simtest               package:multcomp               R Documentation

_S_i_m_u_l_t_a_n_e_o_u_s _C_o_m_p_a_r_i_s_o_n_s

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

     Computes multiplicity adjusted p-value for several multiple
     comparisons.

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

     ## Default S3 method:
     simtest(y, x=NULL, type=c("Dunnett", "Tukey",
             "Sequen", "AVE", "Changepoint", "Williams", "Marcus",
             "McDermott","Tetrade"), cmatrix=NULL,
             alternative=c("two.sided","less", "greater"),
             asympt=FALSE, ttype=c("free","logical"), eps=0.001,
             maxpts=1e+06, nlevel=NULL, nzerocol=c(0,0),...)
     ## S3 method for class 'formula':
     simtest(formula, data=list(), subset, na.action, whichf, ...)
     ## S3 method for class 'lm':
     simtest(y, psubset=NULL, cmatrix = NULL, ttype=c("free","logical"),
              alternative=c("two.sided","less","greater"), asympt=FALSE,
              eps=0.001, maxpts=1000000, ...)

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

       y: a numeric vector of responses or an object of class 'lm' or
          'glm'.

       x: a numeric matrix, the design matrix.

    type: the type of contrast to be used. If type is not specified,
          cmatrix has to be specified.

 cmatrix: the contrast matrix itself can be specified. If 'cmatrix' is
          defined, 'type' is ignored.

alternative: the alternative hypothesis must be one of '"two.sided"'
          (default), '"greater"' or '"less"'.  You can specify just the
          initial letter.

  asympt: a logical indicating whether the (exact) t-distribution or
          the normal approximation should be used.

   ttype: Specifies whether the logical contraint method of Westfall
          (1997) will be used, or whether the uncontrained method will
          be used.

     eps: absolute error tolerance as double.

  maxpts: maximum number of function values as integer.

  nlevel: a vector containing the number of levels for each factor for
          'type == "Tetrade"'.

nzerocol: a vector of two elements defining the number of zero-columns
          to add to the contrast matrix from left (the first element,
          usually 1 for the intercept) and right (usually 0 if no
          covariables are specified). 'nzerocol' is automatically
          determined by 'simint.formula'.

 psubset: a vector of integers or characters indicating for which
          subset of coefficients of a (generalized) linear model    'y'
           simultaneous p-values should be computed.

 formula: a symbolic description of the model to be fit.

    data: an optional data frame containing the variables in the model.
          By default the variables are taken from
          'Environment(formula)', typically the environment from which
          'simint' is called.

  subset: an optional vector specifying a subset of observations to be
          used.

na.action: a function which indicates what should happen when the data
          contain 'NA''s.  Defaults to 'GetOption("na.action")'.

  whichf: if more than one factor is given in the right hand side of
          'formula', 'whichf' can be used to defined the factor to
          compute contrasts of.

     ...: further arguments to be passed to or from methods.

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

     Computes multiplicity adjusted p-value for several multiple
     comparisons. The  implemented algorithms take the logical
     relationships between the hypotheses  and the stochastical
     correlations between the test statistics into account.  Logical
     information is included via the methods described by Westfall
     (1997). Stochastic information is included via the 'pmvt' 
     function. The p-values are  generally the same as the come out in
     a closed test procedure using max-T-type  statistics.  The
     procedure differs in a very subtle way from closed testing,  but
     still controls FWE strongly under point null configurations; see
     Westfall (1997). The present function allows for multiple
     comparisons of generally correlated  means in general linear
     models under the classical ANOVA assumptions, as well  as more
     general approximate procedures for approximately normal and
     generally  correlated parameter estimates.  Either multivariate
     normal or multivariate t  statistics can be used. The interface
     allows the use of the multiple comparison  procedures as for
     example Dunnett and Tukey. The resulting p-values are  not
     associated  with the confidence intervals from 'simint'.

