corCAR1                 package:nlme                 R Documentation

_C_o_n_t_i_n_u_o_u_s _A_R(_1) _C_o_r_r_e_l_a_t_i_o_n _S_t_r_u_c_t_u_r_e

_D_e_s_c_r_i_p_t_i_o_n:

     This function is a constructor for the 'corCAR1' class,
     representing an autocorrelation structure of order 1, with a
     continuous time covariate. Objects created using this constructor
     must be later initialized using the appropriate 'Initialize'
     method.

_U_s_a_g_e:

     corCAR1(value, form, fixed)

_A_r_g_u_m_e_n_t_s:

   value: the correlation between two observations one unit of time
          apart. Must be between 0 and 1. Defaults to 0.2.

    form: a one sided formula of the form '~ t', or '~ t | g',
          specifying a time covariate 't' and,  optionally, a grouping
          factor 'g'. Covariates for this correlation structure need
          not be integer valued.  When a grouping factor is present in
          'form', the correlation structure is assumed to apply only to
          observations within the same grouping level; observations
          with different grouping levels are assumed to be
          uncorrelated. Defaults to '~ 1', which corresponds to using
          the order of the observations in the data as a covariate, and
          no groups.

   fixed: an optional logical value indicating whether the coefficients
          should be allowed to vary in the optimization, or kept fixed
          at their initial value. Defaults to 'FALSE', in which case
          the coefficients are allowed to vary.

_V_a_l_u_e:

     an object of class 'corCAR1', representing an autocorrelation
     structure of order 1, with a continuous time covariate.

_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:

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

     Jones, R.H. (1993) "Longitudinal Data with Serial Correlation: A
     State-space Approach", Chapman and Hall.

     Pinheiro, J.C., and Bates, D.M. (2000) "Mixed-Effects Models in S
     and S-PLUS", Springer, esp. pp. 236, 243.

_S_e_e _A_l_s_o:

     'corClasses',  'Initialize.corStruct', 'summary.corStruct'

_E_x_a_m_p_l_e_s:

     ## covariate is Time and grouping factor is Mare
     cs1 <- corCAR1(0.2, form = ~ Time | Mare)

     # Pinheiro and Bates, pp. 240, 243
     fm1Ovar.lme <- lme(follicles ~
                sin(2*pi*Time) + cos(2*pi*Time),
        data = Ovary, random = pdDiag(~sin(2*pi*Time)))
     fm4Ovar.lme <- update(fm1Ovar.lme,
               correlation = corCAR1(form = ~Time))