Inference On Cross Correlation With Repeated Measures Data
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Inference on Cross Correlation with Repeated Measures Data
Abstract: We discuss the problem of estimating the correlation coefficient between two variables observed in a longitudinal study. We assume that they follow a bivariate normal distribution, and that the repeated measures taken on the same subject follow a multivariate normal model. We consider two cases: when the data are complete and incomplete. First, when all the observations are available, we introduce two estimators: the marginal mean estimator and the estimator based on the mean of Fisher's z values. These two estimators are functions of the sample cross correlations computed at each time point. Asymptotic distributions of the two estimators are given. After comparing these two estimators with the MLE, we find that the performance of the estimator based on the mean of Fisher's z values is as good as that of the MLE. The former estimator is much easier to compute. When some observations are missing with ignorable missing-data mechanism, we propose four estimators: the group weighted mean estimator, the marginal mean estimator, the estimator based on the weighted Fisher's z values, and the weighted marginal mean estimator. In the first approach, we group the data based on the missing pattern, estimate the correlation for each group, and take the weighted average. In the other three approaches, we compute the sample correlation coefficients based on cross-sectional data, and combine the marginal information in different ways. We obtain the asymptotic distributions of these estimators. Using simulation we compare them with the MLE. We find that these estimators are almost as good as the MLE while they are much easier to compute, except for the group weighted mean estimator. We discuss the robustness of these estimators as the nuisance parameters associated with the multivariate normal model vary. Further, we apply our approaches to the data from a dog diet study and an AIDS study separately to illustrate the advantages of the proposed approaches. We also discuss how to test the equality of correlations over time for the cases with complete and incomplete data sets from a multivariate normal model. We compare several tests and conclude that the asymptotic test based on the Fisher's z transformations performs well.
Mixed Effects Models for Complex Data
Although standard mixed effects models are useful in a range of studies, other approaches must often be used in correlation with them when studying complex or incomplete data. Mixed Effects Models for Complex Data discusses commonly used mixed effects models and presents appropriate approaches to address dropouts, missing data, measurement errors,
Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences
This classic text on multiple regression is noted for its nonmathematical, applied, and data-analytic approach. Readers profit from its verbal-conceptual exposition and frequent use of examples. The applied emphasis provides clear illustrations of the principles and provides worked examples of the types of applications that are possible. Researchers learn how to specify regression models that directly address their research questions. An overview of the fundamental ideas of multiple regression and a review of bivariate correlation and regression and other elementary statistical concepts provide a strong foundation for understanding the rest of the text. The third edition features an increased emphasis on graphics and the use of confidence intervals and effect size measures, and an accompanying website with data for most of the numerical examples along with the computer code for SPSS, SAS, and SYSTAT, at www.psypress.com/9780805822236 . Applied Multiple Regression serves as both a textbook for graduate students and as a reference tool for researchers in psychology, education, health sciences, communications, business, sociology, political science, anthropology, and economics. An introductory knowledge of statistics is required. Self-standing chapters minimize the need for researchers to refer to previous chapters.