Dear All,
I’m quite new to Bayesian statistics and brms and would appreciate some help with some (hopefully not too stupid) questions.
Background: I am working with some facial expression data. In the experiment, two groups of participants watched six brief videos (2 positive, 2 negative, 2 neutral), and the intensity of facial affect was recorded during the task. As a result, I have three facial affect intensity time series for each participant. The facial affect intensity values are bounded between 0 and 1. Total N = 134 (control N = 64, patient N = 70).
The facial expression data has a non-linear relationship with time, so I thought a GAMM with zero-one inflated beta family would be a good option. I am interested in an interaction between group and video category:
res_1 <- brm(data = data2,
family = zero_one_inflated_beta(),
bf(facial_affect ~ 1 +
group*video +
s(time, by = interaction(group,video), bs = "cr", k = 15) +
(1 | ID)))
Question 1: The duration of the videos varies, and therefore so does the length of the facial affect times series. The longest time series is 161 time points and the shortest is 123 time points. Is this a problem with GAMMs?
Question 2: I keep running into low bulk and tail ESS with the intercept and group.
Family: zero_one_inflated_beta
Links: mu = logit; phi = identity; zoi = identity; coi = identity
Formula: facial_affect ~ 1 + group * video + s(time, by = interaction(group, video), bs = "cr", k = 15) + (1 | ID)
Data: data2 (Number of observations: 110524)
Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
total post-warmup draws = 4000
Smoothing Spline Hyperparameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
sds(stimeinteractiongroupvideoAN.negative_1) 0.02 0.01 0.00 0.04 1.00 1102
sds(stimeinteractiongroupvideoHC.negative_1) 0.01 0.01 0.00 0.03 1.00 1167
sds(stimeinteractiongroupvideoAN.neutral_1) 0.02 0.01 0.01 0.03 1.00 1273
sds(stimeinteractiongroupvideoHC.neutral_1) 0.02 0.01 0.01 0.04 1.00 1556
sds(stimeinteractiongroupvideoAN.positive_1) 0.10 0.03 0.07 0.17 1.01 1048
sds(stimeinteractiongroupvideoHC.positive_1) 0.06 0.02 0.04 0.11 1.00 1144
Tail_ESS
sds(stimeinteractiongroupvideoAN.negative_1) 1515
sds(stimeinteractiongroupvideoHC.negative_1) 1072
sds(stimeinteractiongroupvideoAN.neutral_1) 1897
sds(stimeinteractiongroupvideoHC.neutral_1) 1862
sds(stimeinteractiongroupvideoAN.positive_1) 1834
sds(stimeinteractiongroupvideoHC.positive_1) 1868
Multilevel Hyperparameters:
~ID (Number of levels: 134)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 0.75 0.05 0.66 0.84 1.02 384 768
Regression Coefficients:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept -3.31 0.09 -3.48 -3.12 1.01 230 395
groupHC -0.01 0.13 -0.26 0.24 1.01 202 367
videoneutral 0.06 0.01 0.04 0.08 1.00 3037 2972
videopositive 0.34 0.01 0.32 0.36 1.00 4017 2989
groupHC:videoneutral 0.03 0.02 -0.00 0.07 1.00 2998 3040
groupHC:videopositive 0.27 0.02 0.24 0.30 1.00 3994 2467
stime:interactiongroupvideoAN.negative_1 -0.01 0.00 -0.02 -0.00 1.00 3804 3071
stime:interactiongroupvideoHC.negative_1 -0.03 0.00 -0.03 -0.02 1.00 4893 3544
stime:interactiongroupvideoAN.neutral_1 -0.02 0.01 -0.05 -0.00 1.00 2189 2628
stime:interactiongroupvideoHC.neutral_1 -0.01 0.01 -0.04 0.01 1.00 2149 2709
stime:interactiongroupvideoAN.positive_1 0.04 0.00 0.03 0.04 1.00 4575 3758
stime:interactiongroupvideoHC.positive_1 0.06 0.00 0.06 0.07 1.00 4448 3275
Further Distributional Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
phi 16.49 0.10 16.29 16.68 1.00 8862 2882
zoi 0.37 0.00 0.37 0.37 1.01 8463 2184
coi 0.00 0.00 0.00 0.00 1.00 6242 2576
I’ve tweaked the priors, but that doesn’t seem to do much to help. I’ve tried simplifying the model by removing the interaction from the smooth term and the fixed effects entirely, but that doesn’t fix the issue. Removing all fixed effects and the interaction seems to make the intercept ESS issue worse. Increasing the number of iterations helps a little but doesn’t remove the problem. I also tried analysing facial affect from just one video only in case the different durations was causing the problems, but the low ESS issue was still there. Does anyone have ideas what could be causing this or how to address it?
Question 3: The pairs plot shows quite strong correlations between the fixed effect slopes and also between the group slope and the intercept. I tried analysing data from just one video with only group as a fixed effect and still ended up with high correlation between group slope and the intercept.
Does this mean there is multicollinearity happening, or is there something else wrong?
I suspect my questions might be related, but I can’t figure out what the underlying cause is. Any ideas would be greatly appreciated!
Thank you, and apologies for the very long post!
- Operating System: MacOS
- brms Version: 2.22.0