We believe that our effective sample size formula makes better sense: in the three-sib sibship case, because each sibship is independent of another, the number of independent samples is at least N/3. Note that the ESS formula involves an operation of rescaling the original sample size N, instead of subtracting a correction term. In order for Cheverud’s formula to have a similar effect, the variance of eigenvalues has to increase with the sample size N. This can be true only if there is a collective correlation for all variables, or if there is haplotype block-block correlation. If the variables (samples) can be split into independent blocks, the effective degrees of freedom (sample size) should always be a rescaled version of the original one. Interestingly, for a model discussed in (Salyakina et al., 2005) where the correlation coefficient within a block is 1 and those between blocks are small non-negative values, the effective number of variables is indeed a rescaled value of the original number of variables.
