References for Non-Parametric Modeling of Longitudinal Data

Nonparametric Modeilng of Longitudinal Data: Major References

General

Muller, H.G. (1988), Nonparametric Regression Analysis of Longitudinal Data, Lecture Notes in Statistics, Springer-Verlag, New Yrok.

Zeger, S. L. and Diggle (1994), "Semiparametric Models for Longitudinal Data with Application to CD4 Cell Numbers in HIV Seroconverters," Biometrics 50 689-699.

Shi, M., Weiss R.E., and Taylor, J.M.G. (1996), “An Analysis of Paediatric CD4 Counts for Acquired Immune Deficiency Syndrome using Flexible Random Curves," Applied Statistics, 45, 151-163.

Zhang, H.P. (1997).”Multivariate Adaptive Splines for the Analysis of Longitudinal Data," Journal of Computational and Graphical Statistics,6, 74-91.

Staniswalis, J.G. and Lee, J.J. (1998), “Nonparametric Regression Analysis of Longitudinal Data," Journal of the American Statistical Association, 93, 1403-1418.

Wu, C. O., Chiang, C. T., and Hoover , D.R. (1998), “Asymptotic Confidence Regions for Kernel Smoothing of a Varying-Coefficient Model With Longitudinal Data," Journal of the American Statistical Association, 93, 1388-1402.

Wang, Y. (1998a), “Mixed-Effects Smoothing Spline ANOVA,"Journal of the Royal Statistical Society, Ser. B, 60, 159-174.

Wang, Y. (1998b), “Smoothing Spline Models With Correlated Random Errors," Journal of the American Statistical Association, 93, 341-348.

Zhang, D., Lin, X., Raz, J., and Sowers, M. (1998), “Semiparametric Stochastic Mixed Models for Longitudinal Data,"Journal of the American Statistical Association, 93, 710-719.

Brumback, B. and Rice, J.A.(1998), "Smoothing Spline Models for the Analysis of Nested and Crossed Samples of Curves," Journal of American Statistist Association 93, 961-994.

Hoover, D. R., Rice, J. A., Wu, C. O., and Yang, L. P. (1998), "Nonparametric Smoothing Estimates of Time-Varying Coefficient Models With Longitudinal Data," Biometrika 85 809-822.

Lin, X., and Zhang, D. (1999), "Inference in Generalized Additive Mixed Models by Using Smoothing Splines," Journal of the Royal Statistical Society, Ser. B 61, 381-400.

Lin, X., and Carroll, R. J. (2000),”Nonparametric Function Estimation for Clustered Data When the Predictor Is Measured Without/With Error," Journal of the American Statistical Association, 95, 520-534.

Fan, J., and Zhang, J. T. (2000), "Two-Step Estimation of Functional Linear Models With Applications to Longitudinal Data," Journal of the Royal Statistical Society, Ser. B 62, 303-322.

Ke, C and Wang, Y. (2001), "Semiparametric Nonlinear Mixed-Effects models and Their applications," Journal of American Statistist Association 96, 1272-1281.

Lin, D. Y. and Ying, Z. (2001), "Semiparametric and Nonparametric Regression Analysis of Longitudinal Data (with discussion)," Journal of American Statistist Association 96, 103-113.

Rice, J. A., and Wu, C. O. (2001),”Nonparametric Mixed Effects Models for Unequally Sampled Noisy Curves," Biometrics, 57, 253-259.

Guo, W.S. (2002), "Functional Mixed Effects Models," Biometrics 58, 121-128.

Guo, W.S. (2002b), “Inference in Smoothing Spline Analysis of Variance," Journal of the Royal Statistical Society Series B,64, 887-889.

Huang, J.Z., Wu, C.O., and Zhou, L. (2002), "Varying-Coefficient Models and Basis Function Approximations for the Analysis of Repeated measurements," Biometrika 89, 111-128.

Welsh, A.H., Lin, X., and Carroll, R.J. (2002), "Marginal longitudinal nonparametric regression: Locality and efficiency of spline and kernel methods," Journal of American Statistist Association 97, 482-493.

Wu, H. and Zhang, J.T. (2002), "Local Polynomial Mixed-Effects Models for Longitudinal Data," Journal of American Statistist Association 97 883-897.

