Fitting time series models for longitudinal survey data under informative sampling |
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| Institution: | 1. Department of Mathematics, Faculty of Science and Technology, Alquds University, Abu-Dies Campus, P.O. Box 20002, East Jerusalem, Palestine;2. Department of Statistics, Hebrew University of Jerusalem, Israel;1. Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX, United States;2. Department of Statistics, Florida State University, Tallahassee, FL, United States;1. University of Nantes, Laboratoire de Mathématiques Jean Leray, 2 rue de la Houssinière, 44322 Nantes, France;2. Inria, Centre Rennes Bretagne Atlantique, Campus universitaire de Beaulieu, 35042 Rennes, France;1. Human Information Processing Laboratory, School of Social Sciences and Humanities, FIN-33014 University of Tampere, Finland;2. Brain Research Unit, O.V. Lounasmaa Laboratory, Aalto University School of Science and Technology, Finland;1. Department of Biostatistics, Boston University, 801 Massachusetts Avenue, Boston, MA 02118, United States;2. Department of Medicine and Department of Health Research and Policy, Stanford University School of Medicine, 900 Blake Wilbur, Stanford, CA 94305, United States;3. Department of Psychiatry and The Dartmouth Institute for Health Policy and Clinical Practice, Geisel School of Medicine, 1 Rope Ferry Rd, Hanover, NH 03755, United States;4. Quantitative Sciences Unit, Department of Medicine, Stanford University School of Medicine, 1070 Arastradero Road, Palo Alto, CA 94304, United States |
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| Abstract: | The purpose of this paper is to account for informative sampling in fitting time series models, and in particular an autoregressive model of order one, for longitudinal survey data. The idea behind the proposed approach is to extract the model holding for the sample data as a function of the model in the population and the first-order inclusion probabilities, and then fit the sample model using maximum-likelihood, pseudo-maximum-likelihood and estimating equations methods. A new test for sampling ignorability is proposed based on the Kullback–Leibler information measure. Also, we investigate the issue of the sensitivity of the sample model to incorrect specification of the conditional expectations of the sample inclusion probabilities. The simulation study carried out shows that the sample-likelihood-based method produces better estimators than the pseudo-maximum-likelihood method, and that sensitivity to departures from the assumed model is low. Also, we find that both the conventional t-statistic and the Kullback–Leibler information statistic for testing of sampling ignorability perform well under both informative and noninformative sampling designs. |
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