Exact and approximate distributions for linear contrasts of means and variances

A Bayesian analysis is presented for the K-group Behrens-Fisher problem. Both exact posterior distributions and approximations were developed for both a general linear contrast of the K means and the K variances, given either proper diffuse or informative conjugate priors. The contrast of variances is a unique feature of the heterogeneous variance model that enables investigators to test specific effects of experimental manipulations on variance. Finally, important-differences were observed between the heterogeneous variance model and the homogeneous model.     

New simulation results for the calibration and inverse median estimation problems

This paper gives the results of a new simulation study for the familiar calibration problem and the less familiar inverse median estimation problem. The latter arises when one wishes to estimate from a linear regression analysis the value of the independent variable corresponding to a specified value of the median of the dependent variable. For example, from the results of a regression analysis between stress and time to failure, one might wish to estimate the stress at which the median time to failure is 10,000 hours. In the study, the mean square error, Pitman closeness, and probability of overestimation are compared for both the calibration problem and the inverse median estimation problem for (1) the classical estimator, (2) the inverse estimator, and (3) a modified version of an estimator proposed by Naszodi (1978) for both a small sample and a moderately large sample situation.     

Analysis of Contingency Tables with Clustered Observations

A new approach is presented for testing independence in contingency tables with clustered observations. The approach is based on the framework of generalized linear mixed models. Under the multinomial logistic link function, the category counts are modelled with random cluster effects and a modified likelihood ratio statistic is used for testing independence. The method is applicable to multi-way tables, and can accommodate multiple levels of clustering. It is illustrated using a benchmark dataset.     

Goodness-of-fit measures of R 2 for repeated measures mixed effect models

Linear mixed effects model (LMEM) is efficient in modeling repeated measures longitudinal data. However, little research has been done in developing goodness-of-fit measures that can evaluate the models, particularly those that can be interpreted in an absolute sense without referencing a null model. This paper proposes three coefficient of determination (R ²) as goodness-of-fit measures for LMEM with repeated measures longitudinal data. Theorems are presented describing the properties of R ² and relationships between the R ² statistics. A simulation study was conducted to evaluate and compare the R ² along with other criteria from literature. Finally, we applied the proposed R ² to a real virologic response data of an HIV-patient cohort. We conclude that our proposed R ² statistics have more advantages than other goodness-of-fit measures in the literature, in terms of robustness to sample size, intuitive interpretation, well-defined range, and unnecessary to determine a null model.     

Jackknifing the Mantel–Haenszel Estimator in Sparse Contingency Tables

This article investigates the performance of two jackknife techniques under an asymptotic model in which the number of 2 × 2 tables increases but the possible marginal configurations remain fixed. These approaches are applied to the Mantel–Haenszel estimator, or transformed versions of this estimator, respectively. The resulting jackknife estimators are shown to be consistent for the common odds ratio. Their asymptotic distributions are derived; they can be used for constructing appropriate sparse-data confidence intervals.     

面板数据的模型建立和检验分析

面板数据分析是数量经济学中一门重要的分支,在经济领域中有着广泛的应用。文章详细地介绍了面板数据的主要类型及模型的建立和检验。     

基于模糊多分配的辽宁煤炭枢纽站选址研究

提出一种模糊多分配p枢纽站中位问题,其中运输成本定义为模糊变量,问题的目标函数是在给定的可信性水平下,最小化总的运输成本。对于梯形和正态运输成本,问题等价于确定的混合整数线性规划问题。在实证分析中,选取了辽宁省煤炭产业的相关面板数据,分析计算在不同可信度水平下煤炭运输枢纽站设立的数量和位置,再利用传统的优化方法(如分枝定界法)求解。经计算,这一模型和求解方法可以用来解决辽宁省煤炭运输的选址问题。     

Statistical Inference for Single‐index Panel Data Models

We study estimation and hypothesis testing in single‐index panel data models with individual effects. Through regressing the individual effects on the covariates linearly, we convert the estimation problem in single‐index panel data models to that in partially linear single‐index models. The conversion is valid regardless of the individual effects being random or fixed. We propose an estimating equation approach, which has a desirable double robustness property. We show that our method is applicable in single‐index panel data models with heterogeneous link functions. We further design a chi‐squared test to evaluate whether the individual effects are random or fixed. We conduct simulations to demonstrate the finite sample performance of the method and conduct a data analysis to illustrate its usefulness.     

Computing factors for exact two-sided tolerance limits for a normal distribution

A self-contained FORTRAN subroutine is provided which computes factors for Wald-Wolfowitz type tolerance limits allowing arbitrary combinations of sample size n and degrees of freedom ν. The exact calculations from our program reveal inadequacies of two existing approximations, especially when ν ? n. Numerous applications where ν ≠ n ? 1 are cited; two of these are discussed and illustrated.     

Asymptotic normality for limiting discrete distributions

Three basic asymptotic normality conditions for limiting discrete distributions are given in terms of differencing operators. Under these conditions one can establish asymptotic normality by directly dealing with the limiting behaviors of distribution functions themselves without resorting to the central limit theorem.     

Identification of outliers in a one-way random effects model

We distinguish between three types of outliers in a one-way random effects model. These are formally described in terms of their position relative to the main part of the observations. We propose simple rules for identifying such outliers and give an example which involves median-based statistics.     

