

hidden(repeated)                             R Documentation

_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_:

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

     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.

     See MacDonald, I.L. and Zucchini, W. (1997) Hidden
     Markov and Other Models for Discrete-valued Time
     Series. Chapman and Hall.

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

     hidden(response, totals=NULL, distribution="Bernoulli", pgamma,
             cmu=NULL, tvmu=NULL, pcmu=NULL, ptvmu=NULL, pshape=NULL,
             pfamily=NULL, delta=1, fscale=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.

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
          hidden Markov transition matrix, where m is the
          number of hidden states.  Rows must sum to one. If
          the matrix contains zeroes or ones, these are
          fixed and not estimated. (Ones cannot appear on
          the diagonal.)  If a 1x1 matrix or a scalar value
          of 1 is given, the independence model is fitted.

     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_:

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

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

     # generate two random Poisson sequences with change-points
     y <- rbind(c(rpois(5,1), rpois(15,5)), c(rpois(15,1), rpois(5,5)))
     mu <- function(p) array(rep(p[1:2],rep(2,2)), c(2,2))
     print(z <- hidden(y,dist="Poisson", cmu=mu, pcmu=c(1,5),
             pgamma=matrix(c(0.9,0.2,0.1,0.8),ncol=2)))
     plot(z, nind=1:2)
     plot(z, nind=1:2, smooth=T)

