Regression Analysis for Correlated Data

Abstract

Correlated data arise in many situations in health research. On the organismal level, there may be measurements on several tumors, both hands, all teeth, and so on. It is usually expected in such cases that the measurements on a given individual are more similar than those on different individuals. We have considered the regression analysis for sets of observations such that within each set observations having a autocorrelation structure, and any two observations between any two sets having a constant correlation coefficient, and variance of all observations are same. In general, the form of the correlation structure is known for a given situation of data set but parameters that are involved in the correlation structure are always unknown. Herein we have developed a robust method of estimating the best linear unbiased estimators of all regression parameters except the intercept, which is often unimportant. In this connection we have also developed a testing procedure for any set of linear hypotheses regarding the unknown regression coefficients. Confidence ellipsoid of a set of estimable functions of regression coefficients have been developed. Index of fit for the fitted regression equation has also been developed. An example with simulated data is given as an illustration of our developed method.

Key Words:

• Compound autocorrelated structure
• confidence ellipsoid
• confidence interval
• correlated observations
• index of fit

Additional information

Notes on contributors

Rabindra Nath Das

R. N. Das is an Associate Professor (Reader) in the Department of Statistics, The University of Burdwan, Golapbag, Rajbati, Burdwa, West Bengal, India. He holds a master’s degree in Statistics from The University of Kalyani, Kalyani, India, and Ph.D. degree in Statistics from The University of Burdwan, Burdwan, India. He is a Post-Doctoral Research Fellow in the Department of Statistics, Seoul National University, Seoul, Korea (September, 2006 to August, 2007). He has authored several articles on Design of Experiments (response surface and block design), Quality Improvement, Data Analysis etc. His special area of interest is on design of experiments, quality improvement, data analysis, regression analysis etc. with correlated observations.