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EMMA accounts for population structure by modeling the variance-covariance matrix as a function of this estimated kinship matrix.
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Modeling the variance-covariance matrix via partial autocorrelations [ 15] may allow the fitting of more complex model.
We accounted for the likelihood of intra-subject correlations of immune response values by modeling an unstructured variance-covariance matrix within subjects.
We used a binary logistic model and the variance-covariance for all models was assumed to be block diagonal, but unstructured within a block defined by subjects.
Therefore, it is more realistic to accommodate the departure from the infinitesimal model while constructing the variance-covariance matrix.
The model included a random polygenic effect, and the variance-covariance matrix was proportional to genome-wide identity by state [ 18].
The model included a random polygenic effect for which the variance-covariance matrix was proportional to genome-wide identity-by-state.
The closeness of the variance-covariance matrix implied by the hypothetical model to the empirical variance-covariance matrix is evaluated through goodness-of-fit indices, including maximum likelihood chi-square values/degrees of freedom ratio, the comparative fit index (CFI), the root mean square errors of approximation (RMSEA), and the non-normed fit index (NNFI).
The variance-covariance for each model was assumed to be block diagonal but unstructured within a block defined by subjects.
This method is equivalent to the variance-covariance estimator presented by Barlow (35).
A closed form formula of the variance-covariance matrix is derived for a Gaussian model.
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