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Inference on cross correlation with repeated measures data

Tang, Yuxiao
http://rave.ohiolink.edu/etdc/view?acc_num=osu1078857542

Abstract Details

2004, Doctor of Philosophy, Ohio State University, Statistics.
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.
Haikady Nagaraja (Advisor)
116 p.
Statistics
cross correlation; repeated measurements; missing data

Recommended Citations

Citations

  • Tang, Y. (2004). Inference on cross correlation with repeated measures data [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1078857542

    APA Style (7th edition)

  • Tang, Yuxiao. Inference on cross correlation with repeated measures data. 2004. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1078857542.

    MLA Style (8th edition)

  • Tang, Yuxiao. "Inference on cross correlation with repeated measures data." Doctoral dissertation, Ohio State University, 2004. http://rave.ohiolink.edu/etdc/view?acc_num=osu1078857542

    Chicago Manual of Style (17th edition)

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© 2004, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.