Dear ling-R-lang-lers,
I am trying to run interactions in linear mixed models with an incomplete factorial design (I do not have all combinations of the factors). I have three sentence conditions (Scondition), and I dummy coded (see summy coding here: https://stats.idre.ucla.edu/r/library/r-library-contrast-coding-systems-for-categorical-variables/#dummy) them as 'pro' and 'syn' as below. But there is no [+pro, -syn] case. I got the warning "fixed-effect model matrix is rank deficient so dropping 2 columns / coefficients" when I included the interaction between pro and syn in the model (the warnings disappeared right away when excluding the interaction). But the interaction was exactly what I am interested. Scondition pro syn canonO 0 0 ScleftO 0 1 ScleftS 1 1 (pro means prosodic focus, syn means syntactic focus. canonO has no focus; ScleftO has only syntactic focus; ScleftS has both syntactic and prosodic focus) I came across this post (https://stats.stackexchange.com/questions/241248/help-with-unbalanced-2x3x4-factorial-ancova/241525#241525), which was similar to my problem. I got NAs for the pro:syn interaction when running step() function to identify non-significant variables. So I am looking for some other way to explore the relationship between syntax and prosody since the dummy coding does not work for the interaction due to the incomplete factorial design. I am also thinking of analysing the sentence conditions as ordered effects (no focus, one focus, two foci maybe?), as the three sentence conditions have no focus, only syntactic focus and both syntactic and prosodic focus. But it does not represent the interaction between prosody and syntax very well. Any help would be appreciated. Thank you for your time. Please do not hesitate to contact me if you need further details. Thanks a lot, Mengzhu
