A unified approach to multilevel sample selection models

Abstract

We propose a unified approach for multilevel sample selection models using a generalized result on skew distributions arising from selection. If the underlying distributional assumption is normal, then the resulting density for the outcome is the continuous component of the sample selection density and has links with the closed skew-normal distribution (CSN). The CSN distribution provides a framework which simplifies the derivation of the conditional expectation of the observed data. This generalizes the Heckman’s two-step method to a multilevel sample selection model. Finite-sample performance of the maximum likelihood estimator of this model is studied through a Monte Carlo simulation.     

Unbiased F Tests for Factorial Experiments for Correlated Data

This paper finds a general form of the correlation matrix that may be used to provide unbiased F tests in a.k-way factorial experiment.     

Influential observations in the analysis of variance

The effect of influentia lob servations on t h e parameter estimates of ordinary l e a s t squares regression models has received considerable attentio n fn the last decade. However, very little attention has been given t o the problem of in fluent ia lobserva- tions in the analysis of variance . The purpose of t h i s paper is t o show by way of examples that influential observations can alter the conclusions of tests of hypotheses in the analysis of variance . Regression diagnostics for identif y in g both extreme points and outliers can be used to reveal potential data and design problems.     

On the coefficient of variation for residence time distributions of some stochastic compartmental models

The study of residence time distributions is motivated by the desire to develop new practical tools for the statistical analysis of compartmental systems. In particular, Gibaldi and Perrier (1982) describe three alternative models for a two-compartment system, which were noted to be "indistinguishable based solely on plasma or urinary excretion data," defining a residence time distribution. In this paper, properties of the coefficient of variation of the residence time distributions are developed for these three models. In addition to the standard Markovian model with exponential retention times, properties are also derived for a non-Markovian model with gamma retention times. A coefficient of variation may be estimated from commonly available elimination data, and may be used in principle to discriminate between these three models.     

Estimation of covariance matrices based on hierarchical inverse-Wishart priors

This paper focuses on Bayesian shrinkage methods for covariance matrix estimation. We examine posterior properties and frequentist risks of Bayesian estimators based on new hierarchical inverse-Wishart priors. More precisely, we give the conditions for the existence of the posterior distributions. Advantages in terms of numerical simulations of posteriors are shown. A simulation study illustrates the performance of the estimation procedures under three loss functions for relevant sample sizes and various covariance structures.     

Accent on Teaching Materials

Estimation of covariance components in the multivariate random-effect model with nested covariance structure is discussed. There are two covariance matrices to be estimated, namely, the between-group and the within-group covariance matrices. These two covariance matrices are most often estimated by forming a multivariate analysis of variance and equating mean square matrices to their expectations. Such a procedure involves taking the difference between the between-group mean square and the within-group mean square matrices, and often produces an estimated between-group covariance matrix that is not nonnegative definite. We present estimators of the two covariance matrices that are always proper covariance matrices. The estimators are the restricted maximum likelihood estimators if the random effects are normally distributed. The estimation procedure is extended to more complicated models, including the twofold nested and the mixed-effect models. A numerical example is presented to illustrate the use of the estimation procedure.     

Accent on Teaching Materials: Notices and Reviews of Important Teaching Materials

This article examines the probabilities of outcomes from rolling dice with the dimension 1 × 1 × r for various values of r. Experiments were conducted by school students and university students. The results of the experiments are given and the probabilities examined using a generalized linear model. Notes are also made about the value of the experiment in teaching the groups of students.     

Book reviews

S.M.Kendall:Multivariate Analysis.Charles Griffin & Co. Ltd., London and High Wycombe 1975, 210 pp

C.T.Leondes (ed.):Control and Dynamic Systems, Advances in Theory and Applications. Vol. 11, Academic Press, New York and London 1974, 516 pp., $ 24.50.

CH. R.Nelson:Applied Time Series Analysis for Managerial Forecasting. Holden Day, Inc., San Francisco 1973, 231 pp., $ 14.95.

B.DE Finetti:Theory of Probability. Vol. 1, 2, John Wiley & Sons, New York, London, Sydney, Toronto. Vol. 1, 1974, 300 pp., £ 7.50 - Vol. 2 1975, 375 pp., £ 10.50.

