A maximum likelihood method for latent class regression involving a censored dependent variable

The standard tobit or censored regression model is typically utilized for regression analysis when the dependent variable is censored. This model is generalized by developing a conditional mixture, maximum likelihood method for latent class censored regression. The proposed method simultaneously estimates separate regression functions and subject membership in K latent classes or groups given a censored dependent variable for a cross-section of subjects. Maximum likelihood estimates are obtained using an EM algorithm. The proposed method is illustrated via a consumer psychology application.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45751/1/11336_2005_Article_BF02294647.pd

Global dynamics of a system governing an algorithm for regression with censored and non-censored data under general errors

We present an investigation into the dynamics of a system, which underlies a new estimating algorithm for regression with grouped and nongrouped data. The algorithm springs from a simplification of the well-known EM algorithm, in which the expectation step of the EM is substituted by a modal step. This avoids awkward integrations when the error distribution is assumed to be general. The sequences generated by the estimating procedure proposed here define our objective system, which is piecewise linear. The study tackles the system's asymptotic stability as well as its speed of convergence to the equilibrium point. In this sense, to reduce the speed of convergence, we propose an alternative estimating procedure. Numerical examples illustrate the theoretical results, compare the proposed procedures and analyze the precision of the estimate

Modal iterative estimation in linear models with unimodal errors and non-grouped and grouped data collected from different sources

Asymptotic distributions, consistency, convergence rate, grouped data, imputation, iterative estimation, linear models, 62F12,

Application of a predictive distribution formula to Bayesian computation for incomplete data models

We consider exact and approximate Bayesian computation in the presence of latent variables or missing data. Specifically we explore the application of a posterior predictive distribution formula derived in Sweeting And Kharroubi (2003), which is a particular form of Laplace approximation, both as an importance function and a proposal distribution. We show that this formula provides a stable importance function for use within poor man’s data augmentation schemes and that it can also be used as a proposal distribution within a Metropolis-Hastings algorithm for models that are not analytically tractable. We illustrate both uses in the case of a censored regression model and a normal hierarchical model, with both normal and Student t distributed random effects. Although the predictive distribution formula is motivated by regular asymptotic theory, it is not necessary that the likelihood has a closed form or that it possesses a local maximum