Mixture models for matched pairs

Mixture models for matched pairs arise when the pair-specific parameter is assumed to be a random quantity. We explore the use of semiparametric maximum-likelihood methods for a family of mixture models for matched pairs. The geometry of mixture likelihoods provides insight into the properties of these models.     

Estimation of treatment effects for heterogeneous matched‐pairs data with probit models

Estimating the effect of medical treatments on subject responses is one of the crucial problems in medical research. Matched‐pairs designs are commonly implemented in the field of medical research to eliminate confounding and improve efficiency. In this article, new estimators of treatment effects for heterogeneous matched‐pairs data are proposed. Asymptotic properties of the proposed estimators are derived. Simulation studies show that the proposed estimators have some advantages over the famous Heckman's estimator, the conditional maximum likelihood estimator, and the inverse probability weighted estimator. We apply the proposed methodology to a data set from a study of low‐birth‐weight infants.     

Fairness of the national health service in Italy: a bivariate correlated random effects model

The primary purpose of this paper is to comprehensively assess households’ burden due to health payments. Starting from the fairness approach developed by the World Health Organization, we analyse the burden of healthcare payments on Italian households by modeling catastrophic payments and impoverishment due to healthcare expenditures. For this purpose, we propose to extend the analysis of fairness in financing contribution through a generalized linear mixed models by introducing a bivariate correlated random effects model, where association between the outcomes is modeled through individual- and outcome-specific latent effects which are assumed to be correlated. We discuss model parameter estimation in a finite mixture context. By using such model specification, the fairness of the Italian national health service is investigated.     

Asymptotic variance approximations for invariant estimators in uncertain asset-pricing models

This article derives explicit expressions for the asymptotic variances of the maximum likelihood and continuously-updated GMM estimators in models that may not satisfy the fundamental asset-pricing restrictions in population. The proposed misspecification-robust variance estimators allow the researcher to conduct valid inference on the model parameters even when the model is rejected by the data. While the results for the maximum likelihood estimator are only applicable to linear asset-pricing models, the asymptotic distribution of the continuously-updated GMM estimator is derived for general, possibly nonlinear, models. The large corrections in the asymptotic variances, that arise from explicitly incorporating model misspecification in the analysis, are illustrated using simulations and an empirical application.     

Likelihood inference for correlated binary data without any information about the joint distributions

We propose a universal robust likelihood that is able to accommodate correlated binary data without any information about the underlying joint distributions. This likelihood function is asymptotically valid for the regression parameter for any underlying correlation configurations, including varying under- or over-dispersion situations, which undermines one of the regularity conditions ensuring the validity of crucial large sample theories. This robust likelihood procedure can be easily implemented by using any statistical software that provides naïve and sandwich covariance matrices for regression parameter estimates. Simulations and real data analyses are used to demonstrate the efficacy of this parametric robust method.     

Estimation for two-way analysis of variance with correlated errors

We consider some estimation and distribution problems encountered in a two way analysis of variance model with only one observation per cell, errors correlated in one level, and the variances are not necessarily equal. The independence criteria for the row and interaction mean sum of squares and distribution of the maximum likelihood estimator of the correlation coefficient are given.     

A copula-based Markov chain model for the analysis of binary longitudinal data

A fully parametric first-order autoregressive (AR(1)) model is proposed to analyse binary longitudinal data. By using a discretized version of a copula, the modelling approach allows one to construct separate models for the marginal response and for the dependence between adjacent responses. In particular, the transition model that is focused on discretizes the Gaussian copula in such a way that the marginal is a Bernoulli distribution. A probit link is used to take into account concomitant information in the behaviour of the underlying marginal distribution. Fixed and time-varying covariates can be included in the model. The method is simple and is a natural extension of the AR(1) model for Gaussian series. Since the approach put forward is likelihood-based, it allows interpretations and inferences to be made that are not possible with semi-parametric approaches such as those based on generalized estimating equations. Data from a study designed to reduce the exposure of children to the sun are used to illustrate the methods.     

