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We evaluate significance by computing the deviance statistic (minus 2 times the log-likelihood; change in deviance is distributed as chi-square, with degrees of freedom equal to the number of parameters deleted from the model) and with the help of 10,000 samples from the posterior distributions of the coefficients using Markov chain Monte Carlo sampling.
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We compared the linear and spline models by computing the difference between the deviances of the fitted two models (Dominici et al. 2002; Samoli et al. 2005).
The likelihood ratio test computes the deviance between two nested models.
We then computed the deviance of the fitted model and summed the deviances for that given threshold over all cities.
To look for this time period, the function 'sensitivity.analysis' systematically computes the deviance R-squared statistic over a range of time periods chosen by the user.
We then computed the deviance of the fitted model for all cities for a given threshold value, and the average deviance for that threshold over all cities.
For each permutation, we ran the GAM using the optimal span of the original data and computed the deviance statistic.
Best fit was identified by computing deviance statistics (G), corresponding p values (p), the likelihood-ratio statistic between deviances for candidate models, and the Akaike Information Criterion AICC).
Model fit was appraised by computing and comparing estimates for deviance and information criterion.
The statistical significance of a logistic regression result was obtained by comparing the deviance with the 'null deviance'.
c The significance of the factor is assessed by comparing the deviance for the model including that factor and the deviance for the null (no factor) model and is indicated by *p<0.05 ***<0.01 *** p<0.001.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com