INTRODUCTION We present an ordinal logistic regression model for identification of items with differential item functioning (DIF) and apply this model to a Mini-Mental State Examination (MMSE) dataset. We employ item response theory ability estimation in our models. Three nested ordinal logistic regression models are applied to each item. Model testing begins with examination of the statistical...

How do we compare the complexities of various classes of structures? The Turing ordinal of a class of structures, introduced by Jockusch and Soare, is defined in terms of the number of jumps required for coding to be possible. The back-and-forth ordinal, introduced by Montalbán, is defined in terms of Σα-types. The back-and-forth ordinal is (roughly) bounded by the Turing ordinal. In this paper...

Article history: Received 25 October 2010 Accepted 31 March 2011 Available online 8 April 2011

Several observations suggest that overlearned ordinal categories (e.g., letters, numbers, weekdays, months) are processed differently than non-ordinal categories in the brain. In synesthesia, for example, anomalous perceptual experiences are most often triggered by members of ordinal categories (Rich et al., 2005; Eagleman, 2009). In semantic dementia (SD), the processing of ordinal stimuli app...

Many applied studies collect one or more ordered categorical predictors, which do not fit neatly within classic regression frameworks. In most cases, ordinal predictors are treated as either nominal (unordered) variables or metric (continuous) variables in regression models, which is theoretically and/or computationally undesirable. In this paper, we discuss the benefit of taking a smoothing sp...

Ordinal models can be seen as being composed from simpler, in particular binary models. This view on ordinal allows to derive a taxonomy of that includes basic regression models, with more complex parameterizations, the class hierarchically structured and recently developed finite mixture The overview is given covers existing shows how extended account for further effects explanatory variables....

We develop an alternative approach to well-ordering proofs beyond the Bachmann-Howard ordinal using transsnite sequences of ordinal notations and use it in order to carry out well-ordering proofs for-ordinal systems. We extend the approach of ordinal systems as an alternative way of presenting ordinal notation systems started in Set98b] and develop ordinal systems, which have in the limit exact...