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 something like the below (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'

	

Incomplete

	

No recall

	

Total Cases

	

Count

	

% of Total

	

Count

	

% of Total

	

Count

	

% of Total

	

Count

	

% of Total

	

Count

	

% Total

's

	

70

	

65

	

9

	

7

	

20

	

18

	

9

	

8

	

108

	

100

of

	

3

	

3

	

72

	

69

	

20

	

19

	

9

	

8

	

108

	

100

Total

	

73

	

34

	

84

	

39

	

41

	

19

	

18

	

9

	

216

	

100



Responses in IN_AN contexts

Structure to be recalled

	

Use of 's

	

Use of 'of'

	

Incomplete

	

No recall

	

Total Cases

	

Count

	

% of Total

	

Count

	

% of Total

	

Count

	

% of Total

	

Count

	

% of Total

	

Count

	

% Total

's

	

68

	

63

	

16

	

15

	

16

	

15

	

8

	

7

	

108

	

100

of

	

12

	

12

	

69

	

65

	

20

	

18

	

5

	

5

	

108

	

100

Total

	

81

	

37

	

86

	

40

	

36

	

17

	

13

	

6

	

206

	

100


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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