logistic                package:VGAM                R Documentation

_L_o_g_i_s_t_i_c _D_i_s_t_r_i_b_u_t_i_o_n _F_a_m_i_l_y _F_u_n_c_t_i_o_n

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

     Estimates the location and scale parameters of the logistic
     distribution by maximum likelihood estimation.

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

     logistic1(llocation="identity", elocation=list(),
               scale.arg=1, method.init=1)
     logistic2(llocation="identity", lscale="loge",
               elocation=list(), escale=list(),
               ilocation=NULL, iscale=NULL, method.init=1, zero=NULL)

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

llocation: Link function applied to the location parameter l. See
          'Links' for more choices.

elocation, escale: List. Extra argument for each of the links. See
          'earg' in 'Links' for general information.

scale.arg: Known positive scale parameter (called s below).

  lscale: Parameter link function applied to the scale parameter s. See
          'Links' for more choices.

ilocation: Initial value for the location l parameter. By default, an
          initial value is chosen internally using 'method.init'.
          Assigning a value will override the argument 'method.init'.

  iscale: Initial value for the scale s parameter. By default, an
          initial value is chosen internally using 'method.init'.
          Assigning a value will override the argument 'method.init'.

method.init: An integer with value '1' or '2' which specifies the
          initialization method. If failure to converge occurs try the
          other value.

    zero: An integer-valued vector specifying which linear/additive
          predictors are modelled as intercepts only.  The default is
          none of them.  If used, choose one value from the set {1,2}.

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

     The two-parameter logistic distribution  has a density that can be
     written as

       f(y;l,s) = exp[-(y-l)/s] / [s * ( 1 + exp[-(y-l)/s] )^2]

     where s>0 is the scale parameter, and l is the location parameter.
     The response -Inf<y<Inf.  The mean of Y (which is the fitted
     value) is l and its variance is pi^2 s^2 / 3.

     'logistic1' estimates the location parameter only while
     'logistic2' estimates both parameters.  By default, eta1=l and
     eta2=log(s) for 'logistic2'.

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

     An object of class '"vglmff"' (see 'vglmff-class'). The object is
     used by modelling functions such as 'vglm', 'rrvglm' and 'vgam'.

_N_o_t_e:

     Fisher scoring is used, and the Fisher information matrix is
     diagonal.

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

     T. W. Yee

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

     Johnson, N. L. and Kotz, S. and Balakrishnan, N. (1994)
     _Continuous Univariate Distributions_, 2nd edition, Volume 1, New
     York: Wiley.  Chapter 15.

     Evans, M., Hastings, N. and Peacock, B. (2000) _Statistical
     Distributions_, New York: Wiley-Interscience, Third edition.

     Castillo, E., Hadi, A. S., Balakrishnan, N. Sarabia, J. S. (2005)
     _Extreme Value and Related Models with Applications in Engineering
     and Science_, Hoboken, N.J.: Wiley-Interscience, p.130.

     deCani, J. S. and Stine, R. A. (1986) A note on Deriving the
     Information Matrix for a Logistic Distribution, _The American
     Statistician_, *40*, 220-222.

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

     'rlogis', 'bilogistic4'.

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

     # location unknown, scale known
     n = 500
     x = runif(n)
     y = rlogis(n, loc=1+5*x, scale=4)
     fit = vglm(y ~ x, logistic1(scale=4), trace=TRUE, crit="c")
     coef(fit, matrix=TRUE)

     # Both location and scale unknown
     n = 2000
     x = runif(n)
     y = rlogis(n, loc=1+5*x, scale=exp(0+1*x))
     fit = vglm(y ~ x, logistic2)
     coef(fit, matrix=TRUE)
     vcov(fit)
     summary(fit)

