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The overdispersion parameter (c-hat) was calculated as the ratio between the mean deviance of simulated models and the deviance of the observed model [18].
15 We also plotted the posterior mean deviance of the individual data points in the inconsistency model against their posterior mean deviance in the consistency model to identify any loops where inconsistency was present (see online supplementary appendix 11).
In addition to this optimal model, we also considered a parsimonious LASSO model with a higher penalty parameter (hereafter called LASSO-se) so that the mean deviance of the model was within one standard error of the LASSO-max average deviance [ 28, 32].
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To account for overdispersion in the data quasi-F tests were performed by calculating ratios of mean deviance changes [34].
This consists of the posterior mean deviance and a term referred to as the "effective number of parameters" (pD) that accounts for a penalty for over-parameterization of the model.
We used the posterior mean deviance as a Bayesian measure of fit or model adequacy as defined by Spiegelhalter et al. [20].
This criterion, an Akaike-like criterion for Bayesian models, assesses the goodness-of-fit of a model using posterior mean deviance.
The first fit of the log linear model (Model 1) found that patch contributed the greatest effect (LRT6 = 1891.405, mean deviance >1; p<0.0001), but a large proportion of the residual variance remained unexplained (Table 2).
Here, p D is given by −D (the posterior mean deviance minus the deviance at the posterior mean) and is interpreted as the effective number of model parameters.
The residual mean deviance was 0.108 and the misclassification rate was 15%.
Again, we ran each parameter set three times and calculated the mean deviance.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com