[R-sig-ME] contradictory odds ratios--a problem with the equation or the interpretation?

[Ben Bolker]

    I don't know, but ... these are very small differences both 
absolutely (odds ratio of 0.4 vs 0.5) and in terms of the confidence 
intervals on each parameter (0.01-0.12 for Mandarin, even wider for 
Spanish).  A lot of the variation among language groups will also be 
included in the 'participant' random effect (since participants are 
effectively nested within language groups).

   If you look at the participant-by-participant predictions (i.e. 
including both the language group and the participant-level random 
effect in the prediction) do the results make more sense?

   Tangentially a little worried about your very high odds ratio for the 
intercept. At the baseline level your subjects have a probability of 
approximately 1-4e-26 (from plogis(58.45, lower.tail=FALSE)) of correct 
association?  Do you have a continuous predictor whose values are far 
from zero so that the model baseline doesn't make sense? This should be 
independent of the other issues, but makes me wonder if you have 
complete separation and/or other sources of numerical instability lurking?

On 5/10/21 1:15 PM, Johnathan Jones wrote:
> Hi all,
> 
> I’m running a generalized linear mixed model in R (4.0.3) and while most
> findings are in-line with what could be expected, I’m getting one that’s
> off. Either I’m mixing something up in my equation or there’s a reasonable
> explanation for my results that I’m not seeing. I'm hoping someone here
> might be able to diagnose the issue.
> 
> 
> *Background*
> 
> I am researching speech perception in second languages (n = 53, 48 items).
> Specifically, I am investigating how well a person's ability to accurately
> perceive words spoken in isolation predicts their ability to perceive words
> spoken in sentences.
> 
> Different language groups have different language transfer issues which
> complicate things.
> 
> Also impacting perception is association--whether you associate the word
> with its sentence context.
> 
> 
> *Variables of interest*
> 
> Outcome variable (Y): perception of a word in a sentence
> 
> Predictor variables:
> 
> - iso1: the participant’s estimated ability to identify a word in isolation
> (a performance score. I’ve used raw and Rasch standardised scores here to
> see if results would change. No dice).
> 
> - iso2: the participant’s estimated ability to discriminate between
> isolated words in sequences (a performance score, as described in iso1).
> 
> - language: what language group the participant is from. Languages include
> English, Mandarin, and Spanish (note: Mandarin consistently outperforms
> Spanish in raw and standard scores]
> 
> - association: whether the participant associates the target word in the
> sentence with the sentence. Association levels include same, different, and
> neutral (it's a little more nuanced, but this communicates what's
> necessary).
> 
> Random variables: participant and item.
> 
> Equation: Y ~ iso1 + iso2 + language + association + (1|participant) +
> (1|item)
> 
> 
> *Outputs *(via sjPlot)
> 
> Predictor                             Odds ratio         CI
> 
> (Intercept)                            58.45                 18.47-184.90
> 
> 
> - Iso1:                                    1.02                   1.00-1.03
> 
> - Iso2:                                    1.03                   1.01-1.04
> 
> - Association [same]:          2.44                   0.23-0.49
> 
> - Association [different]:     0.34                  1.64-3.61
> 
> - Language [Mandarin]:      0.04                  0.01-0.12
> 
> - Language [Spanish]:          0.05                  0.01-.18
> 
> 
> 
> The good from the output:
> 
> Association works out. Participants have greater log odds of obtaining a
> correct answer when they associate the word with its sentential context.
> Not associating the word with the context tends to lead to misperception.
> There is a pretty large effect here.
> 
> The bad from the output:
> 
> Language is yielding opposite results than expected. The Spanish group has
> an odds ratio of .05 while the Mandarin group has an odds ratio of .04.
> This is irregular as Mandarin outperforms Spanish across all tasks
> (evidenced by raw scores and Rasch analysis).
> 
> 
> If the equation looks right, how can it be that a lower performing group
> (by every other task or metric) has a better odds ratio than a higher
> performing group when predicting performance?
> 
> Any ideas as to what I might try to resolve the language variable issue or
> possible interpretations of what I see as a wonky result would be very much
> appreciated.
> 
> 
> Thank you!
> 
> 
> John Jones
> E: johnathan.jones using gmail.com
> SM: linkedin.com/in/johnathanjones
> 
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> 
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