lme                   package:nlme                   R Documentation

_L_i_n_e_a_r _M_i_x_e_d-_E_f_f_e_c_t_s _M_o_d_e_l_s

_D_e_s_c_r_i_p_t_i_o_n:

     This generic function fits a linear mixed-effects model in the
     formulation described in Laird and Ware (1982) but allowing for
     nested random effects. The within-group errors are allowed to be
     correlated and/or have unequal variances.

_U_s_a_g_e:

     lme(fixed, data, random, correlation, weights, subset, method,
         na.action, control, contrasts = NULL)
     ## S3 method for class 'lme':
     update(object, fixed., ..., evaluate = TRUE)

_A_r_g_u_m_e_n_t_s:

  object: an object inheriting from class 'lme', representing a fitted
          linear mixed-effects model.

   fixed: a two-sided linear formula object describing the
          fixed-effects part of the model, with the response on the
          left of a '~' operator and the terms, separated by '+'
          operators, on the right, an 'lmList' object, or a
          'groupedData' object. The method functions 'lme.lmList' and
          'lme.groupedData' are documented separately.

  fixed.: Changes to the fixed-effects formula - see 'update.formula'
          for details.

    data: an optional data frame containing the variables named in
          'fixed', 'random', 'correlation', 'weights', and 'subset'. 
          By default the variables are taken from the environment from
          which 'lme' is called.

  random: optionally, any of the following: (i) a one-sided formula of
          the form '~x1+...+xn | g1/.../gm', with 'x1+...+xn'
          specifying the model for the random effects and 'g1/.../gm'
          the grouping structure ('m' may be equal to 1, in which case
          no '/' is required). The random effects formula will be
          repeated for all levels of grouping, in the case of multiple
          levels of grouping; (ii) a list of one-sided formulas of the
          form '~x1+...+xn | g', with possibly different random effects
          models for each grouping level. The order of nesting will be
          assumed the same as the order of the elements in the list;
          (iii) a one-sided formula of the form '~x1+...+xn', or a
          'pdMat' object with a formula (i.e. a non-'NULL' value for
          'formula(object)'), or a list of such formulas or 'pdMat'
          objects. In this case, the grouping structure formula will be
          derived from the data used to fit the linear mixed-effects
          model, which should inherit from class 'groupedData'; (iv) a
          named list of formulas or 'pdMat' objects as in (iii), with
          the grouping factors as names. The order of nesting will be
          assumed the same as the order of the order of the elements in
          the list; (v) an 'reStruct' object. See the documentation on
          'pdClasses' for a description of the available 'pdMat'
          classes. Defaults to a formula consisting of the right hand
          side of 'fixed'.

correlation: an optional 'corStruct' object describing the within-group
          correlation structure. See the documentation of 'corClasses'
          for a description of the available 'corStruct' classes.
          Defaults to 'NULL', corresponding to no within-group
          correlations.

 weights: an optional 'varFunc' object or one-sided formula describing
          the within-group heteroscedasticity structure. If given as a
          formula, it is used as the argument to 'varFixed',
          corresponding to fixed variance weights. See the
          documentation on 'varClasses' for a description of the
          available 'varFunc' classes. Defaults to 'NULL',
          corresponding to homocesdatic within-group errors.

  subset: an optional expression indicating the subset of the rows of
          'data' that should be used in the fit. This can be a logical
          vector, or a numeric vector indicating which observation
          numbers are to be included, or a  character  vector of the
          row names to be included.  All observations are included by
          default.

  method: a character string.  If '"REML"' the model is fit by
          maximizing the restricted log-likelihood.  If '"ML"' the
          log-likelihood is maximized.  Defaults to '"REML"'.

na.action: a function that indicates what should happen when the data
          contain 'NA's.  The default action ('na.fail') causes 'lme'
          to print an error message and terminate if there are any
          incomplete observations.

 control: a list of control values for the estimation algorithm to
          replace the default values returned by the function
          'lmeControl'. Defaults to an empty list.

contrasts: an optional list. See the 'contrasts.arg' of
          'model.matrix.default'.

     ...: some methods for this generic require additional arguments. 
          None are used in this method.

evaluate: If 'TRUE' evaluate the new call else return the call.

_V_a_l_u_e:

     an object of class 'lme' representing the linear mixed-effects
     model fit. Generic functions such as 'print', 'plot' and 'summary'
     have methods to show the results of the fit. See 'lmeObject' for
     the components of the fit. The functions 'resid', 'coef',
     'fitted', 'fixed.effects', and 'random.effects'  can be used to
     extract some of its components.

_A_u_t_h_o_r(_s):

     Jose Pinheiro jose.pinheiro@pharma.novartis.com and Douglas Bates
     bates@stat.wisc.edu

_R_e_f_e_r_e_n_c_e_s:

     The computational methods are described in Bates, D.M. and
     Pinheiro (1998) and follow on the general framework of Lindstrom,
     M.J. and Bates, D.M. (1988). The model formulation is described in
     Laird, N.M. and Ware, J.H. (1982).  The variance-covariance
     parametrizations are described in <Pinheiro, J.C. and Bates., D.M.
      (1996).   The different correlation structures available for the
     'correlation' argument are described in Box, G.E.P., Jenkins,
     G.M., and Reinsel G.C. (1994), Littel, R.C., Milliken, G.A.,
     Stroup, W.W., and Wolfinger, R.D. (1996), and Venables, W.N. and
     Ripley, B.D. (1997). The use of variance functions for linear and
     nonlinear mixed effects models is presented in detail in Davidian,
     M. and Giltinan, D.M. (1995). 

     Bates, D.M. and Pinheiro, J.C. (1998) "Computational methods for
     multilevel models" available in PostScript or PDF formats at
     http://franz.stat.wisc.edu/pub/NLME/

     Box, G.E.P., Jenkins, G.M., and Reinsel G.C. (1994) "Time Series
     Analysis: Forecasting and Control", 3rd Edition, Holden-Day. 

     Davidian, M. and Giltinan, D.M. (1995) "Nonlinear Mixed Effects
     Models for Repeated Measurement Data", Chapman and Hall.

     Laird, N.M. and Ware, J.H. (1982) "Random-Effects Models for
     Longitudinal Data", Biometrics, 38, 963-974.  

     Lindstrom, M.J. and Bates, D.M. (1988) "Newton-Raphson and EM
     Algorithms for Linear Mixed-Effects Models for Repeated-Measures
     Data", Journal of the American Statistical Association, 83,
     1014-1022. 

     Littel, R.C., Milliken, G.A., Stroup, W.W., and Wolfinger, R.D.
     (1996) "SAS Systems for Mixed Models", SAS Institute.

     Pinheiro, J.C. and Bates., D.M.  (1996) "Unconstrained
     Parametrizations for Variance-Covariance Matrices", Statistics and
     Computing, 6, 289-296.

     Venables, W.N. and Ripley, B.D. (1997) "Modern Applied Statistics
     with S-plus", 2nd Edition, Springer-Verlag.

_S_e_e _A_l_s_o:

     'lmeControl', 'lme.lmList', 'lme.groupedData', 'lmeObject',
     'lmList', 'reStruct', 'reStruct', 'varFunc', 'pdClasses',
     'corClasses', 'varClasses'

_E_x_a_m_p_l_e_s:

     fm1 <- lme(distance ~ age, data = Orthodont) # random is ~ age
     fm2 <- lme(distance ~ age + Sex, data = Orthodont, random = ~ 1)
     summary(fm1)
     summary(fm2)

