My research question is: is the rate of forgetting (slope) influenced by the degree of encoding? So I have three encoding degrees and three time intervals in which I test people using different items.
Hence, what I need to know is if there is an interaction between the degree of encoding and time interval.
My items are 48 words, and I test 16 different ones at each time interval.
First, I fitted a model like this:
model1 <- brm( correct | trials(total) ~ 1 + time * encoding + ( 1 + encoding | ID ), data = data, family = binomial("logit"), file = "model1" )
But then, I realised I need to consider that there will be heterogeneity between the items because some are easier to remember than others. So instead of averaging across items (that will be very much like doing an ANOVA?) I tried to use the 0s and 1s (correct and incorrect responses) to fit another model:
model2 <- brm( correct ~ 1 + time * encoding + ( 1 + time | ID ) + (1 + time + encoding | item), data = databinom, family = bernoulli(), file = "model2" )
I was happy with this, but reading a vignette in brms, I found a comment about a model like this that says: this model completely ignores the guessing probability and will thus likely come to biased estimates and predictions.
However, the words I use don't have 50% chance of being right, because it's not a recognition test. They literally have to write the word down to consider it correct.
All of the above raises the question, do I want to use the binomial family and just forget about the fact that the items are all different? Or should I use the Bernoulli one, which then will tell me the probabilities of getting each item right or wrong, but nothing about the rate of forgetting, which is the number out of 16 that the subjects get correct at the three time intervals.