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 (aka 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:

     float() 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 (hence the name) but the idea is widely applicable.  

     A problem with treatment contrasts is that they are not
     orthogonal. The variances of the treatment contrasts may be
     inflated by a poor choice of reference level, and the correlations
     between them may be very high.  float() associates each level of
     the factor, including the reference level, with a"floating"
     variance (or quasi-variance). Floating variances are not real
     variances, but they can be used to calculate the variance of any
     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 parameter estimates. This model can be fitted by
     minimizing the Kullback-Leibler information divergence between the
     true and distributions for the parameter estimates and the
     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, 'float()' 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 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: vector of coefficients. These are the same as the treatment
          contrasts but the reference level is present with coefficient
          0.

     var: vector of floating (or quasi-) variances

  limits: 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'

