Dear Mengzhu, If you want to test the hypothesis that the three levels are ordered, your three options are:
1) Helmert coding (assuming a balanced design, contrast 1 will compare mean(B) vs. mean (C), contrast 2 will compare mean(A) vs. mean(B, C)) 2) Sliding contrast coding (contrast 1 will compare mean(B) vs. mean (C), contrast 2 will compare mean(A) vs. mean(B)). *<-- I think this is the strongest test of strict ordering.* 3) Polynomial coding (brrr, not preferred for this) For any of these, you'd code the three cells as thee conditions of the same factor, rather than as an interaction of two factors. For sliding contrast coding, see Zach Burchill's zplyr: https://rdrr.io/github/burchill/zplyr/man/contr.slide.html More generally, for coding schemes you might find the following tutorial from Maureen Gillespie helpful: https://hlplab.wordpress.com/2010/05/10/mini-womm/ Florian On Wed, Aug 22, 2018 at 9:23 AM John Kingston <jkings...@linguist.umass.edu> wrote: > Dear Mengzhu, > > You might try Helmert contrasts: > > > Scondition pro syn > > > > canonO 0 -0.667 > > > > ScleftO -0.5 0.333 > > > > ScleftS 0.5 0.333 > > pro would then capture the difference between sentences with vs without > prosodic focus, that both have syntactic focus, and syn would capture > the difference between sentences with vs without syntactic focus. Note > that the choice of sign is arbitrary. > > Best, > John > > On 2018-08-22 04:58, Mengzhu Yan wrote: > > 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 > > [1]) 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 > > [2]), 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 > > > > > > Links: > > ------ > > [1] > > > https://stats.idre.ucla.edu/r/library/r-library-contrast-coding-systems-for-categorical-variables/#dummy > > [2] > > > https://stats.stackexchange.com/questions/241248/help-with-unbalanced-2x3x4-factorial-ancova/241525#241525 > > -- > John Kingston > Professor > Linguistics Department > University of Massachusetts > Integrative Learning Center N412 > 650 N. Pleasant St. > Amherst, MA 01003 > 1-413-545-6833 <(413)%20545-6833>, fax -2792 > jkings...@linguist.umass.edu > http://blogs.umass.edu/jkingstn/ >