Bootstrap methods for bias correction and confidence interval estimation for nonlinear quantile regression of longitudinal data

This paper examines the use of bootstrapping for bias correction and calculation of confidence intervals (CIs) for a weighted nonlinear quantile regression estimator adjusted to the case of longitudinal data. Different weights and types of CIs are used and compared by computer simulation using a logistic growth function and error terms following an AR(1) model. The results indicate that bias correction reduces the bias of a point estimator but fails for CI calculations. A bootstrap percentile method and a normal approximation method perform well for two weights when used without bias correction. Taking both coverage and lengths of CIs into consideration, a non-bias-corrected percentile method with an unweighted estimator performs best.     

Cook's distance in linear longitudinal models

Cook's distance (1977) has become the standard influence diagnostic tool for analyzing cross–sectional regression studies. This paper introduces an analogue of Cook's distance in fixed effects models for longitudinal data. We demonstrate that this statistic is dominated by the effects of nuisance parameters, and hence its effectiveness as an influence measure in the longitudinal data setting is limited.     

Marginal Nested Interactions for Contingency Tables

We introduce a new definition of generalized marginal interactions, called marginal nested interactions, which includes baseline, local, continuation and reverse continuation logits and odds ratios as special cases. The significant aspect of this definition is the inclusion of new types of logits and odds ratios that can handle non-ordinal, ordinal and partially ordered categorical variables in a flexible and appropriate way. It is proved also that the marginal nested interactions define a saturated model of a multi-way contingency table.     

Tables for the Friedman rank test

This note presents tables for Friedman's test for two-way analysis of variance by ranks. These tables are more accurate than those that are presented in the literature. After intensive simulations, we have found for particular critical values some discrepancies with tables published earlier. The tables are also more extensive than those previously available.     

Joint-regression Analysis for Incomplete Two-way Tables

Joint-regression analysis of incomplete two-way tables of genotype-by-environment data is usually carried out using the iterative method of Digby (1979). However, the nonlinear analysis method of Ng & Grunwald (1997) can also be used. The speed of convergence for the Ng & Grunwald method compares favourably with that of Digby, and more importantly the method gives valid inference and hence should be preferred.     

A modified nested-error regression model for small area estimation

A nested-error regression model having both fixed and random effects is introduced to estimate linear parameters of small areas. The model is applicable to data having a proportion of domains where the variable of interest cannot be described by a standard linear mixed model. Algorithms and formulas to fit the model, to calculate EBLUP and to estimate mean-squared errors are given. A Monte Carlo simulation experiment is presented to illustrate the gain of precision obtained by using the proposed model and to obtain some practical conclusions. A motivating application to Spanish Labour Force Survey data is also given.     

Testing for sphericity in a two-way error components panel data model

This article is concerned with sphericity test for the two-way error components panel data model. It is found that the John statistic and the bias-corrected LM statistic recently developed by Baltagi et al. (2011 Baltagi, B. H., Feng, Q., Kao, C. (2011). Testing for sphericity in a fixed effects panel data model. Econometrics Journal 14:25–47.[Crossref], [Web of Science ®] , [Google Scholar])Baltagi et al. (2012 Baltagi, B. H., Feng, Q., Kao, C. (2012). A Lagrange multiplier test for cross-sectional dependence in a fixed effects panel data model. Journal of Econometrics 170:164–177.[Crossref], [Web of Science ®] , [Google Scholar], which are based on the within residuals, are not helpful under the present circumstances even though they are in the one-way fixed effects model. However, we prove that when the within residuals are properly transformed, the resulting residuals can serve to construct useful statistics that are similar to those of Baltagi et al. (2011 Baltagi, B. H., Feng, Q., Kao, C. (2011). Testing for sphericity in a fixed effects panel data model. Econometrics Journal 14:25–47.[Crossref], [Web of Science ®] , [Google Scholar])Baltagi et al. (2012 Baltagi, B. H., Feng, Q., Kao, C. (2012). A Lagrange multiplier test for cross-sectional dependence in a fixed effects panel data model. Journal of Econometrics 170:164–177.[Crossref], [Web of Science ®] , [Google Scholar]). Simulation results show that the newly proposed statistics perform well under the null hypothesis and several typical alternatives.     

How Cox models react to a study-specific confounder in a patient-level pooled dataset: random effects better cope with an imbalanced covariate across trials unless baseline hazards differ

Combining patient-level data from clinical trials can connect rare phenomena with clinical endpoints, but statistical techniques applied to a single trial may become problematical when trials are pooled. Estimating the hazard of a binary variable unevenly distributed across trials showcases a common pooled database issue. We studied how an unevenly distributed binary variable can compromise the integrity of fixed and random effects Cox proportional hazards (cph) models. We compared fixed effect and random effects cph models on a set of simulated datasets inspired by a 17-trial pooled database of patients presenting with ST segment elevation myocardial infarction (STEMI) and non-STEMI undergoing percutaneous coronary intervention. An unevenly distributed covariate can bias hazard ratio estimates, inflate standard errors, raise type I error, and reduce power. While uneveness causes problems for all cph models, random effects suffer least. Compared to fixed effect models, random effects suffer lower bias and trade inflated type I errors for improved power. Contrasting hazard rates between trials prevent accurate estimates from both fixed and random effects models.