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In a few cases was a negative binomial model did not converge at a specified limit (ie, the relative Hessian convergence criterion was greater than 0.0001), a Poisson model that converged normally and provided similar estimates was used instead.

The reconstruction procedure was repeated with a different starting model that converged to a similar reconstruction.

In general, a model that converged with a successful covariance step was considered for further analysis, whereas one with any correlation of parameter estimates >0.95 was rejected as a preliminary model for subsequent model development.

Although statistical comparison provided support only for lower-rank models for all G matrices (Table S4), we used the highest-rank model that converged in all subsequent analyses, for the reasons described in Materials and Methods and File S1.

MrBayes v3.1.2 [ 49], also on the CIPRES portal v2.2, was run for 2 million generations, sampling every 100 generations, with 2 parallel runs of 8 chains each, using a gamma rate distribution with a mixed model that converged on WAG with a posterior probability of 0.99 for both data sets.

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In italics, we report the models that converged but the Hessian matrix was not positive definite.

(B ) A posterior sample of antigenic locations from an equivalent BMDS model that has converged on the alternative solution.

q2: frequency of the risk allele 2; f12, f22, f22: penetrances of genotypes 11, 12 and 22. No.: No. of independent parameters estimated = (no. of parameters in the model - no. of paramodel - not converged to a boundary); lnL: log-likelihood; AIC: Aikaike criterion (-2 lnL + 2 No).

This was critical, as it increased the number of models that converged from roughly 10% (when 1 μM was used uniformly) to nearly 100%.

However, all models converged for our primary sample of all patients with hospital admissions and the results were consistent with those from the models that converged in the disease-specific samples.

Recent developments of algorithms such as integrated nested Laplace approximations (INLA), 100 however, offer opportunities for developing spatial-temporal models that converge rapidly without loss of predictive accuracy and can be run on an ordinary desktop.

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