Wang, N. (2003), “Marginal Nonparametric Kernel Regression Accounting for within-subject correlation," Biometrika, 90, 43-52.

Liang, H., Wu, H., and Carroll, R.J. (2003), "The Relationship Between Virologic and Immunologic Responses in AIDS Clinical Research Using Mixed-Effects Varying-Coefficient Semiparametric Models with Measurement Error," Biostatistics, 4, 297-312.

Wu, H. and Zhang, J.T., (2006), Nonparametric Regression Methods for Longitudinal Data Analysis: Mixed-Effects Modeling Approaches, John Wiley & Sons, New York

Local Polynomial Methods

Hoover, D. R., Rice, J. A., Wu, C. O., and Yang, L. P. (1998), "Nonparametric Smoothing Estimates of Time-Varying Coefficient Models With Longitudinal Data," Biometrika 85 809-822.

Wu, C. O., Chiang, C. T., and Hoover , D.R. (1998), “Asymptotic Confidence Regions for Kernel Smoothing of a Varying-Coefficient Model With Longitudinal Data," Journal of the American Statistical Association, 93, 1388-1402.

Lin, X., and Carroll, R. J. (2000),”Nonparametric Function Estimation for Clustered Data When the Predictor Is Measured Without/With Error," Journal of the American Statistical Association, 95, 520-534.

Fan, J., and Zhang, J. T. (2000), "Two-Step Estimation of Functional Linear Models With Applications to Longitudinal Data," Journal of the Royal Statistical Society, Ser. B 62, 303-322.

Welsh, A.H., Lin, X., and Carroll, R.J. (2002), " Marginal longitudinal nonparametric regression: Locality and efficiency of spline and kernel methods," Journal of American Statistist Association 97, 482-493.

Wu, H. and Zhang, J.T. (2002), " Local Polynomial Mixed-Effects Models for Longitudinal Data," Journal of American Statistist Association 97 883-897.

Wang, N. (2003), “Marginal Nonparametric Kernel Regression Accounting for within-subject correlation," Biometrika, 90, 43-52.

Wu, H. and Liang, H. (2004),”Backfitting Random Varying-Coefficient Models with Time-Dependent Smoothing Covariates," Scan. J. Statist., 31, 3-19.

Smoothing Spline Methods

Brumback, B. and Rice, J.A.(1998), "Smoothing Spline Models for the Analysis of Nested and Crossed Samples of Curves," Journal of American Statistist Association 93, 961-994.

Wang, Y. (1998a), “Mixed-Effects Smoothing Spline ANOVA,"Journal of the Royal Statistical Society, Ser. B, 60, 159-174.

Wang, Y. (1998b), “Smoothing Spline Models With Correlated Random Errors," Journal of the American Statistical Association, 93, 341-348.

Zhang, D., Lin, X., Raz, J., and Sowers, M. (1998), “Semiparametric Stochastic Mixed Models for Longitudinal Data,"Journal of the American Statistical Association, 93, 710-719.

Lin, X., and Zhang, D. (1999), "Inference in Generalized Additive Mixed Models by Using Smoothing Splines," Journal of the Royal Statistical Society, Ser. B 61, 381-400.

Ke, C. and Wang, Y. (2001), "Semiparametric Nonlinear Mixed-Effects models and Their applications," Journal of American Statistist Association 96, 1272-1281.

Gao, F.Y. Wahba, G Klein, R. and Klein (2001), "Smoothing Spline Anova fr Multivariate Bernoulli Obervations, With Application to Ophthalmology Data," Journal of American Statistist Association 96, 127-147.

Guo, W.S. (2002), "Inference in Smoothing Spline Analysis of Variance," Journal of the Royal Statistical Society, Ser. B 61, 887-889.

Guo, W.S. (2002b), “Inference in Smoothing Spline Analysis of Variance," Journal of the Royal Statistical Society Series-B,64, 887-889.

Regression Spline Methods

Shi, M., Weiss R.E., and Taylor, J.M.G. (1996), “An Analysis of Paediatric CD4 Counts for Acquired Immune Deficiency Syndrome using Flexible Random Curves," Applied Statistics, 45, 151-163.

Rice, J. A., and Wu, C. O. (2001),”Nonparametric Mixed Effects Models for Unequally Sampled Noisy Curves," Biometrics, 57, 253-259.

