phmclust               package:mixPHM               R Documentation

_F_i_t_s _m_i_x_t_u_r_e_s _o_f _p_r_o_p_o_r_t_i_o_n_a_l _h_a_z_a_r_d _m_o_d_e_l_s

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

     This function allows for the computation of proportional hazards
     models with different distribution assumptions  on the underlying
     baseline hazard. Several options for imposing proportionality
     restrictions on the hazards are provided. This funtction offers
     several variations of the EM-algorithm regarding the posterior
     computation in the M-step.

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

     phmclust(x, K, method = "separate", Sdist = "weibull", EMstart = NA, 
     EMoption = "classification", EMstop = 0.0001, maxiter = 1000)

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

       x: Data frame or matrix of dimension n*p with survival times
          ('NA''s allowed).

       K: Number of mixture components.

  method: Imposing proportionality restrictions on the hazards:  With
          '"separate"' no restrictions are imposed, '"main.g"' relates
          to a group main effect,  '"main.p"' to variable main effects.
          '"main.gp"' reflects the proportionality assumption over
          groups and variables. '"int.gp"' allows for interactions
          between groups and variables.

   Sdist: Various survival distrubtions such as '"weibull"',
          '"exponential"', and '"rayleigh"'.

 EMstart: Vector of length n with starting values for group membership,
           'NA' indicates random starting values.

EMoption: '"classification"' is based on deterministic cluster
          assignment,  '"maximization"' on deterministic assignment,
          and '"randomization"'  provides a posterior-based randomized
          cluster assignement.

  EMstop: Stopping criterion for EM-iteration.

 maxiter: Maximum number of iterations.

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

     The method '"separate"' corresponds to an ordinary mixture model.
     '"main.g"' imposes proportionality  restrictions over variables
     (i.e., the group main effect allows for free-varying variable
     hazards). '"main.p"'  imposes proportionality restrictions over
     groups (i.e., the variable main effect allows for free-varying
     group hazards). If clusters with only one observation are
     generated, the algorithm stops.

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

     Returns an object of class 'mws' with the following values: 

       K: Number of components

    iter: Number of EM iterations

  method: Proportionality restrictions used for estimation

   Sdist: Assumed survival distribution

likelihood: Log-likelihood value for each iteration

  pvisit: Matrix of prior probabilities due to 'NA structure'

   shape: Matrix with shape parameters

   scale: Matrix with scale parameters

   group: Final deterministic cluster assignment

posteriors: Final probabilistic cluster assignment

    npar: Number of estimated parameters

     aic: Akaike information criterion

     bic: Bayes information criterion

  clmean: Matrix with cluster means

   clmed: Matrix with cluster medians

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

     Mair, P., and Hudec, M. (2007). Analysis of dwell times in Web
     Usage Mining.  Proceedings of the 31st Annual Conference of the
     German Classification Society  on Data Analysis, Machine Learning,
     and Applications.

     Kalbfleisch, J.D., and Prentice, R.L. (1980). The statistical
     analysis of failure  time data. New York: Wiley.

     Celaux, G., and Govaert, G. (1992). A classification EM algorithm
     for clustering and two stochastic versions. Computational
     Statistics and Data Analysis, 14, 315-332.

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

     'stableEM', 'msBIC'

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

     data(webshop)

     ## Fitting a Weibll mixture model (3 components) is fitted with classification EM 
     res1 <- phmclust(webshop, K = 3)
     res1
     summary(res1)

     ## Fitting a Rayleigh Weibull proportional hazard model (2 components, proportional over groups)
     res2 <- phmclust(webshop, K = 2, method = "main.p", Sdist = "rayleigh") 
     res2
     summary(res2)

