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One approach to loosen the restrictive variance assumption involves use of an empirical (or robust or sandwich) variance estimator [ 11- 13] to account for the over-dispersion.
In this paper we have considered two types of informative variance priors: frequentist and empirically informed; and we considered two restrictive variance structures with weakly informative priors: the exchangeable variances approach, and the consistency variances approach.
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Revealed preference (RP) data is typically restrictive in its variance properties, but is an important input into the assessment.
We therefore considered other convenient but less restrictive models where Variance of count in week t = dispersion × average count in week t (1) Models of this form are called quasi-Poisson.
For concern, child android/gynoid fat ratio explained the largest amount of variance, followed by restrictive feeding and SSB intake.
Concentrating on just one gene (for example MTHFR, the most widely studied gene in the folate pathway) would be unnecessarily restrictive and would ignore the variance in the other pathways.
However, in other situations, the common variance assumption might be restrictive, and relaxing s to gene-specific s can be done (see discussion in Section 6).
In those cases, the parsimony of the M×E model can be advantageous; however, the pattern may be too restrictive in cases where the genomic variance cannot be approximated with the structure imposed by the interaction model (Meyer and Kirkpatrick 2008).
In this case, we use a count data model based on the Negative Binomial distribution (which is used after rejecting the equality of mean and variance implied by the more restrictive Poisson distribution), in order to take account of the discrete nature of the new dependent variable.
The restrictive condition of the equality of mean and variance in the Poisson distribution (equidispersion) is the reason that the negative binomial model is often preferred.
However, use of these approaches brings additional restrictive assumptions such as linearity, normality (Gaussian distributed variables), variance constancy (homoscedasticity) etc.
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