hidden               package: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 interactions between
     time-constant and time-varying variables are not possible. Both
     functions are on the (generalized) 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 individual, 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 exponential.

  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 multiplied 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)

