I'm looking to run a linear mixed effect model using lme4, where my dependent variable
one_syllable_words / total_words_generated is a proportion and my random effect
(1 | participant_ID) reflects the longitudinal nature of the design. Independent, fixed effect variables of interest include
timepoint, and interactions between them.
I've come across two main ways to deal with the proportional nature of the DV:
Standard logistic regression / binomial GLM
In my scenario, I envision the lme4 equation looking like this:
glmer(one_syllable_words / total_words_generated ~ age + group + timepoint + age:timepoint + age:group + timepoint:group + (1 | participant_ID), family = "binomial", weights = total_words_generated, data = mydat)
I would apply a transformation to my DV
(DV * (n - 1) + .5)/ n)so that it cannot equal 0 or 1. (There are a few instances where it equals zero, no instances where it equals one.)
I'm unclear whether logistic regression or beta regression is preferred in this example. My DV isn't a clear-cut case of successes and failures (unless we stretch the definition of "success"), so I'm worried logistic regression might not be appropriate. However, I'm having trouble getting a firm grasp on beta regression & all it entails. If beta regression is preferred:
- Why is it preferred?
- What is it doing "behind the scenes" to the data?
- How can it be applied in R?