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.     

Modelling and estimating heavy-tailed non-homogeneous correlated queues: Pareto-inverse gamma HGLM with covariates

Evidence of communication traffic complexity reveals correlation in a within-queue and heterogeneity among queues. We show how a random-effect model can be used to accommodate these kinds of phenomena. We apply a Pareto distribution for arrival (service) time of individual queue for given arrival (service) rate. For modelling potential correlation in arrival (service) times within a queue and heterogeneity of the arrival (service) rates among queues, we use an inverse gamma distribution. This modelling approach is then applied to the cache access log data processed through an Internet server. We believe that our approach is potentially useful in the area of network resource management.     

Discrepancy in regression estimates between log-normal and gamma: some case studies

In regression models with multiplicative error, estimation is often based on either the log-normal or the gamma model. It is well known that the gamma model with constant coefficient of variation and the log-normal model with constant variance give almost the same analysis. This article focuses on the discrepancies of the regression estimates between the two models based on real examples. It identifies that even though the variance or the coefficient of variation remains constant, but regression estimates may be different between the two models. It also identifies that for the same positive data set, the variance is constant under the log-normal model but non-constant under the gamma model. For this data set, the regression estimates are completely different between the two models. In the process, it explains the causes of discrepancies between the two models.     

A power comparison of three tests for design effects in a random effects covariance model

A preliminary testing procedure for design ettecta in a ran-dom effects covariance model is Compared with the usual procedure to see if the power of the latter can be improved. A procedure which ignores the random covariate effects is included for comparison and for study of misspecification effects. Methodology is based on Roebruck's (1982) results for regular linear models.     

A Simulation-based Goodness-of-fit Test for Random Effects in Generalized Linear Mixed Models

Abstract.  The goodness-of-fit of the distribution of random effects in a generalized linear mixed model is assessed using a conditional simulation of the random effects conditional on the observations. Provided that the specified joint model for random effects and observations is correct, the marginal distribution of the simulated random effects coincides with the assumed random effects distribution. In practice, the specified model depends on some unknown parameter which is replaced by an estimate. We obtain a correction for this by deriving the asymptotic distribution of the empirical distribution function obtained from the conditional sample of the random effects. The approach is illustrated by simulation studies and data examples.     

A certain locally most powerful test for one-way random effects model: full distribution and power considerations

We investigate the properties of the locally most powerful nonparametric criterion against logistic alternatives developed by Govindarajulu (1975) for testing one-way random effects modcls. We deduce the appropriate computational forms for the test criterion T and tabulate the critical values of T for α = .01, .05 and 0.10, and various sample sizes. Certain features of the computational methods are discussed. In the tables we retain only those sample sizes beyond which the asymptotic theory is meaningful. We also study the power comparison of the test for two populations with the classical F-test under a range of normal alternatives.     

A multilevel model with autoregressive components for the analysis of tribal art prices

In this paper, we introduce a multilevel model specification with time-series components for the analysis of prices of artworks sold at auctions. Since auction data do not constitute a panel or a time series but are composed of repeated cross-sections, they require a specification with items at the first level nested in time-points. Our approach combines the flexibility of mixed effect models together with the predicting performance of time series as it allows to model the time dynamics directly. Model estimation is obtained by means of maximum likelihood through the expectation–maximization algorithm. The model is motivated by the analysis of the first database ethnic artworks sold in the most important auctions worldwide. The results show that the proposed specification improves considerably over classical proposals both in terms of fit and prediction.     

Functional Coefficient Regression Models for Non-linear Time Series: A Polynomial Spline Approach

Abstract.  We propose a global smoothing method based on polynomial splines for the estimation of functional coefficient regression models for non-linear time series. Consistency and rate of convergence results are given to support the proposed estimation method. Methods for automatic selection of the threshold variable and significant variables (or lags) are discussed. The estimated model is used to produce multi-step-ahead forecasts, including interval forecasts and density forecasts. The methodology is illustrated by simulations and two real data examples.     

