In a latent class IRT model in which the latent classes are ordered on one dimension, the class specific response probabilities are subject to inequality constraints. The number of these inequality constraints increase dramatically with the number of response categories per item, if assumptions like monotonicity or double monotonicity of the cumulative category response functions are postulated. A Markov chain Monte Carlo method, the Gibbs sampler, can sample from the multivariate posterior distribution of the parameters under the constraints. Bayesian model selection can be done by posterior predictive checks and Bayes factors. A simulation study is done to evaluate results of the application of these methods to ordered latent class models in three realistic situations. Also, an example of the presented methods is given for existing data with polytomous items. It can be concluded that the Bayesian estimation procedure can handle the inequality constraints on the parameters very well. However, the application of Bayesian model selection methods requires more research.

This paper demonstrates the feasibility of using the penalty function method to estimate parameters that are subject to a set of functional constraints in covariance structure analysis. Both types of inequality and equality constraints are studied. The approaches of maximum likelihood and generalized least squares estimation are considered. A modified Scoring algorithm and a modified Gauss-Newton algorithm are implemented to produce the appropriate constrained estimates. The methodology is illustrated by its applications to Heywood cases in confirmatory factor analysis, quasi-Weiner simplex model, and multitrait-multimethod matrix analysis.

This paper presents a hierarchical Bayes circumplex model for ordinal ratings data. The circumplex model was proposed to represent the circular ordering of items in psychological testing by imposing inequalities on the correlations of the items. We provide a specification of the circumplex, propose identifying constraints and conjugate priors for the angular parameters, and accommodate theory-driven constraints in the form of inequalities. We investigate the performance of the proposed MCMC algorithm and apply the model to the analysis of value priorities data obtained from a representative sample of Dutch citizens.

Current computer programs for analyzing linear structural models will apparently handle only two types of constraints: fixed parameters, and equality of parameters. An important constraint not handled is inequality; this is particularly crucial for preventing negative variance estimates. In this paper, a method is described for imposing several kinds of inequality constraints in models, without the necessity for having computer programs which explicitly allow such constraints. The examples discussed include the prevention of Heywood cases, extension to inequalities of parameters to be greater than a specified value, and imposing ordered inequalities.

This paper presents an integrated optimal control framework for velocity and steering control of an autonomous pursuit vehicle, where the control objectives satisfy the requirements of collision avoidance and moving target tracking. A distinctive feature of the proposed velocity and steering control is the application of logarithmic penalty functions to both. The control barrier imposed by logarithmic function provides a unique tool in computing a balanced trajectory with optimal tracking error, control effort and safety margin. Trajectories compliant with the safety regulations for autonomous driving have been planned based on estimated intention of the target and the obstacles. Effects of the controller weights have been extensively simulated to assess the performance of the proposed strategy in a variety of dynamic situations. The controller has been validated on a real-life robot by using a shrinking horizon control policy for iterative optimisation.