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The criteria used to end the search were: [a] simple parametric expression, [b] the corresponding function introduced as a transform in the Cox model satisfying the GAM linearity test, and [c] without deteriorating the model fit as assessed by the sum of squares of "deviance residuals" [ 8].
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Models fit to the data were compared by chi-square analysis of deviance.
Statistical significance of a coefficient was tested under full maximum likelihood (ML) estimation, using a Chi-square test of deviance.
Statistical significance of fixed effects was tested by comparing the goodness of fit of different models using a chi-square test of deviance.
Statistical significance was tested by comparing the goodness of fit of a model with, and without the variable, using a chi-square test of deviance.
To handle over-dispersion in the outcome distribution, a scale parameter, estimated by the square root of deviance divided by degrees of freedom, was used to adjust the regression.
This was achieved by minimizing the square of the deviance of our data points to the decay function, searching the parameter space with the assumption of a constant rate of decay.
Chi-square tests from analyses of deviance comparing models with and without the smooth exposure term were performed, and no statistical departures from linearity were apparent at a p < 0.05 level of significance.
Energetic status was the most important factor in predicting the cause of death, with regional and seasonal differences (analysis of deviance, chi-square test for differences between models, terms added sequentially, p < 0.05).
Significance was assessed against the null model by chi squared test of residual deviance, goodness-of-fit by unweighted sum of squares test, and predictive ability by calculation of the c-statistic.
Levels of significance of GLM model fits were tested using analysis of deviance with chi-square distribution.
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CEO of Professional Science Editing for Scientists @ prosciediting.com