A NONPARAMETRIC MIXED‐EFFECTS MODEL FOR CANCER MORTALITY

There are several ways to handle within‐subject correlations with a longitudinal discrete outcome, such as mortality. The most frequently used models are either marginal or random‐effects types. This paper deals with a random‐effects‐based approach. We propose a nonparametric regression model having time‐varying mixed effects for longitudinal cancer mortality data. The time‐varying mixed effects in the proposed model are estimated by combining kernel‐smoothing techniques and a growth‐curve model. As an illustration based on real data, we apply the proposed method to a set of prefecture‐specific data on mortality from large‐bowel cancer in Japan.     

Latent Variable Modelling: A Survey*

Abstract. Latent variable modelling has gradually become an integral part of mainstream statistics and is currently used for a multitude of applications in different subject areas. Examples of ‘traditional’ latent variable models include latent class models, item–response models, common factor models, structural equation models, mixed or random effects models and covariate measurement error models. Although latent variables have widely different interpretations in different settings, the models have a very similar mathematical structure. This has been the impetus for the formulation of general modelling frameworks which accommodate a wide range of models. Recent developments include multilevel structural equation models with both continuous and discrete latent variables, multiprocess models and nonlinear latent variable models.     

A dynamic random-effects model for recovery of skin barrier function: evaluation of the efficacy of different skin care products

Apparently, the use of mathematical and statistical models to describe the structure and function of the skin barrier is rather limited. The skin barrier protects the body against uncontrolled loss of water and desiccation, and prevents environmental substances from entering the skin. A simple measure of the barrier function is the transepidermal water loss (TEWL), which is easy to measure. Healthy skin has low TEWL values, whereas various skin diseases result in high TEWL values and eventually in the development of dry skin. The use of skin care products can protect and prevent dry skin. In this study several different trial formulations are compared with respect to their abilities as skin care products. The study is performed as a longitudinal study on mice, where the skin barrier is broken by means of acetone and then treated with one of the formulations. We analysed the data by means of a semimechanistic random-effects model with similarities to pharmacokinetic models. In the model each formulation is characterized by two parameters: one that corresponds to the initial barrier restoration effect and one that corresponds to the elimination rate.     

Estimation of variance components in the mixed effects models: A comparison between analysis of variance and spectral decomposition

The mixed effects models with two variance components are often used to analyze longitudinal data. For these models, we compare two approaches to estimating the variance components, the analysis of variance approach and the spectral decomposition approach. We establish a necessary and sufficient condition for the two approaches to yield identical estimates, and some sufficient conditions for the superiority of one approach over the other, under the mean squared error criterion. Applications of the methods to circular models and longitudinal data are discussed. Furthermore, simulation results indicate that better estimates of variance components do not necessarily imply higher power of the tests or shorter confidence intervals.     

A Unified Approach of Meta-Analysis: Application to an Antecedent Biomarker Study in Alzheimer's Disease

This article provides a unified methodology of meta-analysis that synthesizes medical evidence by using both available individual patient data (IPD) and published summary statistics within the framework of likelihood principle. Most up-to-date scientific evidence on medicine is crucial information not only to consumers but also to decision makers, and can only be obtained when existing evidence from the literature and the most recent individual patient data are optimally synthesized. We propose a general linear mixed effects model to conduct meta-analyses when individual patient data are only available for some of the studies and summary statistics have to be used for the rest of the studies. Our approach includes both the traditional meta-analyses in which only summary statistics are available for all studies and the other extreme case in which individual patient data are available for all studies as special examples. We implement the proposed model with statistical procedures from standard computing packages. We provide measures of heterogeneity based on the proposed model. Finally, we demonstrate the proposed methodology through a real life example studying the cerebrospinal fluid biomarkers to identify individuals with high risk of developing Alzheimer's disease when they are still cognitively normal.