Hello, I have a couple of years experience with GAMMs and I have run several complex models that have shown some really nice time course effects - well controlled structures too. In a new study, I have what seems like a straightforward Q, but I'd like a bit of insight if possible.

I'll keep the Nature of data simple to reflect the simplest model for which I am experiencing an issue. It is an eye tracking visual world paradigm where we measure whether participants are looking at one character performing an action on another. A narration is either congruent or incongruent to the visual.

Predictor manipulations: 1. Time course (continuous 0 to 2000ms), 2. Congruent (vs incongruent).

Response variable: Proportions of looks to character A (the actor in the language narration) minus proportion of looks to to character B (the receiver/patient in the language narration). [Elogits].

As I say in the Q header: I'm doing a GAMM time course analysis: A sig difference is indicated via Parametric coefficients (= constant difference), but the smooth terms for that condition does not improve model fit. It is quite rare that it occurs that way around, right?

This is the output for the model with the congruent smooth term kept in:

# Parametric coefficients:

# Estimate Std. Error t value Pr(>|t|)

# (Intercept) 1.5851 0.3524 4.498 6.89e-06 ***

# congruentIncongruent_narration -2.3084 0.4045 -5.707 1.16e-08 ***

# ---

# Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

#

# Approximate significance of smooth terms:

# edf Ref.df F p-value

# s(Time):congruentCongruent_narration 4.340 5.432 1.497 0.1358

# s(Time):congruentIncongruent_narration 1.012 1.017 0.071 0.7908

# s(Time,Subject) 257.393 512.000 2.068 1.29e-11 ***

# s(Time,Item) 24.397 44.000 1.882 0.0093 **

# s(Event) 140.766 257.000 2.944 < 2e-16 ***

# s(Time,Event) 114.655 257.000 2.227 < 2e-16 ***

# ---

# Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

#

# R-sq.(adj) = 0.458 Deviance explained = 46.8%

# -ML = 48402 Scale est. = 11.671 n = 28749

So the PCs show a constant difference such that, relative to the congruent condition, the incongruent condition has fewer looks to "character A".

The relevant smooth terms are non-significant: this would suggest that neither the congruent or incongruent conditions differ from zero at any point in time. Fittingly, when I remove them ["s(Time):congruent"] from the model, the term does not improve the fit. HOWEVER, my issue is that the visual of the smooths show that their confidence intervals do not overlap with zero (see attached). So that alone should mean they should be significant in the summary stats, right? In the past that has been the case for me, so I have not had to think twice about it. Also, the difference plot showed they were sig different throughout the whole time course. Is it just the case that all the variance of the congruent vs incongruent levels is explained alone by the constant difference (PCs)? Looking at the time course modulation of congruent (curve with time), I'd think that should not be the case?

I'll add that the residuals look good via gam.check. I've also run binary predictor model: it was a significant difference - of course, that could be the constant difference OR non-linear difference ... so I did an ordered factor model, which suggest both are driving the difference:

# Parametric coefficients:

# Estimate Std. Error t value Pr(>|t|)

# (Intercept) 0.4577 0.2846 1.608 0.108

# congruentOrd.L 1.6814 0.2928 5.742 9.47e-09 ***

# ---

# Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

#

# Approximate significance of smooth terms:

# edf Ref.df F p-value

# s(Time) 1.017 1.023 0.096 0.7584

# s(Time):congruentOrd1 4.457 5.572 2.370 0.0243 *

# s(Time,Subject) 276.129 512.000 2.504 8.24e-15 ***

# s(Time,Item) 24.531 44.000 1.959 0.0112 *

# s(Event) 144.481 257.000 3.334 < 2e-16 ***

# s(Time,Event) 118.989 257.000 2.587 < 2e-16 ***

# ---

# Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

#

# R-sq.(adj) = 0.482 Deviance explained = 49.2%

# -ML = 48098 Scale est. = 11.502 n = 28630

Based on that info as a whole: can anyone provide insight into why the smooths of the original model were non-sig, and did not improve the fit of the model, whilst PCs were sig?

Thank you! It's a headscratcher for me, and I haven't been able to find published similar examples that would help.