NLME: Software for mixed-effects models

Mixed-effects models provide a powerful and flexible tool for the analysis of balanced and unbalanced grouped data. These data arise in several areas of investigation and are characterized by the presence of correlation between observations within the same group. Some examples are repeated measures data, longitudinal studies, and nested designs. Classical modeling techniques which assume independence of the observations are not appropriate for grouped data.

The NLME software comprises a set of S (S-PLUS) functions, methods, and classes for the analysis of both linear and nonlinear mixed-effects models. It extends the linear and nonlinear modeling facilities available in release 3 of S and S-PLUS. Written by José C. Pinheiro and Douglas M. Bates , the NLME software is available for Unix and Windows platforms.

Version 3.3.1 of NLME.

The NLME library has been completely redesigned to emphasize a modular, object-oriented design that facilitates users' incorporating new methods for existing generic functions (e.g. new classes of correlation structures and variance functions). The latest release includes several bug corrections with respect to Release 3.3; no new features have been added.

Getting NLME 3.3.1

• S-PLUS for Unix systems:

  S-PLUS 3.1 through 3.4: nlme3_3_1.tgz [ 1.8M ] (last modified: Thursday, 27-Sep-01 )

  S-PLUS 5.1: nlme_SP5_3_3_1.tgz [ 1.8M ] (last modified: Thursday, 27-Sep-01 )

  S-PLUS 6.0: nlme_SP6_3_3_1.tgz [ 1.7M ] (last modified: Thursday, 27-Sep-01 )

  (NLME 3.3.1 port for S-PLUS 5.1 and 6.0 produced with the help of Saikat DebRoy.)

  A separate directory within this "tarball" contains data sets from the book SAS System for Mixed Models and sample lme analyses.

  Copy the appropriate file (in binary mode) and extract the contents with

       # S-PLUS 3.4
       tar zxf nlme3_3_1.tgz      # if you have the GNU version of tar
       gunzip -d -c nlme3_3.tgz | tar xf -  # otherwise
  
       # S-PLUS 5.1
       tar zxf nlme_SP5_3_3_1.tgz      # if you have the GNU version of tar
       gunzip -d -c nlme_SP5_3_3_1.tgz | tar xf -  # otherwise
  
       # S-PLUS 6.0
       tar zxf nlme_SP6_3_3_1.tgz      # if you have the GNU version of tar
       gunzip -d -c nlme_SP6_3_3_1.tgz | tar xf -  # otherwise
      

  This will create three subdirectories ./NLME, ./NLMEDATA, and ./SAS_Mixed. Read the file ./NLME/INSTALL.

• S-PLUS for Windows (NLME 3.3.1 port for Windows courtesy of Prof. Brian Ripley):

  S-PLUS 3.2 through 4.5 and 2000: nlme331.zip [ 2.5M ] (last modified: Thursday, 27-Sep-01 )

  S-PLUS 6.0: nlme3.zip [ 936k ] (last modified: Thursday, 27-Sep-01 )

  The SAS_Mixed/ directory contains data sets from the book SAS System for Mixed Models and sample lme analyses.

  Copy the appropriate file (in binary mode) and use a zip extractor such as pkunzip or WinZip to expand it. The nlme3.zip file for S-PLUS 6.0 is a drop-in replacement, which should be extracted directly into the library subdirectory of the S-PLUS 6 installation. Read the README.txt and INSTALL files for further instructions.

