hmm-dists                package:msm                R Documentation

_H_i_d_d_e_n _M_a_r_k_o_v _m_o_d_e_l _c_o_n_s_t_r_u_c_t_o_r_s

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

     These functions are used to specify the distribution of the
     response conditionally on the underlying state in a hidden Markov
     model.  A list of these function calls, with one component for
     each state, should be  used for the 'hmodel' argument to 'msm'.
     The initial values for the parameters of the distribution should
     be given as arguments.

_U_s_a_g_e:

     hmmCat(prob, basecat)
     hmmIdent(x)
     hmmUnif(lower, upper)
     hmmNorm(mean, sd)
     hmmLNorm(meanlog, sdlog)
     hmmExp(rate)
     hmmGamma(shape, rate)
     hmmWeibull(shape, scale)
     hmmPois(rate)
     hmmBinom(size, prob)
     hmmTNorm(mean, sd, lower, upper)
     hmmMETNorm(mean, sd, lower, upper, sderr, meanerr=0)
     hmmMEUnif(lower, upper, sderr, meanerr=0)
     hmmNBinom(disp, prob)

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

     'hmmCat' represents a categorical response distribution on the set
     '1, 2, ..., length(prob)'.  The Markov model with
     misclassification is an example of this type of model. The
     categories in this case are (some subset of) the observed states. 

     The 'hmmIdent' distribution is used for underlying states which
     are observed exactly without error.

     'hmmUnif', 'hmmNorm', 'hmmLNorm', 'hmmExp', 'hmmGamma',
     'hmmWeibull', 'hmmPois', 'hmmBinom',  'hmmTNorm' and 'hmmNBinom'
     represent Uniform, Normal, log-Normal, exponential, Gamma,
     Weibull, Poisson, Binomial, truncated Normal and negative binomial
     distributions, respectively, with parameterisations the same as
     the default parameterisations in the corresponding base R
     distribution functions. 

     The 'hmmMETNorm' and 'hmmMEUnif' distributions are truncated
     Normal and Uniform distributions, but with additional Normal
     measurement error on the response. These are generalisations of
     the distributions proposed by Satten and Longini (1994) for
     modelling the progression of CD4 cell counts in monitoring HIV
     disease.  See 'medists' for density, distribution, quantile and
     random generation functions for these distributions.   See also
     'tnorm' for density, distribution, quantile and random generation
     functions for the truncated Normal distribution.  

    prob: ('hmmCat') Vector of probabilities of observing category '1,
          2, ..., length(prob)' respectively.  Or the probability
          governing a binomial or negative binomial distribution.

 basecat: ('hmmCat') Category which is considered to be the "baseline",
          so that during estimation, the probabilities are
          parameterised as probabilities relative to this baseline
          category. By default, the category with the greatest
          probability is used as the baseline. 

       x: ('hmmIdent') Code in the data which denotes the
          exactly-observed state.  

    mean: ('hmmNorm,hmmLNorm,hmmTNorm') Mean defining a Normal, or
          truncated Normal distribution. 

      sd: ('hmmNorm,hmmLNorm,hmmTNorm') Standard deviation defining a
          Normal, or truncated Normal distribution. 

 meanlog: ('hmmNorm,hmmLNorm,hmmTNorm') Mean on the log scale, for a
          log Normal distribution. 

   sdlog: ('hmmNorm,hmmLNorm,hmmTNorm') Standard deviation on the log
          scale, for a log Normal distribution. 

    rate: ('hmmPois,hmmExp,hmmGamma') Rate of a Poisson, Exponential or
          Gamma distribution (see 'dpois', 'dexp', 'dgamma'). 

   shape: ('hmmPois,hmmExp,hmmGamma') Shape parameter of a Gamma or
          Weibull distribution (see 'dgamma', 'dweibull'). 

   scale: ('hmmGamma') Shape parameter of a Gamma distribution (see
          'dgamma'). 

    size: Order of a Binomial distribution (see 'dbinom').

    disp: Dispersion parameter of a negative binomial distribution,
          also called 'size' or 'order'.  (see 'dnbinom').

   lower: ('hmmUnif,hmmTNorm,hmmMEUnif') Lower limit for an Uniform or
          truncated Normal distribution. 

   upper: ('hmmUnif,hmmTNorm,hmmMEUnif') Upper limit for an Uniform or
          truncated Normal distribution. 

   sderr: ('hmmMETNorm,hmmUnif') Standard deviation of the Normal
          measurement error distribution. 

 meanerr: ('hmmMETNorm,hmmUnif') Additional shift in the measurement
          error, fixed to 0 by default.  This may be modelled in terms
          of covariates. 

_D_e_t_a_i_l_s:

     See the PDF manual  'msm-manual.pdf' in the 'doc' subdirectory for
     algebraic definitions of all these distributions.

     Parameters which can be modelled in terms of covariates, on the
     scale of a link function, are as follows.

       PARAMETER NAME  LINK FUNCTION
       'mean'          identity
       'meanlog'       identity
       'rate'          log
       'scale'         log
       'meanerr'       identity
       'prob'          logit

     Parameters 'basecat, lower, upper, size, meanerr' are fixed at
     their initial values. All other parameters are estimated while
     fitting the hidden Markov model, unless the appropriate
     'fixedpars' argument is supplied to 'msm'. 

     For categorical response distributions '(hmmCat)' the outcome
     probabilities initialized to zero are fixed at zero, and the
     probability corresponding to 'basecat' is fixed to one minus the
     sum of the remaining probabilities.  These remaining probabilities
     are estimated, and can be modelled in terms of covariates.

_V_a_l_u_e:

     Each function returns an object of class 'hmodel', which is a list
     containing information about the model.  The only component which
     may be useful to end users is 'r', a function of one argument 'n'
     which returns a random sample of size 'n' from the given
     distribution.

_A_u_t_h_o_r(_s):

     C. H. Jackson chris.jackson@imperial.ac.uk

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

     Satten, G.A. and Longini, I.M.  Markov chains with measurement
     error: estimating the 'true' course of a marker of the progression
     of human immunodeficiency virus disease (with discussion) _Applied
     Statistics_ 45(3): 275-309 (1996).

     Jackson, C.H. and Sharples, L.D. Hidden Markov models for the
     onset and progresison of bronchiolitis obliterans syndrome in lung
     transplant recipients _Statistics in Medicine_, 21(1): 113-128
     (2002).

     Jackson, C.H., Sharples, L.D., Thompson, S.G. and Duffy, S.W. and
     Couto, E.  Multi-state Markov models for disease progression with
     classification error. _The Statistician_, 52(2): 193-209 (2003).

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

     'msm'

