixture cure models

We derive the proper form of the Akaike information criterion for variable selection for mixture cure models, which are often fit via the expectation–maximization algorithm. Separate covariate sets may be used in the mixture components. The selection criteria are applicable to survival models for right-censored data with multiple competing risks and allow for the presence of a non-susceptible group. The method is illustrated on credit loan data, with pre-payment and default as events and maturity as the non-susceptible case and is used in a simulation study.     

Statistical Inference for the Parameter of Pareto Distribution Based on Progressively Typ e-I Interval Censored Sample

In this paper, the estimation of parameters based on a progressively typeI interval censored sample from a Pareto distribution is studied. Different methods of estimation are discussed, which include mid-point approximation estimator, the maximum likelihood estimator and moment estimator. The estimation procedures are discussed in details and compared via Monte Carlo simulations in terms of their biases.     

Obtaining the Maximum Likelihood Estimates in Incomplete R × C Contingency Tables Using a Poisson Generalized Linear Model

Abstract

This article describes estimation of the cell probabilities in an R × C contingency table with ignorable missing data. Popular methods for maximizing the incomplete data likelihood are the EM-algorithm and the Newton-Raphson algorithm. Both of these methods require some modification of existing statistical software to get the MLEs of the cell probabilities as well as the variance estimates. We make the connection between the multinomial and Poisson likelihoods to show that the MLEs can be obtained in any generalized linear models program without additional programming or iteration loops.     

Conditional Logistic Regression With Longitudinal Follow-up and Individual-Level Random Coefficients: A Stable and Efficient Two-Step Estimation Method

The analysis of data generated by animal habitat selection studies, by family studies of genetic diseases, or by longitudinal follow-up of households often involves fitting a mixed conditional logistic regression model to longitudinal data composed of clusters of matched case-control strata. The estimation of model parameters by maximum likelihood is especially difficult when the number of cases per stratum is greater than one. In this case, the denominator of each cluster contribution to the conditional likelihood involves a complex integral in high dimension, which leads to convergence problems in the numerical maximization. In this article we show how these computational complexities can be bypassed using a global two-step analysis for nonlinear mixed effects models. The first step estimates the cluster-specific parameters and can be achieved with standard statistical methods and software based on maximum likelihood for independent data. The second step uses the EM-algorithm in conjunction with conditional restricted maximum likelihood to estimate the population parameters. We use simulations to demonstrate that the method works well when the analysis is based on a large number of strata per cluster, as in many ecological studies. We apply the proposed two-step approach to evaluate habitat selection by pairs of bison roaming freely in their natural environment. This article has supplementary material online.