Govinda J. Weerakkody

Limits of retrospective power analysis

Power analysis after study completion has been suggested to interpret study results. We present 3 methods of estimating power and discuss their limitations. We use simulation studies to show that estimated power can be biased, extremely variable, and severely bounded. We endorse the practice of computing power to detect a biologically meaningful difference as a tool for study planning but suggest that calculation of confidence intervals on the parameter of interest is the appropriate way to gauge the strength and biological meaning of study results.

Estimation of within Model Parameters in Regression Models with a Nested Error Structure

Abstract Restricted randomizations, similar to those in split-plot type experiments, often are adapted to assign quantitative treatment factors to experimental units. Such restrictions result in the experiment having a nested error structure. Sufficient conditions are presented under which ordinary least squares (OLS) estimates of regressor parameters are uniformly minimum variance unbiased (UMVU). If one designs experiments so that these conditions are satisfied, the analysis is straightforward and easy. When these conditions are not met, three different estimators of nested regressor parameters are suggested and compared.

Estimating the correlation coefficient in the presence of correlated observations from a bivariate normal population

Estimation of the correlation coefficient between two variates (p) in the presence of correlated observations from a bivar iate normal population is considered The estimated maximum likelihood estimator (EMLE), an estimate based on the maximum likelihood estimator (MLE), is proposed and studied for the estimation of p For the large sample case , approximate expressions foi the variance and the bias of the Pearson estimate of the correlation coefficient are derived. These expressions suggests that the Pearson’s estimator possesses high mean square error (MSE) in estimating ρ in comparison to the MLE The MSE is particularly high when the observations within clusters aie highly correlated. The Pearson’s estimate, the MLE, and the EMLE aie evaluated in a simulation study This study shows that the proposed EMLE pefoims bettei than the Pearson’s correlation coefficient except when the number of clusters is small.

Assessing the performance of a waste characterization expert system

Scientists at the Mississippi State University Diagnostic Instrumentation and Analysis Laboratory and the Idaho National Engineering and Environmental Laboratory (INEEL) have developed an expert system for a noninvasive characterization of containerized radiological waste. The characterization of the containers is necessary for determining their proper disposition. Three prototypes were developed, with each using a different method of handling uncertainty - a fuzzy system, a Bayesian network system, and a neural network system. The performance of each expert system was assessed to determine how well it modeled the decisions made by the INEEL domain expert. The prototype systems were also analyzed to measure the agreement in their decisions, the domain experts decisions, and the decisions made by two additional experts. The neural network prototype was further analyzed to determine how consistent it was in its assessments. This paper describes the analysis of the performance of the three expert system prototypes.

A poisson-gamma model for two-stage cluster sampling data

We propose a model for count data from two-stage cluster sampling, where observations within each cluster are subjected simultaneously to internal influences and external factors at the cluster level. This model can be seen as a two-stage hierarchical model with local and global predictors. This parameter-driven model causes the counts within a cluster to share a common latent factor and to be correlated. Maximum likelihood (ml) estimation based on an EM algorithm for the model is discussed. Simulation study is carried out to assess the benefit of using ml estimates compared to a standard Poisson regression analysis that ignores the within cluster correlation.

Theory and Methods: Hypothesis Testing in Two‐Stage Cluster Sampling

Correlated observations often arise in complex sampling schemes such as two-stage cluster sampling. The resulting observations from this sampling scheme usually exhibit certain positive intracluster correlation, as a result of which the standard statistical procedures for testing hypotheses concerning linear combinations of the parameters may lack some of the optimal properties that these possess when the data are uncorrelated. The aim of this paper is to present exact methods for testing these hypotheses by combining within and between cluster information much as in Zhou & Mathew (1993).

Testing hypotheses about the common mean of two normal populations

Two simple tests which allow for unequal sample sizes are considered for testing hypothesis for the common mean of two normal populations. The first test is an exact test of size a based on two available t-statistics based on single samples made exact through random allocation of α among the two available t-tests. The test statistic of the second test is a weighted average of two available t-statistics with random weights. It is shown that the first test is more efficient than the available two t-tests with respect to Bahadur asymptotic relative efficiency. It is also shown that the null distribution of the test statistic in the second test, which is similar to the one based on the normalized Graybill-Deal test statistic, converges to a standard normal distribution. Finally, we compare the small sample properties of these tests, those given in Zhou and Mat hew (1993), and some tests given in Cohen and Sackrowitz (1984) in a simulation study. In this study, we find that the second test performs better than...

A note on the recovery of inter-block information in balanced incomplete block designs

Consider the recovery of interblock information in balanced incomplete block designs. It is shown that the recovery of interblock information through the estimated generalized least squares (EGLS) estimator may improve the estimation, provided (b-t) > 4 where b =number of blocks and t =number of treatments. An expression for the variance covariance matrix for the EGLS estimator is provided and its behaviour is studied.

Variance component estimation in multiple regression models having a nested error structure

Multiple regression when regressors are measured on two different sized experimental units involves a nested error structure. This nested error structure consists of two variance components. Sufficient conditions are presented under which UMVU estimators of these variance components exist. When these conditions are not met, two alternative estimators for the two variance components are considered and compared when possible. This paper considers multiple regression models when regressor variables are associated with different sized experimental units resulting in a nested error structure. Nested error structures occur because of restrictions placed on randomizations. This results in experiments similar to splitplot type experiments which involove two different sizes of experimental units. Data resulting from these type of experiments consists of measurements made on larger sized experimental units as well as measurements made on smaller sized experimental units. Split-plot type experiments occur when certa...

Effect of Intracluster Correlation on the R-Square Statistic

R 2 -statistic is a popular and very widely used statistic in regression analysis to estimate the square multiple correlation (SMC), Q 2 , between a response variable Y and p predictor variables, X 1 ....,X p . Numerous articles are available in the statistical literature on the properties of R 2 as an estimator of Q 2 when the observations are uncorrelated. However, relatively little is known about the behavior of R 2 when the available observations are correlated such as the data that result from complex sampling schemes. In this paper, we study the behavior R 2 in the presence of two-stage sampling data. An approximate expressions for the variance and the bias of R 2 in the presence of two-stage cluster sampling data with positive intracluster correlation (Q * ) are obtained. It is evident from these formulas and from a simulation study that R 2 is a poor estimator of Q 2 except when Q * is small. As such, we consider several alternative estimators of Q 2 and evaluate their theoretical properties and finite sample performance using a simulation study.