logistfplot             package:logistf             R Documentation

_P_l_o_t _p_e_n_a_l_i_z_e_d _p_r_o_f_i_l_e _l_i_k_e_l_i_h_o_o_d

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

     This function plots the penalized profile likelihood for a
     specified parameter.

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

     logistfplot(formula = attr(data, "formula"),
         data = sys.parent(), which, pitch = 0.05, limits, alpha = 0.05,
         maxit = 25, maxhs = 5, epsilon = 0.0001, maxstep = 10, firth = TRUE, legends = TRUE)

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

 formula: a formula object, with the response on the left of the 
          operator, and the model terms on the right. The response must
          be a vector with 0 and 1 or FALSE and TRUE for the model
          outcome, where the higher value (1 or TRUE) is modeled. It's
          possible to include contrasts, interactions, nested effects,
          cubic or polynomial splines and all S features as well, e.g.
          'Y ~ X1*X2 + ns(X3, df=4)'. 

    data: a data.frame where the variables named in the formula can be
          found, i. e. the variables containing the binary response and
          the covariates. 

   which: a righthand formula specifying the plotted parameter,
          interaction or general term, e.g. '~ A - 1' or '~ A : C - 1'.
          The profile likelihood of the intercept would be obtained by
          the formula '~ - .'.

   pitch: distances between the interpolated points in standard errors
          of the parameter estimate, the default value is 0.05.

  limits: vector of the minimum and the maximum on the x-scale in
          standard deviations distant form the maximum likelihood. The
          default values are the extremes of both confidence intervals,
          Wald and PL, plus or minus half a standard deviation of the
          parameter, respectively.

   alpha: the significance level (1-alpha the confidence level, 0.05 as
          default).

   maxit: maximum number of iterations (default value is 25)

   maxhs: maximum number of step-halvings per iterations (default value
          is 5)

 epsilon: specifies the maximum allowed change in penalized log
          likelihood to declare convergence. Default value is 0.0001.

 maxstep: specifies the maximum change of (standardized) parameter
          values allowed in one iteration. Default value is 5.

   firth: use of Firth's (1993) penalized maximum likelihood
          ('firth=TRUE', the default) or the standard maximum
          likelihood method ('firth=FALSE') for the logistic
          regression. Note that by specifying 'pl=TRUE' and
          'firth=FALSE' (and probably a lower number of iterations) one
          obtains profile likelihood confidence intervals for maximum
          likelihood logistic regression parameters.

 legends: if 'FALSE', legends in the plot would be omitted (default is
          'TRUE').

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

     This function plots the profile likelihood of a specific parameter
     based on the penalized likelihood.  A symmetric shape of the
     profile penalized log likelihood (PPL) function allows use of Wald
     intervals, while an asymmetric shape demands profile penalized
     likelihood intervals (Heinze & Schemper (2002)). Further
     documentation can be found in Heinze & Ploner (2004).

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

     The object returned is a simple data.frame containing three
     columns which allow reproducing the plot. Each row represents one
     point of the interpolation. The columns are as follows: 

     std: distance from the maximum of the profile likelihood (in
          standard errors of the parameter estimate).

    name: the value of the parameter for the variable name specified in
          argument 'which'.

loglik.pen: the value of the penalized likelihood.

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

     Firth D (1993). Bias reduction of maximum likelihood estimates.
     _Biometrika_ 80, 27-38.

     Heinze G, Schemper M (2002). A solution to the problem of
     separation in logistic regression. _Statistics in Medicine_ 21:
     2409-2419.

     Heinze G, Ploner M (2004). Technical Report 2/2004: A SAS-macro,
     S-PLUS library and R package to perform logistic regression
     without convergence problems. Section of Clinical Biometrics,
     Department of Medical Computer Sciences, Medical University of
     Vienna, Vienna, Austria. <URL:
     http://www.meduniwien.ac.at/user/georg.heinze/techreps/tr2_2004.pd
     f>

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

     logistf, logistftest

