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

John Maindonald john@m@|ndon@|d @end|ng |rom @nu@edu@@u
Mon May 10 22:36:01 CEST 2021

How were the data obtained?  Are they from a designed experiment?
Are the  data balanced, i.e., equal numbers in each factor level and

Is there an interaction between Association and language?
Is it possible that an important explanatory variable has been omitted.

Omission of a key variable or interaction can reverse the apparent
direction of an effect.  Also, check the matrix of correlations between
model parameters.  Remember that the regression coefficients are
telling you how a variable affects outcome when all other variables
are held constant.  If there is a strongish correlation between two
variables, this has implications for the individual coefficients.
Re-parameterization can sometimes help, e.g., in another context
(time to complete a hill race) work with distance and gradient
(height/distance) rather than distance and height, with the effect
of reducing the correlation to close to 0.

John Maindonald             email: john.maindonald using anu.edu.au<mailto:john.maindonald using anu.edu.au>

On 11/05/2021, at 05:15, Johnathan Jones <johnathan.jones using gmail.com<mailto:johnathan.jones using gmail.com>> 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.


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

Random variables: participant and item.

Equation: Y ~ iso1 + iso2 + language + association + (1|participant) +

*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

Thank you!

John Jones
E: johnathan.jones using gmail.com<mailto:johnathan.jones using gmail.com>
SM: linkedin.com/in/johnathanjones<http://linkedin.com/in/johnathanjones>

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