# Cross-classified multilevel model with lagged dependent variable Using R

I am a bit stuck with my model and I wonder if this is even possible using R. Basically I want to use a lagged dependent variable (LDV) in a cross-classified multilevel model (MLM). Following remarks by Allison and others (e.g., https://statisticalhorizons.com/lagged-dependent-variables ) I am assuming that using an LDV in a MLM leads to a bias in which the fixed effect of the LDV is overestimated and other effects underestimated. This seems to be due to a non-zero correlation among the LDV and the random effects in the MLM. Apparently there are ways to model this correlation/dependency explicitly in Stata or when using simpler designs (e.g., two-level MLMs; https://statisticalhorizons.com/wp-content/uploads/AllisonEtAl-Socius2017.pdf ) in R. However, I found no examples on how to do this with more complex designs in R such as mine.

My research question & dataset:

• I want to predict school grades at time = t + 1 from school grades at time = t in interaction with teacher feedback at time = t.
• I have 6 measurement times per student (i.e., random intercepts for students)
• Students are clustered within classes; classes change at each measurement point so are treated as a new class at each measurement point (i.e., random intercepts for class)

I’ve been fitting this MLM using the brm function in R’s brms package (lme4 notation):

grade(t+1) ~ grade*feedback*time + (1 + grade*feedback*time | student) + (1 + grade*feedback | class)


I would be very thankful for any help on how to model the LDV in this MLM. If you could point me to an R code example that would be even greater!