Multiphase mixed-effects models for repeated measures data

Behavior that develops in phases may exhibit distinctively different rates of change in one time period than in others. In this article, a mixed-effects model for a response that displays identifiable regimes is reviewed. An interesting component of the model is the change point. In substantive terms, the change point is the time when development switches from one phase to another. In a mixed-effects model, the change point can be a random coefficient. This possibility allows individuals to make the transition from one phase to another at different ages or after different lengths of time in treatment. Two examples are reviewed in detail, both of which can be estimated with software that is widely available.

[1]  A. Gallant,et al.  Fitting Segmented Polynomial Regression Models Whose Join Points Have to Be Estimated , 1973 .

[2]  R. D. Bock.  Prediction of growth. , 1991 .

[3]  J. Mirowsky,et al.  Age, Depression, and Attrition in the National Survey of Families and Households , 2000 .

[4]  D. Bates,et al.  Nonlinear mixed effects models for repeated measures data. , 1990, Biometrics.

[5]  E. Vonesh,et al.  Linear and Nonlinear Models for the Analysis of Repeated Measurements , 1996 .

[6]  Jan de Leeuw,et al.  Review of Five Multilevel Analysis Programs: BMDP-5V, GENMOD, HLM, ML3, VARCL@@@BMDP-5V@@@GENMOD@@@HLM, Version 2.1@@@ML3, Version 2.2@@@VARCL , 1994 .

[7]  Donald Hedeker,et al.  Application of random-efiects pattern-mixture models for miss-ing data in longitudinal studies , 1997 .

[8]  Harvey Goldstein,et al.  Multilevel modelling of health statistics , 2001 .

[9]  E. A. Sylvestre,et al.  Self Modeling Nonlinear Regression , 1972 .

[10]  Robert Cudeck,et al.  Conditionally Linear Mixed-Effects Models With Latent Variable Covariates , 1999 .

[11]  S. Chaiken.  The Inspection Time Not Studied: Processing Speed Ability Unrelated to Psychometric Intelligence. , 1994 .

[12]  Jan de Leeuw,et al.  Review of Five Multilevel Analysis Programs: BMDP-5V, GENMOD, HLM, ML3, VARCL , 1994 .

[13]  Marie Davidian,et al.  Some Simple Methods for Estimating Intraindividual Variability in Nonlinear Mixed Effects Models , 1993 .

[14]  Christopher H. Morrell,et al.  Estimating Unknown Transition Times Using a Piecewise Nonlinear Mixed-Effects Model in Men with Prostate Cancer , 1995 .

[15]  David G. Payne,et al.  Hypermnesia and reminiscence in recall: A historical and empirical review. , 1987 .

[16]  A. Gallant,et al.  Nonlinear Statistical Models , 1988 .

[17]  Jan de Leeuw,et al.  Introducing Multilevel Modeling , 1998 .

[18]  D. Pauler,et al.  Screening Based on the Risk of Cancer Calculation From Bayesian Hierarchical Changepoint and Mixture Models of Longitudinal Markers , 2001 .

[19]  L B Sheiner,et al.  Estimating population kinetics. , 1982, Critical reviews in biomedical engineering.

[20]  D. Rubin,et al.  Statistical Analysis with Missing Data. , 1989 .

[21]  D. Bates,et al.  Mixed-Effects Models in S and S-PLUS , 2001 .

[22]  S. Hershberger,et al.  Genetic and environmental contributions to the acquisition of a motor skill , 1996, Nature.

[23]  Robert Cudeck,et al.  Nonlinear multilevel models for repeated measures data. , 2003 .

[24]  M. Appelbaum,et al.  Estimating Individual Developmental Functions: Methods and Their Assumptions , 1991 .

[25]  B W Turnbull,et al.  Statistical models for longitudinal biomarkers of disease onset. , 2000, Statistics in medicine.

[26]  L. Skovgaard.  NONLINEAR MODELS FOR REPEATED MEASUREMENT DATA. , 1996 .

[27]  N. Laird,et al.  A Mixture Model for Longitudinal Data with Application to Assessment of Noncompliance , 2000, Biometrics.

[28]  D J Roe.  Comparison of population pharmacokinetic modeling methods using simulated data: results from the Population Modeling Workgroup. , 1997, Statistics in medicine.

[29]  David J. Hand,et al.  Analysis of Repeated Measures , 1990 .

[30]  Naihua Duan,et al.  Multilevel Modeling : Methodological Advances, Issues, and Applications , 2003 .

[31]  D. Bates,et al.  Approximations to the Log-Likelihood Function in the Nonlinear Mixed-Effects Model , 1995 .

[32]  D. Wechsler.  The measurement and appraisal of adult intelligence, 4th ed. , 1958 .

[33]  K. Bradway,et al.  Intelligence at adulthood: A twenty-five year follow-up. , 1962 .

[34]  P. Albert,et al.  Models for longitudinal data: a generalized estimating equation approach. , 1988, Biometrics.

[35]  K. Jöreskog,et al.  LISREL 8: New Statistical Features , 1999 .

[36]  R. Simon,et al.  Flexible regression models with cubic splines. , 1989, Statistics in medicine.

[37]  M. Lindstrom,et al.  Self-modelling with random shift and scale parameters and a free-knot spline shape function. , 1995, Statistics in medicine.

[38]  Patricia L. Smith.  Splines as a Useful and Convenient Statistical Tool , 1979 .

[39]  Richard H. Jones,et al.  Longitudinal Data with Serial Correlation : A State-Space Approach , 1994 .

[40]  S. R. Searle,et al.  Generalized, Linear, and Mixed Models , 2005 .

[41]  D. Lewis,et al.  Quantitative methods in psychology , 1950 .

[42]  R Cudeck,et al.  Mixed-effects Models in the Study of Individual Differences with Repeated Measures Data. , 1996, Multivariate behavioral research.

[43]  Helen Brown,et al.  Applied Mixed Models in Medicine , 2000, Technometrics.

[44]  John J. McArdle,et al.  Multilevel Models From a Multiple Group Structural Equation Perspective , 1996 .

[45]  Roel Bosker,et al.  Multilevel analysis : an introduction to basic and advanced multilevel modeling , 1999 .

[46]  G. Molenberghs,et al.  Linear Mixed Models for Longitudinal Data , 2001 .

[47]  H. Goldstein.  Multilevel Statistical Models , 2006 .

[48]  P. Diggle,et al.  Analysis of Longitudinal Data , 2003 .

[49]  A. F. Smith,et al.  Straight Lines with a Change‐Point: A Bayesian Analysis of Some Renal Transplant Data , 1980 .

[50]  Gary O. Zerbe,et al.  Randomization Analysis of the Completely Randomized Design Extended to Growth and Response Curves , 1979 .

[51]  Geert Molenberghs,et al.  Linear Mixed Models in Practice , 1997 .