float                  package:Epi                  R Documentation

_C_a_l_c_u_l_a_t_e _f_l_o_a_t_e_d _v_a_r_i_a_n_c_e_s

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

     Given a fitted  model object, the 'float()' function calculates
     floating variances (a.k.a. quasi-variances) for a given factor in
     the model.

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

     float(object, factor, iter.max=50)

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

  object: a fitted model object

  factor: character string giving the name of the factor of interest.
          If this is not given, the first factor in the model is used.

iter.max: Maximum number of iterations for EM algorithm

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

     The 'float()' function implements the "floating absolute risk"
     proposal of Easton, Peto and Babiker(1992). This is an alternative
     way of presenting parameter estimates for factors in regression
     models, which avoids some of the difficulties of treatment
     contrasts. It was originally designed for epidemiological studies
     of relative risk, but the idea is widely applicable.

     Treatment contrasts are not orthogonal. Consequently, the
     variances of treatment contrast estimates may be inflated by a
     poor choice of reference level, and the correlations between them
     may also be high. The 'float()' function associates each level of
     the factor with a "floating" variance (or quasi-variance),
     including the reference level.  Floating variances are not real
     variances, but they can be used to calculate the variance error of
     contrast by treating each level as independent.

     Plummer (2003) showed that floating variances can be derived from
     a covariance structure model applied to the variance-covariance
     matrix of the contrast estimates. This model can be fitted by
     minimizing the Kullback-Leibler information divergence between the
     true distribution of the parameter estimates and the simplified
     distribution given by the covariance structure model. Fitting is
     done using the EM algorithm.

     In order to check the goodness-of-fit of the floating variance
     model, the 'float()' function compares the standard errors
     predicted by the model with the standard errors derived from the
     true variance-covariance matrix of the parameter contrasts. The
     maximum and minimum ratios between true and model-based standard
     errors are calculated over all possible contrasts. These should be
     within 5 percent, or the use of the floating variances may lead to
     invalid confidence intervals.

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

     An object of class 'floated'. This is a list with the following
     components 

    coef: A vector of coefficients. These are the same as the treatment
          contrasts but the reference level is present with coefficient
          0.

     var: A vector of floating (or quasi-) variances

  limits: The bounds on the accuracy of standard errors over all
          possible contrasts

_N_o_t_e:

     Menezes(1999) and Firth and Menezes (2004) take a slightly
     different approach to this problem, using a pseudo-likelihood
     approach to fit the quasi-variance model. Their work is
     implemented in the package qvcalc.

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

     Martyn Plummer

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

     Easton DF, Peto J and Babiker GAG (1991) Floating absolute risk:
     An alternative to relative risk in survival and case control
     analysis avoiding an arbitrary reference group. _Statistics in
     Medicine_, *10*, 1025-1035.

     Firth D and Mezezes RX (2004)  Quasi-variances. _Biometrika_ *91*,
     65-80.

     Menezes RX(1999)  More useful standard errors for group and factor
     effects in generalized linear models.  _D.Phil. Thesis_,
     Department of Statistics, University of Oxford.

     Plummer M (2003) Improved estimates of floating absolute risk,
     _Statistics in Medicine_, *23*, 93-104.

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

     'ftrend', 'qvcalc'

