Introduction to Categorical Data Analysis

SUBJECT INDEX 355
ordinal versus nominal treatment
of data, 41–45, 118–119
quasi symmetry, 258–260
scores, choice of, 43–44, 119, 195
testing independence, 41–45, 232
trend in proportions, 41–45
Ordinal quasi symmetry, 258–260
Overdispersion, 80–84, 192–193, 280,
283–284, 304–305
Paired comparisons, 264–266
Parameter constraints, 113, 206, 221
Partial association, 49
partial table, 49
same as marginal association, 224
Partitioning chi-squared, 39–40, 62, 329
Pearson chi-squared statistic, 35, 37, 61
chi-squared distribution, 35–36
comparing proportions, 26
degrees of freedom, 35, 37, 62, 327
goodness of fit, 86, 145–147, 184, 212
independence, 35–38, 41–43, 61, 333
loglinear model, 212
and residuals, 86–87, 148
sample size for chi-squared
approximation, 40, 156–157, 329
sample size, influence on statistic, 61
two-by-two tables, 26, 40
Pearson, Karl, 325–327
Pearson residual, 86–87, 148
Binomial GLM, 148
GLM, 86–87
independence, 38–39
Poisson GLM, 87
Penalized quasi likelihood (PQL), 317
Perfect discrimination, 153
Poisson distribution, 74
mean and standard deviation, 74
negative binomial, connection with, 81
overdispersion, 80–84
generalized linear mixed model, 324
Poisson loglinear model, 75, 205, 324
Poisson regression, 75–84
residuals, 87
Poisson GLM, 74–84, 205, 334–335
Population-averaged effect, 249, 279
Power, 160–162
Practical vs. statistical significance, 61, 140,
218–219
Prior distribution, 317
Probability estimates, 6, 68, 100, 108–109,
176, 245
Probit model, 72–73, 135, 328
Proportional odds model, 182 See also
Cumulative logit model
Proportions
Bayesian estimate, 17
confidence intervals, 9–10, 20, 26
dependent, 34, 244–252
difference of, 26–27, 246–247
estimating using models, 68, 100, 108,
176
independent, 26
inference, 6–16, 26–31
ratio of (relative risk), 27–28, 32
as sample mean, 7
significance tests, 8, 13–16, 19
standard error, 8, 19, 26
P -value and Type I error probability,
14, 20, 47–48
Quasi independence, 261–263, 274, 329
Quasi likelihood, 280
Quasi symmetry, 257–259, 263, 265, 274,
340
R (software). See
www.stat.ufl.edu/∼aa/cda/
software.html
Random component (GLM), 66
Random effects, 298–318, 341–342
bivariate, 311–313
predicting, 299, 303, 313, 316
Random intercept, 298
Ranks, 44–45
Rasch model, 307, 328
Rater agreement, 260–264
Rates, 82–84, 97
Receiver operating characteristic (ROC)
curve, 143–144
Regressive-logistic model, 288–289
Relative risk, 27–28, 32, 328
confidence interval, 28, 58
and odds ratio, 32, 33
Repeated response data, 276