mix                 package:depmixS4                 R Documentation

_M_i_x_t_u_r_e _M_o_d_e_l _S_p_e_c_i_f_i_c_t_i_o_n

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

     'mix' creates an object of class 'mix', an (independent) mixture
     model (as a limit case of dependent mixture models in which all
     observed time series are of length 1), otherwise known latent
     class or mixture model.  For a short description of the package
     see 'depmixS4'.

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

             
             mix(response, data=NULL, nstates, family=gaussian(), 
                     prior=~1, initdata=NULL, respstart=NULL, instart=NULL,...)      
             

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

response: The response to be modeled; either a formula or a list  of
          formulae in the multivariate case; this interfaces to the glm
          distributions. See 'Details'.

    data: An optional data.frame to interpret the variables in the
          response and transition arguments.

 nstates: The number of states of the model.

  family: A family argument for the response. This must be a list of
          family's if the response is multivariate.

   prior: A one-sided formula specifying the density for the prior or
          initial state probabilities.

initdata: An optional data.frame to interpret the variables occuring in
          prior. The number of rows of this data.frame must be equal to
          the number of cases being modeled. See 'Details'.

respstart: Starting values for the parameters of the response models.

 instart: Starting values for the parameters of the prior or initial
          state probability model.

     ...: Not used currently.

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

     The function 'mix' creates an S4 object of class 'mix', which
     needs to be fitted using 'fit' to optimize the parameters.

     The response model(s) are created by call(s) to 'response'
     providing the response formula and the family specifying the error
     distribution.  If response is a list of formulae, the 'response''s
     are assumed to be independent conditional on the latent class.

     The prior density is modeled as a multinomial logistic.  This
     model is created by a call to 'transInit'.

     Starting values may be provided by the respective arguments.  The
     order in which parameters must be provided can be easily studied
     by using the 'setpars' function.

     Linear constraints on parameters can be provided as argument to
     the 'fit' function.

     The print function prints the formulae for the response and prior
     models along with their parameter values.

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

     'mix' returns an object of class 'mix' which has the following
     slots:

response: A list of a list of response models; the first index runs
          over states; the second index runs over the independent 
          responses in case a multivariate response is provided.

   prior: A multinomial logistic model for the initial state
          probabilities.

dens,init: See 'mix-class' help for details.  For internal use.

  ntimes: A vector made by 'rep(1,nrow(data))'; for internal use only.

 nstates: The number of states of the model.

   nresp: The number of independent responses.

   npars: The total number of parameters of the model.  Note: this is
          _not_ the degrees of freedom because there are redundancies
          in the parameters, in particular in the multinomial models
          for the transitions and prior probabilities.

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

     Ingmar Visser

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

     On latent class models: A. L. McCutcheon (1987).  _Latent class
     analysis_.  Sage Publications.

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

     'fit', 'transInit', 'response', 'depmix-methods' for accessor
     functions to 'depmix' objects.

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

     # four binary items on the balance scale task
     data(balance)

     # define a latent class model
     instart=c(0.5,0.5)
     set.seed(1)
     respstart=runif(16)
     # note that ntimes argument is used to make this a mixture model
     mod <- mix(list(d1~1,d2~1,d3~1,d4~1), data=balance, nstates=2,
             family=list(multinomial(),multinomial(),multinomial(),multinomial()),
             respstart=respstart,instart=instart)
     # to see the model
     mod