     The formula interfaces to 'simtest' and 'simint' are  able to work
     with the following situations at the right hand side (the left
     hand side is one continuous variable).

     As long as the contrasts are specified for one single factor of
     interest, any ANOVA or ANCOVA model can be used. If any of the
     covariables is again a factor, specify the factor of interest with
     the 'whichf' option. The remaining (zero) columns are added
     automatically to the contrast matrix (but you can also specify the
     number of zero  columns by hand through 'nzerocol'). One exception
     of supplied contrasts which involve more than one factor are the
     Tetrade contrasts for the analysis of two-fold interactions (see
     'waste' for an example).  In this case only the two-way layout
     model with interactions  may be specified on the right hand side
     of `formula' (continuous covariables  are possible). If a contrast
     matrix is specified (via 'cmatrix') and 'whichf' is missing, the
     complete design matrix is derived from the right hand side of
     'formula' is used, whenever the their dimensions match with those
     of 'cmatrix'. Some toy examples are given in the examples section.

     In all other cases 'csimtest' or 'csimint'  should be used which
     allow a greater flexibility and more potential situations of use
     (e.g. multivariate data, contrasts involving more than 1 factor,
     non-linear models, ...), also the user has to compute the
     estimates, df and covariance matrices on his own.

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

     an object of class 'hmtestp'

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

     Frank Bretz <bretz@ifgb.uni-hannover.de> and  
       Torsten Hothorn <Torsten.Hothorn@rzmail.uni-erlangen.de>

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

     Peter Westfall (1997), Multiple testing of general contrasts using
      logical constraints and  correlations. _Journal of the American
     Statistical Association_ *92*(437), 299-36.

     Frank Bretz, Alan Genz and Ludwig A. Hothorn (2001), On the
     numerical  availability of multiple comparison procedures.
     _Biometrical Journal_, *43*(5), 64-66.

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

     data(cholesterol)

     # adjusted p-values for all-pairwise comparisons in a one-way 
     # layout (tests for restricted combinations)
     simtest(response ~ trt, data=cholesterol, type="Tukey", ttype="logical")

     # some examples for the formula interface, statistically non-sense!

     # response
     y <- rnorm(21)  

     # three factors
     f1 <- factor(c(rep(c("A", "B", "C"), 7)))
     f2 <- factor(c(rep("D", 10), rep("E", 11)))

     # and one continuous covariable
     x <- rnorm(21)
     testdata <- cbind(as.data.frame(y), f1, f2, x)

     # one factor only
     summary(simtest(y ~ f1))

     # one factor only, the same
     summary(simtest(y ~ f1, data=testdata))

     # and a continuous covariable
     summary(simtest(y ~ f1 + x, data=testdata))

     # without intercept
     summary(simtest(y ~ f1 + x - 1, data=testdata))

     # with an additional factor as covariable
     # use `whichf' to specify the term in the model to 
     # calculate p-values or confidence intervals for
     summary(simtest(y ~ f1 + f2 + x - 1, data=testdata, whichf="f1"))

     # with interaction terms
     summary(simtest(y ~ f1*f2 + x - 1, data=testdata, whichf="f1"))

     # inference about the interactions term
     # either Tetrade contrasts 
     summary(simtest(y ~ f1:f2, data=testdata, type="Tetrade"))

     # or a user-defined contrast matrix
     # note: this is a contrast matrix for the interactions only, 
     # the column for the intercept is added automatically
     simtest(y ~ f1:f2, data=testdata, cmatrix=diag(6))

     # works too, if the column for the intercept is included
     summary(simtest(y ~ f1:f2, data=testdata, cmatrix=cbind(0, diag(6))))

     # additional covariable
     summary(simtest(y ~ f1:f2 + x, data=testdata, cmatrix=diag(6)))

     # again with intercept and covariables in included in cmatrix
     summary(simtest(y ~ f1:f2 + x, data=testdata, 
                     cmatrix=cbind(0, diag(6), 0)))

