Anova                  package:car                  R Documentation

_A_n_o_v_a _T_a_b_l_e_s _f_o_r _L_i_n_e_a_r _a_n_d _G_e_n_e_r_a_l_i_z_e_d _L_i_n_e_a_r _M_o_d_e_l_s

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

     Calculates type-II or type-III analysis-of-variance tables for
     model objects produced by `lm' and `glm'. For linear
 models,
     F-tests are calculated; for generalized linear models, 
     likelihood-ratio chisquare, Wald chisquare, or F-tests are
     calculated.

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


     Anova(mod, ...)

     Anova.lm(mod, error, type=c("II", "III"), ...)

     Anova.glm(mod, type=c("II", "III"), test.statistic=c("LR", "Wald", "F"), 
         error, error.estimate=c("pearson", "dispersion", "deviance"))

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

     mod: `lm' or `glm' model object.

   error: for a linear model, an `lm' model object from which the
          error sum of squares and degrees of freedom are to be
          calculated. For 
 F-tests for a generalized linear model, a
          `glm' object from which the
 dispersion is to be estimated.
          If not specified, `mod' is used.

    type: type of test, `"II"' or `"III"'.

test.statistic: for a generalized linear model, whether to calculate 
          `"LR"' (likelihood-ratio), `"Wald"', or `"F"' tests.

error.estimate: for F-tests for a generalized linear model, base the
          dispersion estimate on the Pearson residuals (`pearson', the
          default); use the
 dispersion estimate in the model object
          (`dispersion'), which, e.g., is
 fixed to 1 for binomial and
          Poisson models; or base the dispersion estimate on
 the
          residual deviance (`deviance').

     ...: arguments to be passed to `linear.hypothesis'; only use
          `white.adjust' for a linear model.

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

     So-called type-II tests are calculated according to the principle
     of marginality,
 testing each term after all others, except
     ignoring the term's higher-order relatives;
 so-called type-III
     tests violate marginality, testing 
 each term in the model after
     all of the others. Be
 very careful in formulating the model for
     type-III tests, or the hypotheses tested
 will not make sense. As
     implemented here, type-II Wald tests 
 for generalized linear
     models are actually
 differences of Wald statistics.

     For all but type-II likelihood-ratio and F tests for generalized
     linear models, 
 `Anova' finds the test statistics without
     refitting the model.

     The standard R `anova' function calculates sequential (type-I)
     tests.
 These rarely test meaningful hypotheses.

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

     An object of class `anova', usually printed.

_W_a_r_n_i_n_g:

     Be careful of type-III tests.

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

     John Fox jfox@mcmaster.ca

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

     Fox, J. (1997)
 Applied Regression, Linear Models, and Related
     Methods. Sage.

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

     `linear.hypothesis', `anova'

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


     data(Moore)
     mod<-lm(conformity~fcategory*partner.status, data=Moore, 
       contrasts=list(fcategory=contr.sum, partner.status=contr.sum))
     Anova(mod)
     ## Anova Table (Type II tests)
     ##
     ## Response: conformity
     ##                         Sum Sq Df F value   Pr(>F)
     ## fcategory                 11.61  2  0.2770 0.759564
     ## partner.status           212.21  1 10.1207 0.002874
     ## fcategory:partner.status 175.49  2  4.1846 0.022572
     ## Residuals                817.76 39                 
     Anova(mod, type="III")
     ## Anova Table (Type III tests)
     ##
     ## Response: conformity
     ##                          Sum Sq Df  F value    Pr(>F)
     ## (Intercept)              5752.8  1 274.3592 < 2.2e-16
     ## fcategory                  36.0  2   0.8589  0.431492
     ## partner.status            239.6  1  11.4250  0.001657
     ## fcategory:partner.status  175.5  2   4.1846  0.022572
     ## Residuals                 817.8 39                   

