```
Eyesight example: test symmetry

McNemar's Chi-squared test

data:  xtabs(count ~ r + l, data = eyes)
McNemar's chi-squared = 19.107, df = 6, p-value = 0.003987

Electon example: test symmetry

McNemar's Chi-squared test

data:  xtabs(~w97 + w05, data = elections)
McNemar's chi-squared = NaN, df = 6, p-value = NA

McNemar's Chi-squared test

data:  xtabs(~w97 + w05c, data = elections)
McNemar's chi-squared = NaN, df = 6, p-value = NA

Eye Symmetry via Poisson Regression
1      2      3      4      5      6      7      8      9
1520.0  250.0  120.5   51.0  250.0 1512.0  397.0   80.0  120.5
10     11     12     13     14     15     16
397.0 1772.0  192.0   51.0   80.0  192.0  492.0

Eyesight example: fit symmetry via genmod

Call:
glm(formula = count ~ factor(paste(r, l)) - 1, family = poisson,
data = eyes)

Deviance Residuals:
[1]  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0

Coefficients:
Estimate Std. Error z value Pr(>|z|)
factor(paste(r, l))1 1  6.19848    0.04508  137.49   <2e-16 ***
factor(paste(r, l))1 2  5.18739    0.07474   69.40   <2e-16 ***
factor(paste(r, l))1 3  4.40672    0.11043   39.91   <2e-16 ***
factor(paste(r, l))1 4  3.58352    0.16667   21.50   <2e-16 ***
factor(paste(r, l))2 1  5.32301    0.06984   76.21   <2e-16 ***
factor(paste(r, l))2 2  7.47986    0.02376  314.87   <2e-16 ***
factor(paste(r, l))2 3  5.89164    0.05256  112.10   <2e-16 ***
factor(paste(r, l))2 4  4.76217    0.09245   51.51   <2e-16 ***
factor(paste(r, l))3 1  4.35671    0.11323   38.48   <2e-16 ***
factor(paste(r, l))3 2  6.06843    0.04811  126.13   <2e-16 ***
factor(paste(r, l))3 3  7.32119    0.02572  284.68   <2e-16 ***
factor(paste(r, l))3 4  5.45532    0.06537   83.45   <2e-16 ***
factor(paste(r, l))4 1  4.18965    0.12309   34.04   <2e-16 ***
factor(paste(r, l))4 2  4.82028    0.08980   53.68   <2e-16 ***
factor(paste(r, l))4 3  5.58350    0.06131   91.06   <2e-16 ***
factor(paste(r, l))4 4  7.32647    0.02565  285.64   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for poisson family taken to be 1)

Null deviance: 8.5693e+04  on 16  degrees of freedom
Residual deviance: 2.2737e-13  on  0  degrees of freedom
AIC: 149.38

Number of Fisher Scoring iterations: 2

X2.stat DF  Pr(>|X^2|)
1 18.8197  6 0.004479225

Eyesight example: fit sat. model to test symmetry
X2.stat DF Pr(>|X^2|)
1 7.224664  3 0.06507147

Eyesight example: fit sat. model to test quasisym.

Quasisymmetry via CATMOD title2;

Marginal symmetry via CATMOD

Quasiindependence via GENMOD

Call:
glm(formula = count ~ factor(r) + factor(l) + factor(qi), family = poisson,
data = eyes)

Deviance Residuals:
1        2        3        4        5        6        7
0.0000   4.7352  -5.2834  -0.1783   4.1642   0.0000   0.5516
8        9       10       11       12       13       14
-6.2875  -3.5775  -1.4254   0.0000   5.6736  -2.2159  -4.0338
15       16
4.8330   0.0000

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept)  3.75453    0.08312  45.171  < 2e-16 ***
factor(r)2   1.14422    0.07292  15.691  < 2e-16 ***
factor(r)3   1.23874    0.07236  17.119  < 2e-16 ***
factor(r)4   0.45698    0.07552   6.051 1.44e-09 ***
factor(l)2   1.04849    0.06837  15.335  < 2e-16 ***
factor(l)3   1.06689    0.06927  15.403  < 2e-16 ***
factor(l)4   0.17689    0.07481   2.364   0.0181 *
factor(qi)1  2.44394    0.09456  25.846  < 2e-16 ***
factor(qi)2  1.53262    0.06998  21.899  < 2e-16 ***
factor(qi)3  1.26103    0.07042  17.908  < 2e-16 ***
factor(qi)4  2.93805    0.07883  37.269  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for poisson family taken to be 1)

Null deviance: 8692.33  on 15  degrees of freedom
Residual deviance:  199.11  on  5  degrees of freedom
AIC: 338.49

Number of Fisher Scoring iterations: 4

Polychoric Correlation
[1] 0.7702114
Call: cohen.kappa1(x = x, w = w, n.obs = n.obs, alpha = alpha, levels = levels)

Cohen Kappa and Weighted Kappa correlation coefficients and confidence boundaries
lower estimate upper
unweighted kappa  0.58      0.6  0.61
weighted kappa    0.69      0.7  0.71

Number of subjects = 7477
```