Some features of NLME 3.3.1

• Maximum likelihood and restricted maximum likelihood estimation
• Multilevel models for data with multiple nested grouping levels. These incorporate novel computational methods, described in the Bell Labs Technical Memorandum Computational Methods for Multilevel Models, available available here as PostScript or as Portable Document Format.
• a new class, called groupedData, for representing data grouped according to one or more nested factors. Methods for plotting, summarizing, and fitting groupedData objects are also included.
• extensive use of Trellis plots for exploring grouped data and checking models fitted to such data. The plot methods for fitted objects include a formula argument which gives them unlimited flexibility for generating diagnostic plots.
• new classes of positive-definite matrices for modeling the random effects covariance structure, including general, diagonal, multiple of the identity, compound symmetry, and block-diagonal positive-definite matrices. Users can also define their own classes of positive-definite matrices.
• redesigned classes of correlation structures for modeling dependence among the within-group errors, including ARMA(p,q) models, spatial correlation structures (Gaussian, exponential, etc.) with and without nugget effects, and general correlation with no particular structure. Users can extend the NLME library by writing their own classes of correlation structures.
• redesigned classes of variance functions using arbitrary covariates and grouping of parameters (the previous version used the fitted values as the covariate for the built-in variance functions). Because the correlation structure and the variance function are independently specified, heterogeneous AR1, ARMA, etc. models are handled naturally. User-defined variance functions can be used to extend the NLME library.
• a gls function for fitting linear models with correlation structures and/or variance functions. You can think of it as lme without random effects, or lm with correlation structures and variance functions.
• a gnls function for fitting nonlinear models with correlation structures and/or variance functions. You can think of it as nlme without random effects, or nls with correlation structures and variance functions.
• an extensive set of examples. A separate directory contains groupedData objects for the datasets used in the book SAS System for Mixed Models, by Littel, Milliken, Stroup, and Wolfinger. Sample lme analyses that parallel the PROC MIXED analyses from that book are also given. We hope this will enable people who are familiar with PROC MIXED to learn lme more quickly.

Documentation

Mixed-Effects Models in S and S-PLUS A book published by Springer-Verlag describes the use of NLME in detail and includes many examples of real-life applications involving linear and nonlinear mixed-effects models.

The distribution of NLME 3.3.1 available at this site includes a (relatively incomplete) User's Guide in PDF format. Also included with this distribution is a PDF file with all help files available in NLME 3.3.1. On-line help is available for all functions and fitted objects in the NLME 3.3.1 library.

Documentation on NLME 2.1 is included in chapter 2 (pp. 19-79) of S-PLUS Version 3.4 for Unix Supplement , Data Analysis Products Division, MathSoft, Seattle. The complements to W. Venables and B. Ripley's Modern Applied Statistics with S-PLUS books include new sections on the NLME modeling facilities.

A general reference on nonlinear mixed effects models is M. Davidian and D. Giltinan, Nonlinear Models for Repeated Measurement Data, Chapman and Hall, 1995.

Additional references

• Newton-Raphson and EM Algorithms for Linear Mixed-Effects Models for Repeated Measures
  M. J. Lindstrom and D. M. Bates (1988)
  Journal of the American Statistical Association 83, pp. 1014-1022
• Nonlinear Mixed-Effects Models for Repeated Measures Data
  M. J. Lindstrom and D. M. Bates (1990)
  Biometrics 46 , pp. 673-687
• Approximations to the Log-Likelihood Function in the Nonlinear Mixed-Effects Model
  J. C. Pinheiro and D. M. Bates (1995)
  Journal of Computational and Graphics Statistics 4, pp. 12-35
• Model Building for Nonlinear Mixed-Effects Models
  J. C. Pinheiro and D. M. Bates (1995)
  Technical Report 91 , Department of Biostatistics, University of Wisconsin - Madison
• Unrestricted Parametrizations for Variance-Covariance Matrices
  J. C. Pinheiro and D. M. Bates (1996)
  Statistics and Computing 6, pp. 289-296
• Software Design for Longitudinal Data Analysis
  D. M. Bates and J. C. Pinheiro (1997)
  Modeling Longitudinal and Spatially Correlated Data: Methods, Applications, and Future Directions , Springer-Verlag, New York.
  (slides from the presentation) (4-up slides from the presentation)
• Software Design for Population Pharmacokinetic Analysis D. M. Bates and J. C. Pinheiro (1997). Presented at the International Association for Statistical Computing conference in Los Angeles. (slides from the presentation)
• Robust Estimation in Linear Mixed-Effects Models Using the Multivariate t-Distribution
  J. C. Pinheiro, C. Liu, and Y. Wu (1997)
  
• Graphical Methods for Data with Multiple Levels of Nesting
  J. C. Pinheiro and D. M. Bates (1997)
  presented at the 1997 Joint Statistical Meetings
• Future Directions in Software for Mixed-Effects Models: Version 3.0 of NLME
  J. C. Pinheiro and D. M. Bates (1997)
  slides from a presentation at the 1997 International S-PLUS User Conference (4-up slides from the presentation)
• Computing REML or ML Estimates for Linear or Nonlinear Mixed-Effects Models
  D. M. Bates and J. C. Pinheiro (1999)