Explore the vast range of titles available.

The ϕ -divergence association models for two-way contingency tables is a family of models that includes the association and correlation models as special cases. We present this family of models, discussing its features and demonstrating the role of ϕ -divergence in building this family. The most parsimonious member of this family, the model of ϕ -scaled uniform local association, is considered in detail. It is implemented and representative examples are commented on.

The aging intensity (AI), defined as the ratio of the instantaneous hazard rate and a baseline hazard rate, is a useful tool for the describing reliability properties of a random variable corresponding to a lifetime. In this work, the concept of AI is introduced in step-stress accelerated life testing (SSALT) experiments, providing new insights to the model and enabling the further clarification of the differences between the two commonly employed cumulative exposure (CE) and tampered failure rate (TFR) models. New AI-based estimators for the parameters of a SSALT model are proposed and compared to the MLEs in terms of examples and a simulation study.

In this article, we propose a generalized estimating equations (GEE) approach for correlated ordinal or nominal multinomial responses using a local odds ratios parameterization. Our motivation lies upon observing that: (i) modeling the dependence between correlated multinomial responses via the local odds ratios is meaningful both for ordinal and nominal response scales and (ii) ordinary GEE methods might not ensure the joint existence of the estimates of the marginal regression parameters and of the dependence structure. To avoid (ii), we treat the so-called \"working\" association vector α as a \"nuisance\" parameter vector that defines the local odds ratios structure at the marginalized contingency tables after tabulating the responses without a covariate adjustment at each time pair. To estimate α and simultaneously approximate adequately possible underlying dependence structures, we employ the family of association models proposed by Goodman. In simulations, the parameter estimators with the proposed GEE method for a marginal cumulative probit model appear to be less biased and more efficient than those with the independence \"working\" model, especially for studies having time-varying covariates and strong correlation.

We consider simple ordinal model-based probability effect measures for comparing distributions of two groups, adjusted for explanatory variables. An \"ordinal superiority\" measure summarizes the probability that an observation from one distribution falls above an independent observation from the other distribution, adjusted for explanatory variables in a model. The measure applies directly to normal linear models and to a normal latent variable model for ordinal response variables. It equals ϕ(β/√2) for the corresponding ordinal model that applies a probit link function to cumulative multinomial probabilities, for standard normal cdf ϕ and β effect that is the coefficient of the group indicator variable. For the more general latent variable model for ordinal responses that corresponds to a linear model with other possible error distributions and corresponding link functions for cumulative multinomial probabilities, the ordinal superiority measure equals exp(β)/[1 + exp(β)] with the log–log link and equals approximately exp(β/√2)/[1 + exp(β/√2)] with the logit link, where β is the group effect. Another ordinal superiority measure generalizes the difference of proportions from binary to ordinal responses. We also present related measures directly for ordinal models for the observed response that need not assume corresponding latent response models. We present confidence intervals for the measures and illustrate with an example.

The quasisymmetry (QS) model for square contingency tables is revisited, highlighting properties and features on the basis of its alternative definitions. More parsimonious QS-type models, such as the ordinal QS model for ordinal classification variables and models based on association models (AMs) with homogeneous row and column scores, are discussed. All these models are linked to the local odds ratios (LOR). QS-type models and AMs were extended in the literature for generalized odds ratios other than LOR. Furthermore, in an information-theoretic context, they are expressed as distance models from a parsimonious reference model (the complete symmetry for QS and the independence for AMs), while they satisfy closeness properties with respect to Kullback–Leibler (KL) divergence. Replacing the KL by ϕ divergence, flexible classes of QS-type models for LOR, AMs for LOR, and AMs for generalized odds ratios were generated. However, special QS-type models that are based on homogeneous AMs for LOR have not been extended to ϕ-divergence-based classes so far, or the QS-type models for generalized odds ratios. In this work, we develop these missing extensions, and discuss QS-type models and their generalizations in depth. These flexible families enrich the modeling options, leading to models of better fit and sound interpretation, as illustrated by representative examples.

We present a Bayesian approach for the analysis of rating data when a scaling component is taken into account, thus incorporating a specific form of heteroskedasticity. Model-based probability effect measures for comparing distributions of several groups, adjusted for explanatory variables affecting both location and scale components, are proposed. Markov Chain Monte Carlo techniques are implemented to obtain parameter estimates of the fitted model and the associated effect measures. An analysis on students’ evaluation of a university curriculum counselling service is carried out to assess the performance of the method and demonstrate its valuable support for the decision-making process.

In step-stress modeling with the cumulative exposure model it is well known that, for underlying exponential distributions, explicit expressions can be obtained for maximum likelihood estimators of parameters as well as for their conditional density functions or conditional moment generation functions, given their existence. Applying a failure rate based approach instead, similar results can be also obtained for underlying lifetime distributions out of a general scale family of distributions, which allows for a flexible modeling. Exemplarily, respective results are presented for Type-I and Type-II censored experiments.

Professors Piccolo and Simone summarize an impressive body of research dealing with CUB models and their extensions. The original ideas in Piccolo (2003) now have been extended to address the many relevant issues that one encounters in analyzing ordinal data. Our comments below reflect not so much a criticism of CUB models as reasons we’re not convinced that we should prefer this family of models over standard models that we have long used.

This work deals with the analysis of longitudinal ordinal responses. The novelty of the proposed approach is in modeling simultaneously the temporal dynamics of a latent trait of interest, measured via the observed ordinal responses, and the answering behaviors influenced by response styles, through hidden Markov models (HMMs) with two latent components. This approach enables the modeling of (i) the substantive latent trait, controlling for response styles; (ii) the change over time of latent trait and answering behavior, allowing also dependence on individual characteristics. For the proposed HMMs, estimation procedures, methods for standard errors calculation, measures of goodness of fit and classification, and full-conditional residuals are discussed. The proposed model is fitted to ordinal longitudinal data from the Survey on Household Income and Wealth (Bank of Italy) to give insights on the evolution of households financial capability.

This article proposes new approaches for optimal planning of step-stress accelerated life testing models. The experiment considered is time constrained with the tested items not monitored continuously but inspected at particular time points instead. The inspection points are primarily the points of stress level change and the experiment’s termination point, but the inclusion of additional intermediate inspection points is possible. The underlying lifetimes in each stress level follow a general-scale family of distributions having, among others, the exponential and the Weibull as special cases. For this model, the optimal allocation of the inspection points is studied in terms of the classical A-, C-, D- and E-optimality criteria, as well as in the context of minimizing the probability of nonexistence of the maximum likelihood estimators of the model’s parameters. For the determination of the inspection intervals’ length, a deterministic and a hazard rate-based approach are introduced. Simulation study results indicate that these new approaches outperform the standard ones of equal spacing and equal probability. All the considered designs are comparatively evaluated and discussed on the basis of simulation studies.