mgcv::gam(): NA parametric coefficient in a model with two categorical variables + model interpretation
Q1: It looks like the model is not fully identifiably given the data and as a result igcCAT.ideo has been set to zero - there is no sensible test to conduct with such a term, hence the NAs in the test stat an p-value fields. Q2: A separate (centred) smooth is estimated for each level of igc. If you want a baseline (igcCAT.pseudo) smooth, and difference smooths for the rest of the levels of igc then you need to set igc to be an ordered factor, and use something like... ~ igc + s(ctrial) + s(ctrial,by=igc) - see section on `by' variables in ?gam.models. best, Simon
On 22/05/16 23:29, Fotis Fotiadis wrote:
Hallo all I am using a gam model for my data. m2.4<-bam(acc~ 1 + igc + s(ctrial, by=igc) + shape + s(ctrial, by=shape) + s(ctrial, sbj, bs = "fs", m = 1) , data=data, family=binomial) igc codes condition and there are four levels (CAT.pseudo, CAT.ideo,PA.pseudo, PA.ideo), and shape is a factor (that cannot be considered random effect) with four levels too (rand21, rand22, rand23, rand30). Here is the summary of the model
summary(m2.4)
Family: binomial
Link function: logit
Formula:
acc ~ 1 + igc + s(ctrial, by = igc) + shape + s(ctrial, by = shape) +
s(ctrial, sbj, bs = "fs", m = 1)
Parametric coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 3.5321 0.1930 18.302 < 2e-16 ***
igcCAT.ideo 0.0000 0.0000 NA NA
igcPA.ideo -0.3650 0.2441 -1.495 0.1348
igcPA.pseudo -0.2708 0.2574 -1.052 0.2928
shaperand22 -0.1390 0.1548 -0.898 0.3693
shaperand23 0.3046 0.1670 1.823 0.0682 .
shaperand30 -0.5839 0.1163 -5.020 5.16e-07 ***
---
Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
Approximate significance of smooth terms:
edf Ref.df Chi.sq p-value
s(ctrial):igcCAT.pseudo 3.902 4.853 74.787 1.07e-14 ***
s(ctrial):igcCAT.ideo 2.293 2.702 13.794 0.001750 **
s(ctrial):igcPA.ideo 1.000 1.000 11.391 0.000738 ***
s(ctrial):igcPA.pseudo 3.158 3.815 20.411 0.000413 ***
s(ctrial):shaperand21 2.556 3.316 31.387 1.46e-06 ***
s(ctrial):shaperand22 1.000 1.000 0.898 0.343381
s(ctrial):shaperand23 2.304 2.850 6.144 0.118531
s(ctrial):shaperand30 4.952 5.947 27.806 0.000144 ***
s(ctrial,sbj) 221.476 574.000 1502.779 < 2e-16 ***
---
Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
Rank: 652/655
R-sq.(adj) = 0.405 Deviance explained = 43.9%
fREML = 24003 Scale est. = 1 n = 18417
I am not sure how this model works, but I guess it creates four smooths for
each level of condition, and four smooths for each level of shape.
There is also the intercept of the model, set at the reference level of
condition (CAT.pseudo) and at the reference level of shape (rand21). Each
parametric term represents the difference of each level of each of the two
factors from the intercept.
I have two questions
Q1:
Does anyone now why I get NA results in the second line of the parametric
terms?
Q2:
The term igcCAT.ideo denotes the difference in the intercept between
(A): condition=igcCAT.ideo, and
(B): (condition=igcCATpseudo ) &(shape=rand21).
But what is the value (level) of shape for (A)?
Is it the reference level? Or is it, perhaps, the "grand mean" of the shape
variable?
Thank you in advance for your time,
Fotis
Simon Wood, School of Mathematics, University of Bristol BS8 1TW UK +44 (0)117 33 18273 http://www.maths.bris.ac.uk/~sw15190