P.Erdördos, J. Spencer:Probabilistic Methods in Combinatorics. Akadémic Press, New York and London; Akadémiai Kiadó, Budapest 1974, 106 pp., $ 11.75.

J.S.R.Ustagi:Variational Methods in Statistics.Academic Press, New York and London 1975.

J.S.Rustagi:Optimizing Methods in Statistics.Academic Press, New York and London 1971,488 pp., $ 17.00.

Karl V. Bury:Statistical Models in Applied Science. John Wiley & Sons, New York-London-Sydney-Toronto 1975,.625 pp., £ 15.60; $ 28.00.

Michael R. Anderberg:Cluster Analysis for Applications. Academic Press, New York-San Francisco-London 1973, 359 pp., $ 27,–.

J.L.Fleiss:Statistical Methods for Rates and Proportions. John Wiley & Sons, New York-London-Sydney-Toronto 1973. 223 pp., £ 6.50.

J.Tanur et al. (Ed.):Statistics:A Guide to the Unknown. Holden Day, Inc., San Francisco 1972, 430 pp.

H.VÁliaho, T. Pekkonen:A Procedure for Stepwise Regression Analysis.Akademie-Verlag, Berlin 1976, 90 pp., 18,– M.

M.Reinfeldt, U. TrÁnkle:Signifikanztabellen statistischer Testvertellungen. R. Oldenbourg Verlag, Mnchen, Wien 1976, 151 S., DM 44,–.

R.E.Barlow, D.J.Batholomew, J.M.Bremner, H.D.Brunk:Statistical Inference Under Order Restrictions.(The Theory and Applications of Isotonic Regression.) John Wiley & Sons, New York 1972, 388 pp., £ 7.50.

H.J.Larson:Introduction to Probability Theory and Statistical Inference. Wiley, New York 1974, 430 pp., £ 6.85.

R.A.Carlson:Statistics. Holden Day, Inc., San Francisco 1973, 393 pp.

E. Page:Queueing Theory in OR. Butterworths, London 1972, 187 pp., £ 3.60.

H.Krampe, J.Kubat, W.Runge:Bedienungsmodelle. Ein Leitfaden für die praktische Anwendung, Verlag Die Wirtachaft, Berlin 1973, 512 S., 79,– M.

G.S.Fishman:Concepts and Methods in Discrete Events Digital Simulation. John Wiley & Sons, New York 1973, 385 pp., £ 8,75.     

Tests for Symmetry Based on the One-Sample Wilcoxon Signed Rank Statistic

ABSTRACT

The one-sample Wilcoxon signed rank test was originally designed to test for a specified median, under the assumption that the distribution is symmetric, but it can also serve as a test for symmetry if the median is known. In this article we derive the Wilcoxon statistic as the first component of Pearson's X ² statistic for independence in a particularly constructed contingency table. The second and third components are new test statistics for symmetry. In the second part of the article, the Wilcoxon test is extended so that symmetry around the median and symmetry in the tails can be examined seperately. A trimming proportion is used to split the observations in the tails from those around the median. We further extend the method so that no arbitrary choice for the trimming proportion has to be made. Finally, the new tests are compared to other tests for symmetry in a simulation study. It is concluded that our tests often have substantially greater powers than most other tests.     

Distance-based approach in univariate longitudinal data analysis

In this paper, we propose a methodology to analyze longitudinal data through distances between pairs of observations (or individuals) with regard to the explanatory variables used to fit continuous response variables. Restricted maximum-likelihood and generalized least squares are used to estimate the parameters in the model. We applied this new approach to study the effect of gender and exposure on the deviant behavior variable with respect to tolerance for a group of youths studied over a period of 5 years. Were performed simulations where we compared our distance-based method with classic longitudinal analysis with both AR(1) and compound symmetry correlation structures. We compared them under Akaike and Bayesian information criterions, and the relative efficiency of the generalized variance of the errors of each model. We found small gains in the proposed model fit with regard to the classical methodology, particularly in small samples, regardless of variance, correlation, autocorrelation structure and number of time measurements.