Sampling, WLS, and Mixed Models

Mixed models may be defined with or without reference to sampling, and can be used to predict realized random effects, as when estimating the latent values of study subjects measured with response error. When the model is specified without reference to sampling, a simple mixed model includes two random variables, one stemming from an exchangeable distribution of latent values of study subjects and the other, from the study subjects` response error distributions. Positive probabilities are assigned to both potentially realizable responses and artificial responses that are not potentially realizable, resulting in artificial latent values. In contrast, finite population mixed models represent the two-stage process of sampling subjects and measuring their responses, where positive probabilities are only assigned to potentially realizable responses. A comparison of the estimators over the same potentially realizable responses indicates that the optimal linear mixed model estimator (the usual best linear unbiased predictor, BLUP) is often (but not always) more accurate than the comparable finite population mixed model estimator (the FPMM BLUP). We examine a simple example and provide the basis for a broader discussion of the role of conditioning, sampling, and model assumptions in developing inference.

The log-exponentiated Weibull regression model for interval-censored data

In interval-censored survival data, the event of interest is not observed exactly but is only known to occur within some time interval. Such data appear very frequently. In this paper, we are concerned only with parametric forms, and so a location-scale regression model based on the exponentiated Weibull distribution is proposed for modeling interval-censored data. We show that the proposed log-exponentiated Weibull regression model for interval-censored data represents a parametric family of models that include other regression models that are broadly used in lifetime data analysis. Assuming the use of interval-censored data, we employ a frequentist analysis, a jackknife estimator, a parametric bootstrap and a Bayesian analysis for the parameters of the proposed model. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess global influences. Furthermore, for different parameter settings, sample sizes and censoring percentages, various simulations are performed; in addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended to a modified deviance residual in log-exponentiated Weibull regression models for interval-censored data. (C) 2009 Elsevier B.V. All rights reserved.

A multivariate ultrastructural errors-in-variables model with equation error

This paper deals with asymptotic results on a multivariate ultrastructural errors-in-variables regression model with equation errors Sufficient conditions for attaining consistent estimators for model parameters are presented Asymptotic distributions for the line regression estimators are derived Applications to the elliptical class of distributions with two error assumptions are presented The model generalizes previous results aimed at univariate scenarios (C) 2010 Elsevier Inc All rights reserved

On the skew-normal calibration model

In this article, we present the EM-algorithm for performing maximum likelihood estimation of an asymmetric linear calibration model with the assumption of skew-normally distributed error. A simulation study is conducted for evaluating the performance of the calibration estimator with interpolation and extrapolation situations. As one application in a real data set, we fitted the model studied in a dimensional measurement method used for calculating the testicular volume through a caliper and its calibration by using ultrasonography as the standard method. By applying this methodology, we do not need to transform the variables to have symmetrical errors. Another interesting aspect of the approach is that the developed transformation to make the information matrix nonsingular, when the skewness parameter is near zero, leaves the parameter of interest unchanged. Model fitting is implemented and the best choice between the usual calibration model and the model proposed in this article was evaluated by developing the Akaike information criterion, Schwarz`s Bayesian information criterion and Hannan-Quinn criterion.

A semi-Markov multistate model for estimation of the mean quality-adjusted survival for non-progressive processes

We discuss the estimation of the expected value of the quality-adjusted survival, based on multistate models. We generalize an earlier work, considering the sojourn times in health states are not identically distributed, for a given vector of covariates. Approaches based on semiparametric and parametric (exponential and Weibull distributions) methodologies are considered. A simulation study is conducted to evaluate the performance of the proposed estimator and the jackknife resampling method is used to estimate the variance of such estimator. An application to a real data set is also included.

Estimation of the mean quality-adjusted survival using a multistate model for the sojourn times

In clinical trials, it may be of interest taking into account physical and emotional well-being in addition to survival when comparing treatments. Quality-adjusted survival time has the advantage of incorporating information about both survival time and quality-of-life. In this paper, we discuss the estimation of the expected value of the quality-adjusted survival, based on multistate models for the sojourn times in health states. Semiparametric and parametric (with exponential distribution) approaches are considered. A simulation study is presented to evaluate the performance of the proposed estimator and the jackknife resampling method is used to compute bias and variance of the estimator. (C) 2007 Elsevier B.V. All rights reserved.

Improved maximum-likelihood estimation in a regression model with general parametrization

We analyse the finite-sample behaviour of two second-order bias-corrected alternatives to the maximum-likelihood estimator of the parameters in a multivariate normal regression model with general parametrization proposed by Patriota and Lemonte [A. G. Patriota and A. J. Lemonte, Bias correction in a multivariate regression model with genereal parameterization, Stat. Prob. Lett. 79 (2009), pp. 1655-1662]. The two finite-sample corrections we consider are the conventional second-order bias-corrected estimator and the bootstrap bias correction. We present the numerical results comparing the performance of these estimators. Our results reveal that analytical bias correction outperforms numerical bias corrections obtained from bootstrapping schemes.