jtest                 package:lmtest                 R Documentation

_J _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:

     'jtest' performs the Davidson-MacKinnon J test for comparing
     non-nested models.

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

      jtest(formula1, formula2, data = list(), vcov. = NULL, ...)

_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
          'jtest' is called from.

   vcov.: a function for estimating the covariance matrix of the
          regression coefficients, e.g., 'vcovHC'.

     ...: further arguments passed to 'coeftest'.

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

     The idea of the J test is the following: if the first model
     contains the correct set of regressors, then including the fitted
     values of the second model into the set of regressors should
     provide no significant  improvement. But if it does, 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
     included into model 2 and vice versa. The J test statistic is
     simply the marginal test of the fitted values in the augmented
     model. This is performed by 'coeftest'.

     For further details, see the references.

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

     An object of class '"anova"' which contains the coefficient
     estimate of the fitted values in the augmented regression plus
     corresponding standard error, test statistic and p value.

_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:

     'coxtest', '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)

