Analysis of Ordinal Categorical Data, Second Edition by Alan Agresti(auth.)

By Alan Agresti(auth.)

Statistical science’s first coordinated guide of equipment for studying ordered express information, now absolutely revised and up to date, maintains to give functions and case stories in fields as different as sociology, public future health, ecology, advertising, and pharmacy. Analysis of Ordinal express facts, moment Edition offers an creation to simple descriptive and inferential equipment for specific facts, giving thorough insurance of recent advancements and up to date tools. specific emphasis is put on interpretation and alertness of tools together with an built-in comparability of the to be had techniques for studying ordinal facts. Practitioners of facts in govt, (particularly pharmaceutical), and academia will wish this new edition.Content:
Chapter 1 advent (pages 1–8):
Chapter 2 Ordinal chances, ratings, and Odds Ratios (pages 9–43):
Chapter three Logistic Regression types utilizing Cumulative Logits (pages 44–87):
Chapter four different Ordinal Logistic Regression types (pages 88–117):
Chapter five different Ordinal Multinomial reaction versions (pages 118–144):
Chapter 6 Modeling Ordinal organization constitution (pages 145–183):
Chapter 7 Non?Model?Based research of Ordinal organization (pages 184–224):
Chapter eight Matched?Pairs info with Ordered different types (pages 225–261):
Chapter nine Clustered Ordinal Responses: Marginal versions (pages 262–280):
Chapter 10 Clustered Ordinal Responses: Random results types (pages 281–314):
Chapter eleven Bayesian Inference for Ordinal reaction info (pages 315–344):

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The estimated standard error for each ordinal log odds ratio is SE= - ^ + ^ — + ^ — y nXij nkij+\ nXi+\j + ^ nki+\j+\ . 12) When the region of the table covered by an odds ratio increases, the odds ratio has larger counts in the four cells. Thus, the sample log odds ratio value tends to be more precise as an estimator of the population value. For example, with standard sampling schemes, logö^ has smaller standard error than logÖ^ or logö^°, which have smaller standard errors than logö^. A confidence interval for a log ordinal odds ratio is sample log odds ratio ± z„/2(SE).

The weight is inversely proportional to the estimated variance. This scheme approximates the measure in the class of weighted averages that has the smallest variance. , Liu and Agresti 1996; Liu 2003). Such summary measures have limited usefulness when there are multiple control variables. It is then more informative to use a modeling approach, as discussed starting in Chapter 3. This enables us to check the fit of the assumed association structure and to compare models of different complexities.

B l J J J n s ' \-P(Y=j I Y = j or Y = j + 1) As a set of logits, the adjacent-categories logits are equivalent to the baselinecategory logits commonly used to model nominal response variables. Those logits pair each category with a baseline category, typically the last one, as log(jij/nc), j = 1 , . . , c — 1. ,c-1. Either set is sufficient in the sense that it determines the logits for all Q pairs of response categories. ,c-l. 3) Continuation-ratio logit models are useful when a sequential mechanism determines the response outcome, in the sense that an observation must potentially occur in category j before it can occur in a higher category (Tutz 1991).

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