tobit                  package:VGAM                  R Documentation

_T_o_b_i_t _M_o_d_e_l

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

     Fits a Tobit model to a univariate response.

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

     tobit(Lower = 0, Upper = Inf, lmu="identity", lsd="loge",
           imethod=1, zero=2)

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

   Lower: Numeric of length 1, it is the value L described below. Any
          value of the linear model  x_i^T beta that is less than this
          value is assigned this value. Hence this should be the
          smallest possible value in the response variable.

   Upper: Numeric of length 1, it is the value U described below.  Any
          value of the linear model  x_i^T beta that is greater than
          this value is assigned this value. Hence this should be the
          largest possible value in the response variable.

lmu, lsd: Parameter link functions applied to the mean and standard
          deviation parameters. See 'Links' for more choices. The
          standard deviation is a positive quantity, therefore a log
          link  is its default.

 imethod: Initialization method. Either 1 or 2, this specifies two
          methods for obtaining initial values for the parameters.

    zero: An integer vector, containing the value 1 or 2. If so, the
          mean or standard deviation respectively are modelled as an
          intercept only. Setting 'zero=NULL' means both
          linear/additive predictors are modelled as functions of the
          explanatory variables.

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

     The Tobit model can be written

                      y_i^* = x_i^T  beta +  e_i

     where the e_i ~ N(0,sigma^2) independently and i=1,...,n. However,
     we measure y_i = y_i^* only if y_i^* > L and y_i^* < U for some
     cutpoints L and U. Otherwise we let y_i=L or y_i=U, whatever is
     closer.  The Tobit model is thus a multiple linear regression but
     with censored responses if it is below or above certain cutpoints.

     The defaults for 'Lower' and 'Upper' correspond to the classical
     Tobit model.  By default, the mean x_i^T beta is the first
     linear/additive predictor, and the log of the standard deviation
     is the second linear/additive predictor.  The Fisher information
     matrix for uncensored data is diagonal. The fitted values are the
     estimates of x_i^T beta.

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

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

_N_o_t_e:

     The response must be univariate.  If there is no censoring then
     'normal1' is recommended instead.  Any value of the response less
     than 'Lower' or greater than 'Upper' will be assigned the value
     'Lower' and 'Upper' respectively, and a warning will be issued.
     The fitted object has components 'censoredL' and 'censoredU' in
     the 'extra' slot which specifies whether observations are censored
     in that direction.

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

     Thomas W. Yee

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

     Tobin, J. (1958). Estimation of relationships for limited
     dependent variables. _Econometrica_ *26*, 24-36.

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

     'normal1', 'cnormal1'. 'dcnormal1'.

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

     ## Not run: 
     n = 1000
     x = seq(-1, 1, len=n)
     f = function(x) 1 + 4*x
     ystar = f(x) + rnorm(n)
     Lower = 1
     Upper = 4
     y  = pmax(ystar, Lower)
     y  = pmin(y, Upper)
     plot(x, y, main="Tobit model", las=1)
     legend(-0.9, 3, c("Truth", "Estimate"), col=c("Blue", "Red"), lwd=2)
     table(y==Lower | y==Upper)   # How many censored values?
     fit = vglm(y ~ x, tobit(Lower=Lower, Upper=Upper), trace=TRUE)
     table(fit@extra$censoredL)
     table(fit@extra$censoredU)
     coef(fit, matrix=TRUE)
     lines(x, f(x), col="blue", lwd=2)  # The truth
     lines(x, fitted(fit), col="red", lwd=2, lty="dashed")  # The estimate
     summary(fit)
     ## End(Not run)

