

chidden(repeated)                            R Documentation

_C_o_n_t_i_n_u_o_u_s_-_T_i_m_e _H_i_d_d_e_n _M_a_r_k_o_v _C_h_a_i_n _M_o_d_e_l_s

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

     `chidden' fits a two or more state hidden Markov chain
     model to Bernoulli, binomial, Poisson, or categorical
     (multinomial) data in continuous time. All series on
     different individuals are assumed to start at the same
     time point. If the time points are equal, discrete
     steps, use `hidden'.

     The two mean functions are additive so that interac-
     tions between time-constant and time-varying variables
     are not possible. Both functions are on the (general-
     ized) logit scale for the Bernoulli, binomial, and
     multinomial distributions and on the log scale for the
     Poisson distribution.

     The algorithm will run more quickly if the most fre-
     quently occurring time step is scaled to be equal to
     unity.

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

     chidden(response, totals=NULL, times=NULL, distribution="Bernoulli",
             pgamma, cmu=NULL, tvmu=NULL, pcmu=NULL, ptvmu=NULL,
             pshape=NULL, pfamily=NULL, delta=1, 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 or three column matrices with counts
          or category indicators, times, and possibly totals
          (if the distribution is binomial), for each indi-
          vidual, one matrix or dataframe of counts, or an
          object of class, response (created by `restovec')
          or repeated (created by `rmna'). If there is only
          one series, a vector of responses may be supplied
          instead.

  totals: If response is a matrix, a corresponding matrix of
          totals if the distribution is binomial. Ignored if
          response has class, response or repeated.

   times: If `response' is a matrix, a vector of correspond-
          ing times, when they are the same for all individ-
          uals. Ignored if response has class, response or
          repeated.

distribution: Bernoulli, Poisson, multinomial, binomial,
          exponential, beta binomial, negative binomial,
          normal, inverse Gauss, logistic, gamma, Weibull,
          Cauchy, Laplace, Levy, Pareto, gen(eralized)
          gamma, gen(eralized) logistic, Hjorth, Burr,
          gen(eralized) Weibull, gen(eralized) extreme
          value, gen(eralized) inverse Gauss, or power expo-
          nential.

  pgamma: A square mxm matrix of initial estimates of the
          continuous-time hidden Markov transition matrix,
          where m is the number of hidden states. Rows can
          either sum to zero or the diagonal elements can be
          zero, in which case they will be replaced by minus
          the sum of the other values on the rows. If the
          matrix contains zeroes off diagonal, these are
          fixed and not estimated.

     cmu: A time-constant mean function returning an array
          with one row for each individual, one column for
          each state of the hidden Markov chain, and, if
          multinomial, one layer for each category but the
          last.

    tvmu: A time-varying mean function returning an array
          with one row for each time point (maximum number
          of time points for all individuals if unequal),
          one column for each state of the hidden Markov
          chain, and, if multinomial, one layer for each
          category but the last. This is usually a function
          of time; it is the same for all individuals.

    pcmu: Initial estimates of the unknown parameters in
          `cmu'.

   ptvmu: Initial estimates of the unknown parameters in
          `tvmu'.

  pshape: Initial estimate(s) of the dispersion parameter,
          for those distributions having one. This can be
          one value or a vector with a different value for
          each state.

 pfamily: Initial estimate of the family parameter, for
          those distributions having one.

   delta: Scalar or vector giving the unit of measurement
          (always one for discrete data) for each response
          value, set to unity by default. For example, if a
          response is measured to two decimals, delta=0.01.
          If the response is transformed, this must be mul-
          tiplied by the Jacobian. For example, with a log
          transformation, `delta=1/response'. Ignored if
          response has class, response or repeated.

  others: Arguments controlling `nlm'.

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

     A list of class `hidden' is returned.

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

     J.K. Lindsey

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

     `gar', `gnlmm', `hidden', `kalcount', `mexp', `nbkal',
     `read.list', `rmna', `restovec'.

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

     # model for one randomly-generated binary series
     y <- c(rbinom(10,1,0.1), rbinom(10,1,0.9))
     mu <- function(p) array(p, c(1,2))
     print(z <- chidden(y, times=1:20, dist="Bernoulli",
             pgamma=matrix(c(-0.1,0.2,0.1,-0.2),ncol=2),
             cmu=mu, pcmu=c(-2,2)))
     mexp(z$gamma)
     plot(z)
     print(z <- chidden(y, times=(1:20)*2, dist="Bernoulli",
             pgamma=matrix(c(-0.05,0.1,0.05,-0.1),ncol=2),
             cmu=mu, pcmu=c(-2,2)))
     mexp(z$gamma) %*% mexp(z$gamma)
     plot(z)

