|
April 26, 2002
32nd Annual SCASA Meeting
Student Paper Abstracts
- Kirby Jackson (Department of Epidemiology and Biostatistics, USC) Generalized Residual for Multivariate Survival and Frailty Models
A generalized survival residual appropriate for frailty models is proposed. This residual generalizes the usual Cox-Snell residuals to the case of correlated survival data and can be used in the investigation of a variety of frailty models. This residual is shown to have a multivariate exponential distribution with unit exponential margins and association parameters depending only on the frailty distribution. The distribution of this residual is given in terms of Laplace transforms of functions of observed survival times. However, the bivariate version of this distribution can also be generated as an Archimedean copula. Using the residual possible measures of association are discussed. This residual may have major implications for the analysis of frailty assumptions model fit and definition and estimation of dependence parameters in multivariate survival models. The two most common frailty models, those based on either the gamma distribution or the positive stable distribution are relatively easy to examine using these residuals.
- M.A. Tomlinson (Department of Statistics, USC) Lower Bounds for Percentiles in a Cumulative Damage Model for Strength of Materials
A discrete cumulative damage approach with a gamma process describing "initial damage" gives a new statistical model for the strength of carbon fibrous composites. The model is an accelerated test form of an inverse Gaussian distribution that fits carbon micro-composite strength data better than previous models. Asymptotic lower confidence bounds for small percentiles of the strength distribution are obtained based on Bonferonni's inequality and the Fisher information. Simulation results indicate that the asymptotic Bonferonni lower bounds are quite conservative, and bootstrap methods for improving the bounds are considered.
- Heather Ridings (Department of Statistics, USC) K Sample Distribution-Free Tests of Location
Consider a one factor experiment with k >= 3 levels and assume the model X_
ij = theta_i + e_ij. The normal theory approach for testing the equality of the
theta_i's is a one factor one-way ANOVA. However, when the assumption of norma
l errors is not met, one can use a distribution-free test, such as the Kruskal-W
allis test to test the equality of the theta_i's. The null distribution of this
test and a distribution-free test based on Normal Scores will be discussed, alo
ng with alpha = 0.10, 0.05, and 0.01 critical points of each. Also, the large s
ample chi^2 approximations will be examined for both tests.
- Alexander I. Petrisor (Department of Environmental Health Sciences, USC) An Application of Kriging in the Study of Spatial Variability of Bacterial Biofilms Using Confocal Microscopy, Digital Image Processing, and Geographical Information Systems
Biofilms are formed by bacterial colonies encapsulated in an extra-cellular polymeric substances matrix. The study of biofilms is facilitated by advances in microscopy, such as the scanning confocal laser microscopy technique used in conjunction with digital imaging processing to assess the structure of biofilms and spatial variability within biofilms. The purpose of this study is to utilize digital images of biofilms used in conjunction with fluorescent lectin probes to develop a tool used in the study of biofilm formation and growth, bacterial colonization, and determination of enzymatic activities. Images of sections through biofilms are enhanced using various digital image techniques and transformed in a classified map to be analyzed using ArcView GIS. This process may introduce errors at various steps and result into lack of information for some regions. Kriging was used in an attempt to fill in the gaps and produce smooth, continuous maps of the sections. Our results are inconclusive and it is arguable whether kriging produces better maps, suggesting the necessity for deeper investigations.
- J. Patrick Meyer (Department of Educational Psychology, USC) On the Use of Nonparametric Statistics in DIF Analysis
Existing methods for assessing differential item functioning (DIF) are typically limited to large samples. Testing accommodations, Computer Adaptive Tests, and school or district level test evaluations are situations in which one or both groups in a DIF analysis would be small. The present study investigated the use of nonparametric approaches to DIF analysis in a small sample of examinees who responded to a math attitude survey composed of polytomous items. The Wilcoxon Rank Sum test and the Van der Waerden Normal Scores test were used for exact probability analyses of items while the Cochran-Mantel-Haenszel was used for the asymptotic analysis. In addition, an effect size analysis was conducted using the standardized mean difference (SMD) approach. Results suggested that the exact methods produced better results than the CMH.
|