Huang, J.Z., Wu, C.O., and Zhou, L. (2002), “Varying-Coefficient Models and Basis Function Approximations for the analysis of repeated measurements," Biometrika, 89, 111-128.

Wu, H. and Zhang, J.T. (2002),”The Study of Long-Term HIV Dynamics Using Semiparametric Nonlinear Mixed-effects Models," Statistics in Medicine, 21, 3655-3675.

Semiparametric models

Zeger, S. L. and Diggle (1994), "Semiparametric Models for Longitudinal Data with Application to CD4 Cell Numbers in HIV Seroconverters," Biometrics 50 689-699.

Zhang, D., Lin, X., Raz, J., and Sowers, M. (1998), “Semiparametric Stochastic Mixed Models for Longitudinal Data,"Journal of the American Statistical Association, 93, 710-719.

Lin, D. Y. and Ying, Z. (2001), "Semiparametric and Nonparametric Regression Analysis of Longitudinal Data (with discussion)," Journal of American Statistist Association 96, 103-113.

Ke, C. and Wang, Y. (2001), "Semiparametric Nonlinear Mixed-Effects models and Their applications," Journal of American Statistist Association 96, 1272-1281.

Welsh, A.H., Lin, X., and Carroll, R.J. (2002), " Marginal longitudinal nonparametric regression: Locality and efficiency of spline and kernel methods," Journal of American Statistist Association 97, 482-493.

Wu, H. and Zhang, J.T. (2002),”The Study of Long-Term HIV Dynamics Using Semiparametric Nonlinear Mixed-Effects Models," Statistics in Medicine, 21, 3655-3675.

Sun, Y. and Wu, H.(2003), "A General Additive Semiparametric Time-Varying Regression Model for Longitudinal Data," Submitted.

Time-varying coefficient models

Hoover, D. R., Rice, J. A., Wu, C. O., and Yang, L. P. (1998), "Nonparametric Smoothing Estimates of Time-Varying Coefficient Models With Longitudinal Data," Biometrika 85 809-822.

Wu, C. O., and Chiang, C. T. (1998), " Kernel Smoothing on Varying Coefficient Models
With Longitudinal Dependent Variable," Statistic Sinica 10 433-456.

Wu, C. O., Chiang, C. T., and Hoover , D.R. (1998), Asymptotic Confidence Regions for Kernel Smoothing of a Varying-Coefficient Model With Longitudinal Data," Journal of American Statistist Association 93 1388-1402.

Huang, J.Z., Wu, C.O., and Zhou, L. (2002), "Varying-Coefficient Models and Basis Function Approximations for the Analysis of Repeated measurements," Biometrika 89, 111-128.

Wu, H. and Liang, H. (2004), “Backfitting Random Varying-Coefficient Models with Time-Dependent Smoothing Covariates," Scan. J. Statist., 31, 3-19.

Mixed-effects modeling nonparametric approach

Zhang D, Lin X, Raz J, and Sowers M (1998), " Semiparametric Stochastic Mixed Model for Longitudinal data," Journal of American Statistist Association 93, 710-719.

Wang, Y. (1998), " Mixed-Effects Smoothing Spline ANOVA," Journal of the Royal Statistical Society, Ser. B 60 159-174.

Wu, H. and Zhang, J.T. (2002),”The Study of Long-Term HIV Dynamics Using Semiparametric Nonlinear Mixed-Effects Models,"Statistics in Medicine, 21, 3655-3675.

Guo, W.S. (2002a), "Functional Mixed Effects Models," Biometrics 58 121-128.

Liang, H., Wu, H., and Carroll, R.J. (2003), "The Relationship Between Virologic and Immunologic Responses in AIDS Clinical Research Using Mixed-Effects Varying-Coefficient Semiparametric Models with Measurement Error," Biostatistics, 4, 297-312.

Wu, H. and Zhang, J.T. (2002), " Local Polynomial Mixed-Effects Models for Longitudinal Data," Journal of American Statistist Association 97 883-897.

Wu, H. and Liang, H. (2004),”Backfitting Random Varying-Coefficient Models with Time-Dependent Smoothing Covariates,"Scan. J. Statist., 31, 3-19.

