We are using GAM in mgcv (Wood), relatively new users, and wonder if anyone can advise us on a problem we are encountering as we analyze many short time series datasets. For each dataset, we have four models, each with intercept, predictor x (trend), z (treatment), and int (interaction between x and z). Our models are
Model 1: gama1.1 <- gam(y~x+z+int, family=quasipoisson) ##no smooths Model 2: gama1.2 <- gam(y~x+z+s(int, bs="cr"), family=quasipoisson) ##smooth the interaction Model 3: gama1.3 <- gam(y~s(x, bs="cr")+z+int, family=quasipoisson) ##smooth the trend Model 4: gama1.4 <- gam(y~s(x, bs="cr")+z+s(int, bs="cr"), family=quasipoisson) ##smooth trend and interaction We have three questions. One question is simple. We occasionally obtain edf =1 and Ref.df=1 for some smoothed predictors (x, int). Because Wood says that edf can be interpreted roughly as functional form (quadratic, cubic etc) + 1, this would imply x^0 functional form for the predictor, and that doesn't make a lot of sense. Does such a result for edf and rdf indicate a problem (e.g., collinearity) or any particular interpretation? The other two questions concern which model fits the data best. We do look at the usual various fit statistics (R^2, Dev, etc), but our question concerns using the anova function to do model comparisons, e.g., anova(gama2.1,gama2.2, test="Chisq"). 1. Is there research on the power of the model comparison test? Anecdotally, the test seems to reject the null even in cases that would appear to have only small differences. These are not hugely long time series, ranging from about 17 to about 49, so we would not have thought them to yield large power. 2. More important, in a few cases, we are getting a result that looks like this: anova(gamb1.1,gamb1.2, test="Chisq") Analysis of Deviance Table Model 1: y ~ x + z + int Model 2: y ~ x + z + s(int, bs = "cr") Resid. Df Resid. Dev Df Deviance P(>|Chi|) 1 30 36.713 2 30 36.713 1.1469e-05 1.0301e-05 6.767e-05 *** We are inclined to think that the significance p value here is simply a result of rounding error in the computation of the df difference and deviance difference, and that we should treat this as indicating the models are not different from each other. Has anyone experienced this before? Is our interpretation reasonable? Thanks to anyone who is able to offer advice. Will Shadish -- View this message in context: http://r.789695.n4.nabble.com/GAM-Chi-Square-Difference-Test-tp4636523.html Sent from the R help mailing list archive at Nabble.com. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
