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Computing Confidence Intervals for Predicting New Observations in the Linear Mixed Model

Computing Confidence Intervals for Predicting New Observations in the Linear Mixed Model. Lloyd J. Edwards Kunthel By Department of Biostatistics, UNC-CH A. Jackson Stenner Gary L. Williamson Robert F. (Robin) Baker MetaMetrics, Inc. Outline. Introduction Basic Work with Growth Curves

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Computing Confidence Intervals for Predicting New Observations in the Linear Mixed Model

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  1. Computing Confidence Intervals for Predicting New Observations in the Linear Mixed Model Lloyd J. Edwards Kunthel By Department of Biostatistics, UNC-CH A. Jackson Stenner Gary L. Williamson Robert F. (Robin) Baker MetaMetrics, Inc. SAMSI Longitudinal Working Group

  2. Outline • Introduction • Basic Work with Growth Curves • Prediction Error in the Mixed Linear Model • New Software SAMSI Longitudinal Working Group

  3. Introduction • MetaMetrics’ perspective • Unification of measurement • Characterization of measurement error • Life-span developmental approach • Fitting models to data vs. fitting data to models • Longitudinal Working Group • Mutual interests (growth, mixed models, etc.) • Collaboration (theoretical, practical interests) • Summer GRA (production of new software) SAMSI Longitudinal Working Group

  4. Growth Curve Basics • Growth Model • Multilevel formulation • Mixed Model • Data Sets • NC • Palm Beach • Example SAMSI Longitudinal Working Group

  5. Growth Model Multilevel formulation Level 1: Lti = 0i + 1iTIMEti + eti Level 2: 0i = 00 + r0i 1i = 10 + r1i Mixed model formulation Lti = 00 + 10TIMEti + r0i + r1iTIMEti + eti SAMSI Longitudinal Working Group

  6. SAMSI Longitudinal Working Group

  7. Prediction Scenarios forTwo-Level Models Prediction and prediction intervals for: • all observations in the data set • one student in the data set, on future measurement occasions (given yi, Xi, Zi) • a new student who is not in the data set SAMSI Longitudinal Working Group

  8. General Mixed ModelFormulation Prediction Limits of the form: SAMSI Longitudinal Working Group

  9. Characterizing prediction error • Distinctions • Simple linear case versus • Mixed Model analog versus SAMSI Longitudinal Working Group

  10. Characterizing prediction error • Benefits • obtain best predicted status • state confidence limits for prediction • reduce apparent measurement error • consistent with a parametric form SAMSI Longitudinal Working Group

  11. New Software • SAS IML • Current features • Three prediction scenarios • Simple assumptions for error covariances • Restricted to two-level MLMs • Limited ability to incorporate covariates • Available at: http://www.unc.edu/~kby/ SAMSI Longitudinal Working Group

  12. Further Research • Assumption of i.i.d. within-subject errors • Literature suggests more complex error covariance structures. • Chi and Reinsel (1989, JASA) extend to AR(1) errors • We extend to general within-subject error covariance structure. SAMSI Longitudinal Working Group

  13. Closing Third Lexile National Reading Conference June 19-21, 2006 Developing Tomorrow’s Readers...Today http://www.Lexile.com SAMSI Longitudinal Working Group

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