Additional comparisons of designs to estimate variance components in a two-way classification model

In this paper, the research of Muse and Anderson is extended to include additional comparisons of designs, featuring planned unbalance, for the estimation of variance components in a two-way cross classification model. Their results are extended to Include the following: (i) a small sample study of the original off-diagonal (OD) design and (ii) an asymptotic maximum likelihood investigation of three modifica-tions of the balanced diagonal rectangles (BD) design and one modification of the 01) design to permit the estimation of row, column, interaction and error variance components. Also a general iterative least.     

Testing equality of correlation coefficients for paired binary data from multiple groups

Paired binary data arise naturally when paired body parts are investigated in clinical trials. One of the widely used models for dealing with this kind of data is the equal correlation coefficients model. Before using this model, it is necessary to test whether the correlation coefficients in each group are actually equal. In this paper, three test statistics (likelihood ratio test, Wald-type test, and Score test) are derived for this purpose. The simulation results show that the Score test statistic maintains type I error rate and has satisfactory power, and therefore is recommended among the three methods. The likelihood ratio test is over conservative in most cases, and the Wald-type statistic is not robust with respect to empirical type I error. Three real examples, including a multi-centre Phase II double-blind placebo randomized controlled trial, are given to illustrate the three proposed test statistics.     

The costs of using incomplete response data for the exponential regression model

This paper investigates the asymptotic and small sample costs of using incomplete response data, Situations are identified where the information loss is substantial, Moreover, the small sample properties of the estimators are even worse than suggested by their asymptotic counterparts. These results provide the practitioner with guidance as to the severity of the costs he can incur, This is especially helpful when he cars choose the type of incomplete data that he observes.     

Pairwise- and marginal-likelihood estimation for the mixed Rasch model with binary data

A marginal–pairwise-likelihood estimation approach is examined in the mixed Rasch model with the binary response and logit link. This method belonging to the broad class of composite likelihood provides estimators with desirable asymptotic properties such as consistency and asymptotic normality. We study the performance of the proposed methodology when the random effect distribution is misspecified. A simulation study was conducted to compare this approach with the maximum marginal likelihood. The different results are also illustrated with an analysis of the real data set from a quality-of-life study.     

Generalised quasi‐likelihood inference in a semi‐parametric binary dynamic mixed logit model

There exists a recent study where dynamic mixed‐effects regression models for count data have been extended to a semi‐parametric context. However, when one deals with other discrete data such as binary responses, the results based on count data models are not directly applicable. In this paper, we therefore begin with existing binary dynamic mixed models and generalise them to the semi‐parametric context. For inference, we use a new semi‐parametric conditional quasi‐likelihood (SCQL) approach for the estimation of the non‐parametric function involved in the semi‐parametric model, and a semi‐parametric generalised quasi‐likelihood (SGQL) approach for the estimation of the main regression, dynamic dependence and random effects variance parameters. A semi‐parametric maximum likelihood (SML) approach is also used as a comparison to the SGQL approach. The properties of the estimators are examined both asymptotically and empirically. More specifically, the consistency of the estimators is established and finite sample performances of the estimators are examined through an intensive simulation study.     

Estimation of a semiparametric recursive bivariate probit model in the presence of endogeneity

The classic recursive bivariate probit model is of particular interest to researchers since it allows for the estimation of the treatment effect that a binary endogenous variable has on a binary outcome in the presence of unobservables. In this article, the authors consider the semiparametric version of this model and introduce a model fitting procedure which permits to estimate reliably the parameters of a system of two binary outcomes with a binary endogenous regressor and smooth functions of continuous covariates. They illustrate the empirical validity of the proposal through an extensive simulation study. The approach is applied to data from a survey, conducted in Botswana, on the impact of education on women's fertility. Some studies suggest that the estimated effect could have been biased by the possible endogeneity arising because unobservable confounders (e.g., ability and motivation) are associated with both fertility and education. The Canadian Journal of Statistics 39: 259–279; 2011 © 2011 Statistical Society of Canada     

A hybrid method to estimate the full parametric hazard model

Abstract

In this paper, we propose a hybrid method to estimate the baseline hazard for Cox proportional hazard model. In the proposed method, the nonparametric estimate of the survival function by Kaplan Meier, and the parametric estimate of the logistic function in the Cox proportional hazard by partial likelihood method are combined to estimate a parametric baseline hazard function. We compare the estimated baseline hazard using the proposed method and the Cox model. The results show that the estimated baseline hazard using hybrid method is improved in comparison with estimated baseline hazard using the Cox model. The performance of each method is measured based on the estimated parameters of the baseline distribution as well as goodness of fit of the model. We have used real data as well as simulation studies to compare performance of both methods. Monte Carlo simulations carried out in order to evaluate the performance of the proposed method. The results show that the proposed hybrid method provided better estimate of the baseline in comparison with the estimated values by the Cox model.     

