[R-sig-ME] Comparing Odds ratios in two different binomial GLMM

[Tibor Kiss]

Dear list,

I have a question concerning the comparison of two binomial GLMMs (random intercept models) with partially different factors. I am investigating possible syntactic realizations of German prepositions (English: "on the bus" etc.). The question emerges from my comparison of a model for the preposition *mit* (with) and *unter* (under), for reference, the glmm at calls are provided below. 

The two GLMMs have a factor in common with seven levels (nominal_dep_mod), where the levels describe whether the noun in the phrase ("bus" in the example above) shows an extension or not (like – somewhat artificially – "on the bus straight out of Compton"). I would like to compare the odds ratios for this common factor, and if I just compare them, then the results are what I would expect from looking into the data:  for one of the prepositions one level of nominal_dep_mod has a much stronger influence than for the other preposition: an odds ratio of 64 vs. an odds ratio of 4, while the other levels are on a par. Simplifying things somewhat, the  factor nominal_dep_mod determines whether the presence of an extension makes the realization of a determiner (*the*) more or less likely. So for one preposition, it makes it much more likely, while for the other, it makes it just more likely. 

The contrasts for both models are set so that nominal_dep_mod starts with the same reference level (no extension). 

But the other fixed effects for the two models differ, partly because the interpretation of the prepositions play a role, and the possible interpretations of *with* differ from the ones for *under*. Furthermore, the model for *mit* has more fixed effects than the other one, and the fixed effects have more (and different) levels  – and naturally, the random effects differ in number, as well in their contribution to the models.  

I have added the two calls as well as the xtabs for nominal_dep_mod for reference. 

My perhaps somewhat basic question is: Given the two models, am I justified to assume the interpretation of the odds ratio given above?

Thanks a lot.

With kind regards

Tibor


> unter.050315.glmm at call
glmer(formula = determiner ~ nominal_dep_mod + adja_in_hit + 
    TN_LEX_nominalisierung + prep_meaning + (1 | target_noun_lemma), 
    data = unter.050315.data, family = binomial(), contrasts = list(prep_meaning = contr.treatment(levels(unter.050315.data$prep_meaning), 2), 
    nominal_dep_mod = contr.treatment(levels(unter.050315.data$nominal_dep_mod), 4)))  

> xtabs(~prep_meaning, unter.050315.data)
prep_meaning
konditional       lokal       modal     regiert  restriktiv   zuordnung     zustand 
        363        3026         759          63         101        1003          23 

> mit.050315.glmm at call
glmer(formula = determiner ~ adja_in_hit + nominal_dep_mod + 
    TN_LEX_nominalisierung + prep_meaning + TN_LEX_GN_Kommunikation + 
    TN_LEX_GN_Besitz + TN_LEX_GN_Attribut + TN_LEX_GN_Geschehen + 
    (1 | target_noun_lemma), data = mit.050315.data, family = binomial(), 
    contrasts = list(prep_meaning = contr.treatment(levels(mit.050315.data$prep_meaning), 14), nominal_dep_mod = contr.treatment(levels(mit.050315.data$nominal_dep_mod), 4)))

> xtabs(~prep_meaning, mit.050315.data)
prep_meaning
abhaengigkeit   beteiligung   bezugspunkt     indikator   konditional korrespondenz         modal   realisation       regiert    restriktiv 
           52           3346           441                    204           733             1                             4826           361          3298            26 
stellungnahme      temporal       vorgang vorhandensein     zuordnung 
           30               69                 439          3582                  10 




   	 	
Prof. Dr. Tibor Kiss, Sprachwissenschaftliches Institut
Ruhr-Universität Bochum D-44780 Bochum
Office: +49-234-322-5114

 


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