Generalized linear regression models incorporating original outcome distributions

ABSTRACT

In this article, we propose an approach for incorporating continuous and discrete original outcome distributions into the usual exponential family regression models. The new approach is an extension of the works of Suissa (1991 Suissa, S. (1991). Binary methods for continuous outcomes: A parametric alternative. J. Clin. Epidemiol. 44:241–248.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) and Suissa and Blais (1995 Suissa, S., Blais, L. (1995). Binary regression with continuous outcomes. Stat. Med. 14:247–255.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), which present methods to estimate the risk of an event defined in a sample subspace of an original continuous outcome variable. Simulation studies are presented in order to illustrate the performance of the developed methodology. Real data sets are analyzed by using the proposed models.     

On the use of between–within models to adjust for confounding due to unmeasured cluster-level covariates

Between–within models are generalized linear mixed models (GLMMs) for clustered data that incorporate a random intercept together with fixed effects for within-cluster and between-cluster covariates; the between-cluster covariates represent the cluster means of the within-cluster covariates. One popular use of these models is to adjust for confounding of the effect of within-cluster covariates due to unmeasured between-cluster covariates. Previous research has shown via simulations that using this approach can yield inconsistent estimators. We present theory and simulations as evidence that a primary cause of the inconsistency is heteroscedasticity of the linearized version of the GLMM used for estimation.     

Dimension test approach of heteroscedasticity in the linear model

Heteroscedasticity testing has a long history and is still an important matter in the linear model. There exist many types of tests, but they are limited in use to their own specific cases and sensitive to normality. Here, we propose a dimension test approach to heteroscedasticity. The proposed test overcomes the shortcomings of the existing methods, so that it is robust to normality and is unified in sense that it is applicable in the linear model with multi-dimensional response. Numerical studies confirm that the proposed test is favorable over the existing tests with moderate sample sizes, and real data analysis is presented.     

Confidence intervals for coefficients of variation in two-parameter exponential distributions

This article examines confidence intervals for the single coefficient of variation and the difference of coefficients of variation in the two-parameter exponential distributions, using the method of variance of estimates recovery (MOVER), the generalized confidence interval (GCI), and the asymptotic confidence interval (ACI). In simulation, the results indicate that coverage probabilities of the GCI maintain the nominal level in general. The MOVER performs well in terms of coverage probability when data only consist of positive values, but it has wider expected length. The coverage probabilities of the ACI satisfy the target for large sample sizes. We also illustrate our confidence intervals using a real-world example in the area of medical science.     

A note on adaptation in garch models

In the framework of the Engle-type (G)ARCH models, I demonstrate that there is a family of symmetric and asymmetric density functions for which the asymptotic efficiency of the semiparametric estimator is equal to the asymptotic efficiency of the maximum likelihood estimator. This family of densities is bimodal (except for the normal). I also chracterize the solution to the problem of minimizing the mean squared distance between the parametric score and the semiparametric score in order to search for unimodal densities for which the semiparametric estimator is likely to perform well. The LaPlace density function emerges as one of these cases.     

Numerical Study of Small Sample Variances of Estimators of Variance Components in the Two-Way Factorial Model

Many estimation procedures have been proposed for estimating variance components in unbalanced factorial models. A large proportion of these are based on the solution to a system of linear equations obtained from a set of quadratic forms and their expected value. This paper will present a numerical study of the small sample variance of eight variance component estimators of this type. The variances will be compared to the Bhattacharyya lower bound for unbiased estimators.     

On the heterogeneity of fecundability

We propose to use a general mixing distribution in modeling the heterogeneity of the fecundability of couples. We introduce a sequence of parameters called canonical moments, which is in one to one correspondence with the moments, to characterize the mixing distribution. By using the bootstrap method, we can estimate the standard errors of our estimates. Our method modifies the usual moment estimates so that the resulting mixing distribution is always supported on [0, 1]. Moreover, the downward bias of the moment estimate of the number of support points would be reduced. Our approach can be used for censored data. The application of our technique in finding the sterile subpopulation is also discussed. The theory is illustrated with several data examples and simulations.