Frailty modeling for clustered survival data: an application to birth interval in Bangladesh

The present work demonstrates an application of random effects model for analyzing birth intervals that are clustered into geographical regions. Observations from the same cluster are assumed to be correlated because usually they share certain unobserved characteristics between them. Ignoring the correlations among the observations may lead to incorrect standard errors of the estimates of parameters of interest. Beside making the comparisons between Cox's proportional hazards model and random effects model for analyzing geographically clustered time-to-event data, important demographic and socioeconomic factors that may affect the length of birth intervals of Bangladeshi women are also reported in this paper.     

Identifiability and bias reduction in the skew-probit model for a binary response

The skew-probit link function is one of the popular choices for modelling the success probability of a binary variable with regard to covariates. This link deviates from the probit link function in terms of a flexible skewness parameter. For this flexible link, the identifiability of the parameters is investigated. Next, to reduce the bias of the maximum likelihood estimator of the skew-probit model we propose to use the penalized likelihood approach. We consider three different penalty functions, and compare them via extensive simulation studies. Based on the simulation results we make some practical recommendations. For the illustration purpose, we analyse a real dataset on heart-disease.     

Computational approximation of the likelihood ratio for testing the existence of change-points in a heteroscedastic series

In this work, we present a computational method to approximate the occurrence of the change-points in a temporal series consisting of independent and normally distributed observations, with equal mean and two possible variance values. This type of temporal series occurs in the investigation of electric signals associated to rhythmic activity patterns of nerves and muscles of animals, in which the change-points represent the actual moments when the electrical activity passes from a phase of silence to one of activity, or vice versa. We confront the hypothesis that there is no change-point in the temporal series, against the alternative hypothesis that there exists at least one change-point, employing the corresponding likelihood ratio as the test statistic; a computational implementation of the technique of quadratic penalization is employed in order to approximate the quotient of the logarithmic likelihood associated to the set of hypotheses. When the null hypothesis is rejected, the method provides estimations of the localization of the change-points in the temporal series. Moreover, the method proposed in this work employs a posteriori processing in order to avoid the generation of relatively short periods of silence or activity. The method is applied to the determination of change-points in both experimental and synthetic data sets; in either case, the results of our computations are more than satisfactory.     

Application of 'delete = replace' to deletion diagnostics for variance component estimation in the linear mixed model

Summary.  'Delete = replace' is a powerful and intuitive modelling identity. This paper extends previous work by stating and proving the identity in more general terms and extending its application to deletion diagnostics for estimates of variance components obtained by restricted maximum likelihood estimation for the linear mixed model. We present a new, fast, transparent and approximate computational procedure, arising as a by-product of the fitting process. We illustrate the effect of the deletion of individual observations, of 'subjects' and of arbitrary subsets. Central to the identity and its application is the conditional residual.     

On the one parameter unit-Lindley distribution and its associated regression model for proportion data

In this paper considering an appropriate transformation on the Lindley distribution, we propose the unit-Lindley distribution and investigate some of its statistical properties. An important fact associated with this new distribution is that it is possible to obtain the analytical expression for bias correction of the maximum likelihood estimator. Moreover, it belongs to the exponential family. This distribution allows us to incorporate covariates directly in the mean and consequently to quantify their influences on the average of the response variable. Finally, a practical application is presented to show that our model fits much better than the Beta regression.     

Estimation of parameters of a polynomial model under intra class correlation structure for incomplete longitudinal data

The problem of analyzing and modeling incomplete longitudinal data arising from clinical and epidemiological studies are discussed, A method for handling arbitrarily missing observations under the intra class correlation structure and a polynomial model is developed. Explicit expressions for likelihood equations and information matrix for a second degree polynomial model are provided. The method is illustrated through an example.