Rank-based analysis of repeated measures block designs

A rank-based inference is developed for repeated measures balanced incomplete block and randomized complete block designs using a suitable dispersion function. Asymptotic distributions of rank estimators are developed after establishing approximate linearity of the gradient vector of the dispersion function. Unlike available nonparametric procedures for those designs, estimation and testing are tied together. Three different test statistics are developed for testing the linear hypotheses. Friedman's (1937) statistic and Durbin's (1951) statistic are particular cases of one of the three proposed statistics. An estimate of a scale parameter which appears in the ARE expression as well as as in the variences and covariances of the rank estimators is discussed.     

Sample design for observing classes of objects

We consider optimal sample designs for observing classes of objects. Suppose we will take a simple random sample of equal-sized sectors from a study population and observe the classes existing on these sectors. The classes might be many different things, for example, herbaceous plant species (in sampling quadrats), microinvertebrate species (in sampling cores), and side effects from a drug (in conducting medical trials). Under a nonparametric mixture model and data from a previous related study, we first estimate the optimal number of sample sectors of a given size. Then for negative binomial dispersions of individuals with a common aggregation parameter k, we consider the optimal size as well as number of sample sectors. A simple test exists to check our common k assumption and our optimal size method requires far less data than would be required by a grid method or other method which utilizes data from sample sectors of several different sizes.     

P-value adjustment for multiple binary endpoints

The p-value-based adjustment of individual endpoints and the global test for an overall inference are the two general approaches for the analysis of multiple endpoints. Statistical procedures developed for testing multivariate outcomes often assume that the multivariate endpoints are either independent or normally distributed. This paper presents a general approach for the analysis of multivariate binary data under the framework of generalized linear models. The generalized estimating equations (GEE) approach is applied to estimate the correlation matrix of the test statistics using the identity and exchangeable working correlation matrices with the model-based as well as robust estimators. The objectives of the approaches are the adjustment of p-values of individual endpoints to identify the affected endpoints as well as the global test of an overall effect. A Monte Carlo simulation was conducted to evaluate the overall family wise error (FWE) rates of the single-step down p-value adjustment approach from two adjustment methods to three global test statistics. The p-value adjustment approach seems to control the FWE better than the global approach Applications of the proposed methods are illustrated by analyzing a carcinogenicity experiment designed to study the dose response trend for 10 tumor sites, and a developmental toxicity experiment with three malformation types: external, visceral, and skeletal.     

The Relative Size of Windfall Income and the Permanent Income Hypothesis

A reconciliation is offered for the diverse test results on Friedman's permanent income hypothesis. A large data sample of those receiving windfall income in the Bureau of Labor Statistics' 1972–1973 Consumer Expenditure Survey is divided according to the size of the windfall relative to estimated permanent income. A pattern of a declining marginal propensity to consume windfall income as the relative size of the windfall increases is apparent. These results support the permanent income hypothesis for relatively large windfalls.     

The True Cost-of-Living Index With Changing Preferences

This article investigates the theoretical and empirical properties of a true cost-of-living index under conditions of changing preferences. A family of true indexes is defined based on the notion of the current utility function. A particular index, based on the previous period's utility level, is then defined. Given this definition, a true cost-of-living index is computed based on a quadratic expenditure system estimated with quarterly data from 1960–1981. For empirical purposes, changes in preferences are represented by the linear habit formation hypothesis. This index is then compared with Paasche and Laspeyres indexes. The true cost-of-living index grows somewhat faster than either the Paasche or Laspeyres index. It also displays considerably more variability.     

A modification of watson's statistic for goodness-of-fit

A modification of Watson's statistic is suggested for dealing with stochastically ordered alternatives in the goodness-of-fit setting.     

Testing for lack of fit in linear multiresponse models based on exact or near replicates

Three procedures for testing the adequacy of a proposed linear multiresponse regression model against unspecified general alternatives are considered. The model has an error structure with a matrix normal distribution which allows the vector of responses for a particular run to have an unknown covariance matrix while the responses for different runs are uncorrelated. Furthermore, each response variable may be modeled by a separate design matrix. Multivariate statistics corresponding to the classical univariate lack of fit and pure error sums of squares are defined and used to determine the multivariate lack of fit tests. A simulation study was performed to compare the power functions of the test procedures in the case of replication. Generalizations of the tests for the case in which there are no independent replicates on all responses are also presented.     

Evaluation of an analysis approach used to account for extra-variation in clustered categorical responses

This article presents the results of a simulation study investigating the performance of an approach developed by Miller and Landis (1991) for the analysis of clustered categorical responses. Evaluation of this “two-step” approach, which utilizes the method of moments to estimate the extra-variation pardmeters and subsequently incorporates these parameters into estimating equations for modelling the marginal expectations, is carried out in an experimental setting involving a comparison between two groups of observations. We assume that data for both groups are collected from each cluster and responses are measured on a three-point ordinal scale. The performance of the estimators used in both “steps” of the analysisis investigated and comparisons are made to an alternative analysismethod that ignores the clustering. The results indicate that in the chosen setting the test for a difference between groups generally operatbs at the nominal α=0.05 for 10 or more clusters and hasincreasing power with both an increasing number of clusters and an inrreasing treatment effect. These results provide a striking contrasc to those obtained from an improper analysis that ignores clustering.     

R×C ecological inference: bounds, correlations, flexibility and transparency of assumptions

Summary.  Despite its potential pitfalls, ecological inference is an unavoidable part of some quantitative settings, including US voting rights litigation. In such applications, the analyst will typically encounter two-way tables with more than two rows and columns. Although several ecological inference methods are currently available for 2×2 tables, there are fewer options for analysing general R × C tables, and virtually none that model counts as opposed to fractions. We propose a count R × C method that respects the bounds deterministically, that allows for complex relationships between internal cell quantities, that is easily extensible and that results from transparent assumptions. We study the method via simulation, and then apply it to an example that is drawn from the state of Texas relevant to recent redistricting litigation there.