rms.curv                package:MASS                R Documentation

_R_e_l_a_t_i_v_e _C_u_r_v_a_t_u_r_e _M_e_a_s_u_r_e_s _f_o_r _N_o_n-_L_i_n_e_a_r _R_e_g_r_e_s_s_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     Calculates the root mean square parameter effects and intrinsic
     relative curvatures, c^theta and c^iota, for a fitted nonlinear
     regression, as defined in Bates & Watts, section 7.3, p. 253 et
     seq.

_U_s_a_g_e:

     rms.curv(obj)

_A_r_g_u_m_e_n_t_s:

     obj: Fitted model object of class '"nls"'.  The model must be
          fitted using the default algorithm. 

_D_e_t_a_i_l_s:

     The method of section 7.3.1 of Bates & Watts is implemented.  The
     function 'deriv3' should be used generate a model function with
     first derivative (gradient) matrix and second derivative (Hessian)
     array attributes.  This function should then be used to fit the
     nonlinear regression model.

     A print method, 'print.rms.curv', prints the 'pc' and 'ic'
     components only, suitably annotated.

     If either 'pc' or 'ic' exceeds some threshold (0.3 has been
     suggested) the curvature is unacceptably high for the planar
     assumption.

_V_a_l_u_e:

     A list of class 'rms.curv' with components 'pc' and 'ic' for
     parameter effects and intrinsic relative curvatures multiplied by
     sqrt(F), 'ct' and 'ci' for c^theta and c^iota (unmultiplied), and
     'C' the C-array as used in section 7.3.1 of Bates & Watts.

_R_e_f_e_r_e_n_c_e_s:

     Bates, D. M, and Watts, D. G. (1988) _Nonlinear Regression
     Analysis and its Applications._ Wiley, New York.

_S_e_e _A_l_s_o:

     'deriv3'

_E_x_a_m_p_l_e_s:

     # The treated sample from the Puromycin data
     mmcurve <- deriv3(~ Vm * conc/(K + conc), c("Vm", "K"),
                       function(Vm, K, conc) NULL)
     Treated <- Puromycin[Puromycin$state == "treated", ]
     (Purfit1 <- nls(rate ~ mmcurve(Vm, K, conc), data = Treated,
                     start = list(Vm=200, K=0.1)))
     rms.curv(Purfit1)
     ##Parameter effects: c^theta x sqrt(F) = 0.2121
     ##        Intrinsic: c^iota  x sqrt(F) = 0.092

