coxtest                package:lmtest                R Documentation

_C_o_x _T_e_s_t _f_o_r _C_o_m_p_a_r_i_n_g _N_o_n-_N_e_s_t_e_d _M_o_d_e_l_s

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

     'coxtest' performs the Cox test for comparing two non-nested
     models.

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

     coxtest(formula1, formula2, data = list())

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

formula1: either a symbolic description for the first model to be
          tested, or a fitted object of class '"lm"'.

formula2: either a symbolic description for the second model to be
          tested, or a fitted object of class '"lm"'.

    data: an optional data frame containing the variables in the model.
          By default the variables are taken from the environment which
          'coxtest' is called from.

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

     The idea of the Cox test is the following: if the first model
     contains the correct set of regressors, then a fit of the
     regressors from the  second model to the fitted values from first
     model should have no further explanatory value. But if it has, it
     can be concluded that model 1 does not contain the correct set of
     regressors.

     Hence, to compare both models the fitted values of model 1 are
     regressed on model 2 and vice versa. A Cox test statistic is
     computed for each auxiliary model which is asymptotically standard
     normally distributed.

     For further details, see the references.

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

     An object of class '"anova"' which contains the estimate plus
     corresponding standard error, z test statistic and p value for
     each auxiliary test.

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

     R. Davidson & J. MacKinnon (1981). Several Tests for Model
     Specification in the Presence of Alternative Hypotheses.
     _Econometrica_, *49*, 781-793.

     W. H. Greene (1993), _Econometric Analysis_, 2nd ed. Macmillan
     Publishing Company, New York.

     W. H. Greene (2003). _Econometric Analysis_, 5th ed. New Jersey,
     Prentice Hall.

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

     'jtest', 'encomptest'

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

     ## Fit two competing, non-nested models for aggregate 
     ## consumption, as in Greene (1993), Examples 7.11 and 7.12

     ## load data and compute lags
     data(USDistLag)
     usdl <- na.contiguous(cbind(USDistLag, lag(USDistLag, k = -1)))
     colnames(usdl) <- c("con", "gnp", "con1", "gnp1")

     ## C(t) = a0 + a1*Y(t) + a2*C(t-1) + u
     fm1 <- lm(con ~ gnp + con1, data = usdl)

     ## C(t) = b0 + b1*Y(t) + b2*Y(t-1) + v
     fm2 <- lm(con ~ gnp + gnp1, data = usdl)

     ## Cox test in both directions:
     coxtest(fm1, fm2)

     ## ...and do the same for jtest() and encomptest().
     ## Notice that in this particular case they are coincident.
     jtest(fm1, fm2)
     encomptest(fm1, fm2)

