pgam                  package:pgam                  R Documentation

_P_o_i_s_s_o_n-_G_a_m_m_a _A_d_d_i_t_i_v_e _M_o_d_e_l_s

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

     Fit Poisson-Gamma Additive Models using the roughness penalty
     approach

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

     pgam(formula, dataset, omega = 0.8, beta = 0.1, offset = 1, digits = getOption("digits"),
     na.action="na.exclude", maxit = 100, eps = 1e-06, lfn.scale=1, control = list(), 
     optim.method = "L-BFGS-B", bkf.eps = 0.001, bkf.maxit = 100, se.estimation = "numerical", 
     verbose = TRUE)

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

 formula: a model formula. See 'formparser' for details

 dataset: a data set in the environment search path. Missing data is
          temporarily not handled

   omega: initial value for the discount factor

    beta: vector of initial values for covariates coefficients. If a
          sigle value is supplied it is replicated to fill in the whole
          vector

  offset: default is 1. Other value can be supplied here

  digits: number of decimal places for printing information out

na.action: action to be taken if missing values are found. Default is
          '"na.exclude"' and residuals and predictions are padded to
          fit the length of the data. If '"na.fail"' then the process
          will stop if missing values are found. If '"na.omit"' the
          process will continue without padding though. If '"na.pass"'
          the process will stop due to errors

   maxit: convergence control iterations

     eps: convergence control criterion

lfn.scale: scales the likelihood function and is passed to 'control' in
          'optim'. Value must be positive to ensure maximization

 control: convergence control of 'optim'. See its help for details

optim.method: optimization method passed to 'optim'. Different methods
          can lead to different results, so the user must attempt to
          the trade off between speed and robustness. For example,
          'BFGS' is faster but sensitive to starting values and
          'L-BFGS-B' is more robust but slower. See its help for
          details.

 bkf.eps: convergence control criterion for the backfitting algorithm

bkf.maxit: convergence control iterations for the backfitting algorithm

se.estimation: if 'numerical' numerical standard error of parameters
          are returned. If 'analytical' then analytical extraction of
          the standard errors is performed. By setting it to 'none'
          standard error estimation is avoided

 verbose: if 'TRUE' information during estimation process is printed
          out

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

     The formula is parsed by 'formparser' in order to extract all the
     information necessary for model fit. Split the model into two
     parts regarding the parametric nature of the model. A model can be
     specified as following:

            Y~f(sf_{r})+V1+V2+V3+g(V4,df_{4})+g(V5,df_{5})

     where sf_{r} is a seasonal factor with period r and df_{i} is the
     degree of freedom of the smoother of the _i_-th covariate.
     Actually, two new formulae will be created:

                     ~sf_{1}+...+sf_{r}+V1+V2+V3

     and

                                ~V4+V5

     These two formulae will be used to build the necessary datasets
     for model estimation. _Dummy_ variables reproducing the seasonal
     factors will be created also.

     Models without explanatory variables must be specified as in the
     following formula

                                Y~NULL


     There are a lot of details to be written. It will be very soon.

     Specific information can be obtained on functions help.

     This algorithm fits fully parametric Poisson-Gamma model also.

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

     List containing an object of class 'pgam'.

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

     Washington Leite Junger wjunger@ims.uerj.br and Antonio Ponce de
     Leon ponce@ims.uerj.br

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

     Junger, W. L. (2004) Modelo Poisson-Gama Semi-Paramérico: Uma
     Abordagem de Penalização por Rugosidade. MSc Thesis. Rio de
     Janeiro, PUC-Rio, Departamento de Engenharia Elétrica

     Harvey, A. C., Fernandes, C. (1989) Time series models for count
     data or qualitative observations. Journal of Business and Economic
     Statistics, 7(4):407-417

     Campos, E. L., De Leon, A. C. M. P., Fernandes, C. A. C. (2003)
     Modelo Poisson-Gama para Séries Temporais de Dados de Contagem -
     Teoria e Aplicações. 10a ESTE - Escola de Séries Temporais e
     Econometria

     Green, P. J., Silverman, B. W. (1994) Nonparametric Regression and
     Generalized Linear Models: a roughness penalty approach. Chapman
     and Hall, London

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

     'predict.pgam', 'formparser', 'residuals.pgam', 'backfitting'

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

     library(pgam)
     data(aihrio)
     attach(aihrio)
     form <- ITRESP5~f(WEEK)+HOLIDAYS+rain+PM+g(tmpmax,7)+g(wet,3)
     m <- pgam(form,aihrio,omega=.8,beta=.01,maxit=1e2,eps=1e-4,optim.method="BFGS")

     summary(m)

