[R-lang] Post-hoc comparison for incorrect responses in glmer

[Francesco]

I have reposted this as some tabular information got jumbled by the
ASCII/HTML difference.

I'm trying to understand how to obtain a z and p value for pairwise
comparisons on probability of the non-default outcome of a binary
categorical variable.

My data set includes a binary categorical DV (correct or incorrect). In
a nutshell, I'm looking at Chinese speakers of English's choice of  's
or /of /possessives when recalling a sentence that contained either of
the two possessive structures 's or/of/. This choice is, however,
moderated by the animacy of the elements participating in the possessive
construction. That is, the sentence to be recalled had either structure
AN_IN or IN_AN which makes for a second IV with two levels.

The data obtained looks approximately like the below, values
are not calculated exactly (my apologies for not
reorganising this according to correct vs incorrect for display purposes).


Responses in AN_IN contexts

structure to be recalled    Use of 's              Use of 'of'

			count    % of total    count  % of total
's			135         64		14       7

'of' 			15	    10		120      63



Responses in IN_AN contexts

structure to be recalled    Use of 's              Use of 'of'

			count    % of total    count  % of total
's			101         60		12       7

'of' 			25	    10		150      62


What I'm trying to get to the bottom of is whether the proportion of
mismatches (incorrect response) when recalling/of/  and 's sentences for
one semantic combination (say IN_AN) is significantly higher or lower
than the other (AN_IN in top table). This means whether, in the IN_AN
contexts, counts of 12 and 16 for use of 's in/of/  contexts and use of
/of/  in 's contexts respectively are significantly higher than their
counterparts in the other table.

If my understanding is correct, the model I have fit tells me there is a
significant effect for semantic context
but the z and p value apply to the log-odds of obtaining a CORRECT
response. Right?


Generalized linear mixed model fit by maximum likelihood ['glmerMod']

Family: binomial ( logit )

Formula: Correct2 ~ Semantics + (1 + Syntax | ID)

Data: CodedQ3

AICBIClogLikdeviance

236.6061255.5098 -113.3030226.6061

Random effects:

Groups NameVariance Std.Dev. Corr

ID(Intercept) 0.78430.8856

Syntaxs4.04862.0121-0.80

Number of obs: 324, groups: ID, 27

Fixed effects:

Estimate Std. Error z value Pr(>|z|)

(Intercept)-3.02110.3735-8.088 6.07e-16 ***

SemanticsIN_AN1.12490.41702.6980.00698 **

---

Signif. codes:0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Correlation of Fixed Effects:

(Intr)

SmntcsIN_AN -0.792



Setting other considerations of model fit and collinearity aside for the
moment, if I want to obtain a z and p value for the difference between
proportions of INCORRECT responses by semantic context, how should I
proceed?

In passing, could someone also point out how I would look at pairwise
comparisons once I factor in interactions, as if, for example, I had
included an interaction for Syntax in the model above.

The comparisons would look like this:

syntaxof:IN_AN vs. syntaxof:AN_IN
syntax's:IN_AN vs syntax's:AN_IN

->where 'correct' is the reference level for the DV;

syntaxof:IN_AN vs. syntaxof:AN_IN
syntax's:IN_AN vs syntax's:AN_IN

->where 'incorrect' is the reference level of the DV.

Any guidance is much appreciated.

-- 
Frank Romano

Sabanci University
website: http://sabanciuniv.academia.edu/FrancescoRomano

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