I have a time-series data set that contains an outcome variable which is continuous and two factor predictors (one with 6 levels and one with 2 levels).
I would like to model the non-linear interaction of the two factor variables on the continuous variable.
This is the model I have so far:
library(mgcv)
model <- bam(
outcome ~
factor_1 + factor_2 +
s(time, k = 9) +
s(time, by = factor_1, k = 9) +
s(time, by = factor_2, k = 9),
data = df
)
summary(model)
Family: gaussian
Link function: identity
Formula:
outcome ~ factor_1 + factor_2 + s(time, k = 9) + s(time, by = factor_1,
k = 9) + s(time, by = factor_2, k = 9)
Parametric coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2612.72 23.03 113.465 <2e-16 ***
factor_1b 33.19 27.00 1.229 0.22
factor_2z -488.52 27.00 -18.093 <2e-16 ***
---
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) 2.564 3.184 6.408 0.000274 ***
s(time):factor_1b 1.000 1.001 0.295 0.587839
s(time):factor_2z 2.246 2.792 34.281 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
R-sq.(adj) = 0.679 Deviance explained = 69.1%
fREML = 1359.6 Scale est. = 37580 n = 207
Now I would like to add a non-linear interaction of factor_1 and factor_2 with time for the effect on outcome, so that the smoothers in every combination could differ (for example: factor_2 has a stronger non-linear effect for some levels of factor_1). Something like s(time, factor_1, factor_2) or s(time, factor_1, by = factor_2) does not work.
Including an interaction of two factors using interaction() seems to do the job.
library(mgcv)
# The following assumes factors are ordered with treatment contrast.
model <- bam(
outcome ~
interaction(factor_1, factor_2) +
s(time, k = 9) +
s(time, by = interaction(factor_1, factor_2), k = 9),
data = df
)