Wu, H. and Zhang, J.T., (2006), Nonparametric Regression Methods for Longitudinal Data Analysis: Mixed-Effects Modeling Approaches, John Wiley & Sons, New York

Inference methods (tests, classification/discrimination etc)

Wu, C. O., Chiang, C. T., and Hoover , D.R. (1998), "Asymptotic Confidence Regions for Kernel Smoothing of a Varying-Coefficient Model With Longitudinal Data," Journal of American Statistist Association 93 1388-1402.

Lin, X., and Zhang, D. (1999), "Inference in Generalized Additive Mixed Models by Using Smoothing Splines," Journal of the Royal Statistical Society, Ser. B 61, 381-400.

James, G.M., Hastie, T.J. and Sugar, C.A. (2000), "Principal Component Models for Sparse Functional Data, " Biometrika, 87, 587-602.

James, G.M. and Hastie, T. J. (2001), "Functional Linear Discriminant Analysis for Irregularly Sampled Curves," Journal of the Royal Statistical Society, Ser. B 63, 533-550.

Wu, H. and Zhang, J.T. (2002), "The Study of Long-Term HIV Dynamics Using Semiparametric Nonlinear Mixed-Effects Models," Statistics in Medicine 21 3655-3675.

James, G.M. and Sugar, C.A. (2003), "Clustering for Sparsely Sampled Functional Data," Journal of the American Statistical Association, 98, 397-408.

Sugar, C.A. and James, G.M. (2003), "Identifying Groups in Data: An Information Theoretic Approach," Journal of the American Statistical Association, 98. 750-763.

Sun, Y. and Wu, H. (2003), "AUC-Based Tests for Nonparametric Functions with Longitudinal Data," Statistica Sinica, 13, 593-612.

Zhang, D. and Lin, X. (2003), "Hypothesis Testing in Semiparametric Additive Mixed Models," Biostatistics 4, 57-74.

Introductory References for Students and New Researchers

Zeger, S. L. and Diggle (1994), "Semiparametric Models for Longitudinal Data with Application to CD4 Cell Numbers in HIV Seroconverters," Biometrics 50, 689-699.

Brumback, B. and Rice, J.A.(1998), "Smoothing Spline Models for the Analysis of Nested and Crossed Samples of Curves," Journal of American Statistist Association 93, 961-994.

Hoover, D. R., Rice, J. A., Wu, C. O., and Yang, L. P. (1998), "Nonparametric Smoothing Estimates of Time-Varying Coefficient Models With Longitudinal Data," Biometrika 85 809-822.

Lin, X., and Zhang, D. (1999), "Inference in Generalized Additive Mixed Models by Using Smoothing Splines," Journal of the Royal Statistical Society, Ser. B 61, 381-400.

Fan, J., and Zhang, J. T. (2000), "Two-Step Estimation of Functional Linear Models With Applications to Longitudinal Data," Journal of the Royal Statistical Society, Ser. B 62, 303-322.

Ke, C and Wang, Y. (2001), "Semiparametric Nonlinear Mixed-Effects models and Their applications," Journal of American Statistist Association 96, 1272-1281.

Lin, D. Y. and Ying, Z. (2001), "Semiparametric and Nonparametric Regression Analysis of Longitudinal Data (with discussion)," Journal of American Statistist Association 96, 103-113.

Guo, W.S. (2002), "Functional Mixed Effects Models," Biometrics 58, 121-128.

Huang, J.Z., Wu, C.O., and Zhou, L. (2002), "Varying-Coefficient Models and Basis Function Approximations for the Analysis of Repeated measurements," Biometrika 89, 111-128.

Welsh, A.H., Lin, X., and Carroll, R.J. (2002), "Marginal longitudinal nonparametric regression: Locality and efficiency of spline and kernel methods," Journal of American Statistist Association 97, 482-493.

Wu, H. and Zhang, J.T. (2002), "Local Polynomial Mixed-Effects Models for Longitudinal Data," Journal of American Statistist Association 97, 883-897.

Liang, H., Wu, H., and Carroll, R.J. (2003), "The Relationship Between Virologic and Immunologic Responses in AIDS Clinical Research Using Mixed-Effects Varying-Coefficient Semiparametric Models with Measurement Error," Biostatistics, 4, 297-312.

Wu, H. and Zhang, J.T., (2006), Nonparametric Regression Methods for Longitudinal Data Analysis: Mixed-Effects Modeling Approaches, John Wiley & Sons, New York