

nbkal(repeated)                              R Documentation

_N_e_g_a_t_i_v_e _B_i_n_o_m_i_a_l _M_o_d_e_l _w_i_t_h _K_a_l_m_a_n _U_p_d_a_t_e

_D_e_s_c_r_i_p_t_i_o_n_:

     `nbkal' fits a negative binomial regression with Kalman
     update over time. The variance is proportional to the
     mean function, whereas, for `kalcount' with exponential
     intensity, it is a quadratic function of the mean.

     Marginal and individual profiles can be plotted using
     `profile' and `iprofile' and residuals with
     `plot.residuals'.

_U_s_a_g_e_:

     nbkal(response, times, mu, preg, pdepend, kalman=TRUE,
             print.level=0, ndigit=10, gradtol=0.00001, steptol=0.00001,
             fscale=1, iterlim=100, typsiz=abs(p), stepmax=10*sqrt(p%*%p))

_A_r_g_u_m_e_n_t_s_:

response: A list of two column matrices with counts and cor-
          responding times for each individual, one matrix
          or dataframe of counts, or an object of class,
          response (created by `restovec') or repeated (cre-
          ated by `rmna').

   times: When response is a matrix, a vector of possibly
          unequally spaced times when they are the same for
          all individuals or a matrix of times. Not neces-
          sary if equally spaced. Ignored if response has
          class, response or repeated.

      mu: The mean function.

    preg: The initial parameter estimates for the mean func-
          tion.

 pdepend: The estimates for the dependence parameters,
          either one or three.

  kalman: If TRUE, fits the kalman update model, otherwise,
          a standard negative binomial distribution.

  others: Arguments controlling `nlm'.

_V_a_l_u_e_:

     A list of classes `nbkal' and `recursive' is returned.

_A_u_t_h_o_r_(_s_)_:

     J.K. Lindsey

_R_e_f_e_r_e_n_c_e_s_:

     Lambert, P. (1996) Applied Statistics 45, 31-38.

     Lambert, P. (1996) Biometrics 52, 50-55.

_S_e_e _A_l_s_o_:

     `gar', `gnlmm', `gnlr', `iprofile' `kalcount', `pro-
     file' `read.list', `rmna', `restovec', `tcctomat',
     `tvctomat'.

_E_x_a_m_p_l_e_s_:

     y <- matrix(rnbinom(20,5,0.5), ncol=5)
     times <- matrix(rep(seq(10,50,by=10),4), ncol=5, byrow=T)
     y0 <- matrix(rep(rnbinom(5,5,0.5),4), ncol=5, byrow=T)
     mu <- function(p) p[1]*log(y0)+(times<30)*p[2]*
             (times-30)+(times>30)*p[3]*(times-30)
     nbkal(y, preg=c(1.3,0.008,-0.05), times=times, pdep=1.2, mu=mu)

