Prediction and classification are two very active areas in modern data analysis. In this paper, prediction with nonlinear optimal scaling transformations of the variables is reviewed, and extended to the use of multiple additive components, much in the spirit of statistical learning techniques that are currently popular, among other areas, in data mining. Also, a classification/clustering method is described that is particularly suitable for analyzing attribute-value data from systems biology (genomics, proteomics, and metabolomics), and which is able to detect groups of objects that have similar values on small subsets of the attributes.

Psychological, psychophysical and physiological research indicates that people switch between two covert attention states, local and global attention, while visually exploring complex scenes. The focus in the local attention state is on specific aspects and details of the scene, and on examining its content with greater visual detail. The focus in the global attention state is on exploring the informative and perceptually salient areas of the scene, and possibly on integrating the information contained therein. The existence of these two visual attention states, their relative prevalence and sequence in time has remained empirically untested to date. To fill this gap, we develop a psychometric model of visual covert attention that extends recent work on hidden Markov models, and we test it using eye-movement data. The model aims to describe the observed time series of saccades typically collected in eye-movement research by assuming a latent Markov process, indicative of the brain switching between global and local covert attention. We allow subjects to be in either state while exploring a stimulus visually, and to switch between them an arbitrary number of times. We relax the no-memory-property of the Markov chain. The model that we develop is estimated with MCMC methodology and calibrated on eye-movement data collected in a study of consumers' attention to print advertisements in magazines.

Liechty, Pieters, and Wedel (2003) report an eye-tracking experiment that is taken to support the distinction between two states of covert visual attention: local versus global. We discuss several logical problems with this dichotomy and their experiment, and then provide an alternate account of their data using a model, E-Z Reader, that requires only a single attention state.

Liechty, Pieters & Wedel (2003) developed a hidden Markov Model (HMM) to identify the states of an attentional process in an advertisement viewing task. This work is significant because it demonstrates the benefits of stochastic modeling and Bayesian estimation in making inferences about cognitive processes based on eye movement data. One limitation of the proposed approach is that attention is conceptualized as an autonomous random process that is affected neither by the overall layout of the stimulus nor by the visual information perceived during the current fixation. An alternative model based on the input-output hidden Markov model (IOHMM; Bengio, 1999) is suggested as an extension of the HMM. The need for further studies that validate the HMM classification results is also discussed.

We argue that our research objectives in Liechty, Pieters, and Wedel (2003) are to provide generalizable insights into covert visual attention to complex, multimodal stimuli in their natural context, through inverse inference from eye-movement data. We discuss the most important issues raised by Feng (2003) and Reichle and Nelson (2003), in particular the task definition, inclusion of ad features, object-based versus space-based attention and the evidence for the where and what streams.

This paper proposes a general approach to accounting for individual differences in the extreme response style in statistical models for ordered response categories. This approach uses a hierarchical ordinal regression modeling framework with heterogeneous thresholds structures to account for individual differences in the response style. Markov chain Monte Carlo algorithms for Bayesian inference for models with heterogeneous thresholds structures are discussed in detail. A simulation and two examples based on ordinal probit models are given to illustrate the proposed methodology. The simulation and examples also demonstrate that failing to account for individual differences in the extreme response style can have adverse consequences for statistical inferences.

A loading matrix has perfect simple structure if each row has at most one nonzero element. It is shown that if there is an orthogonal rotation of an initial loading matrix that has perfect simple structure, then orthomax rotation with 0 ≤γ ≤ 1 of the initial loading matrix will produce the perfect simple structure. In particular, varimax and quartimax will produce rotations with perfect simple structure whenever they exist.

This paper provides a statistical framework for estimating higher-order characteristics of the response time distribution, such as the scale (variability) and shape. Consideration of these higher order characteristics often provides for more rigorous theory development in cognitive and perceptual psychology (e.g., Luce, 1986). RT distribution for a single participant depends on certain participant characteristics, which in turn can be thought of as arising from a distribution of latent variables. The present work focuses on the three-parameter Weibull distribution, with parameters for shape, scale, and shift (initial value). Bayesian estimation in a hierarchical framework is conceptually straightforward. Parameter estimates, both for participant quantities and population parameters, are obtained through Markov Chain Monte Carlo methods. The methods are illustrated with an application to response time data in an absolute identification task. The behavior of the Bayes estimates are compared to maximum likelihood (ML) estimates through Monte Carlo simulations. For small sample size, there is an occasional tendency for the ML estimates to be unreasonably extreme. In contrast, by borrowing strength across participants, Bayes estimation “shrinks” extreme estimates. The results are that the Bayes estimators are more accurate than the corresponding ML estimators.