summary.scaleboot         package:scaleboot         R Documentation

_P-_v_a_l_u_e _C_a_l_c_u_l_a_t_i_o_n _f_o_r _M_u_l_t_i_s_c_a_l_e _B_o_o_t_s_t_r_a_p

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

     'summary' method for class '"scaleboot"' and '"scalebootv"'.

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

     ## S3 method for class 'scaleboot':
     summary(object,models=names(object$fi),k=1:3,s=1,sp=-1,...)

     ## S3 method for class 'scalebootv':
     summary(object,models=attr(object,"models"),k=1:3,...)

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

  object: an object used to select a method. 

  models: character vector of model names. If numeric,
          'names(object$fi)[models]' is used for each '"scaleboot"'
          object.

       k: numeric vector of k for calculating p-values.

       s: sigma_0^2

      sp: sigma_p^2

     ...: further arguments passed to and from other methods.

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

     For each model, a class of approximately unbiased p-values,
     indexed by k=1,2,..., is calculaed.  The p-values are named 
     'k.1', 'k.2', ..., where k=1 ('k.1') corresponds to the ordinary
     bootstrap probability, and k=2 ('k.2') corresponds to the
     third-order accurate p-value of Shimodaira (2002). As the k value
     increases, the bias of testing decreases, although the p-value
     becomes less stable numerically and the monotonicity of rejection
     regions becomes worse. Typically, k=3 provides a reasonable
     compromise. The 'sbpval' method is available to extract p-values
     from the '"summary.scaleboot"' object.

     The p-value is defined as

 p_k = 1 - Phi( sum_{j=0}^{k-1} frac{(sigma_p^2-sigma_0^2)^j}{j!}  frac{d^j psi(x|beta)}{d x^j}Bigr|_{sigma_0^2} ),

     where psi(sigma^2|beta) is the model specification function,
     sigma_0^2 is the evaluation point for the Taylor series, and
     sigma_p^2 is an additional parameter. Typically, we do not change
     the default values sigma_0^2=1 and sigma_p^2=-1.

     The p-values are justified only for good fitting models. By
     default, the model which minimizes the AIC value is selected. We
     can modify the AIC value by using the 'sbaic' function. We also
     diagnose the fitting by using the 'plot' method.

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

     'summary.scaleboot' returns an object of the class
     '"summary.scaleboot"', which is inherited from the class
     '"scaleboot"'. It is a list containing all the components of class
     '"scaleboot"' and the following components: 

      pv: matrix of p-values of size 'length(models)' * 'length(k)'
          with elements p_k.

      pe: matrix of standard errors of p-values.

    best: a list consisting of components 'model' for the best fitting
          model name, 'aic' for its AIC value, 'pv' for a vector of
          p-values, and 'pe' for a vector of standard errors.

   parex: a list of components 'k', 's', and 'sp'.

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

     Hidetoshi Shimodaira

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

     'sbfit', 'sbpsi', 'sbpval', 'sbaic'.

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

     data(mam15)
     ## For a single hypothesis
     a <- mam15.relltest[["t4"]] # an object of class "scaleboot"
     summary(a) # calculate and print p-values (k=1:3)
     summary(a,k=1:4) # up to "k.4" p-value.

     ## For multiple hypotheses
     b <- mam15.relltest[1:15] # an object of class "scalebootv"
     summary(b) # calculate and print p-values (k=1:3)
     summary(b,k=1:4) # up to "k.4" p-value.

