The difference in deviances of the two models was compared with a χ-distribution with five degrees of freedom.
When the degrees of freedom for the smoothed term were near their minimum value, we examined whether the trend was described sufficiently by a linear regression using Akaike's information criterion (AIC) and analysis of deviance between the two models.
As with the MMN response, peak latencies were submitted to analysis to test for differences in rate of processing deviance detection between the two groups.
The percentage of the deviance explained by the two factor model in continent and trend varied between analyses, from over 80% for all lung cancer and for adeno in females, to under 25% for squamous in males.
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).
Firstly, we evaluated the deviance information criterion between the two sets of analyses, which favoured random effects models.
Indeed, when the Fis value indicated no significant deviance from HWE with the two classes of markers, the significant Fit value (mainly due to between species differentiation with a high positive Fst value) is close to double for the CHom markers (0.80/0.40 for Fit and 0.80/0.45 for Fst).
The difference in deviance of two nested models has a χ2 distribution with degrees of freedom equal to the number of additional parameters in the larger model.
The difference in deviance of two models can be used as a test statistic with a χ distribution, with the number of different parameters as the degrees of freedom (Hayes 2006).
Analysis of deviance was performed comparing the log-likelihood ratio estimates of the two models.
Of the two alkaline phosphatase genes, phoX had a significant relationship with Pi concentration (p-value = 0.003, deviance F-test, d.f. = 37), but phoA did not (p-value = 0.313, deviance F-test, d.f. = 37).
