The Role of Conditional Likelihoods in Latent Variable Modeling

In psychometrics, the canonical use of conditional likelihoods is for the Rasch model in measurement. Whilst not disputing the utility of conditional likelihoods in measurement, we examine a broader class of problems in psychometrics that can be addressed via conditional likelihoods. Specifically, we consider cluster-level endogeneity where the standard assumption that observed explanatory variables are independent from latent variables is violated. Here, “cluster” refers to the entity characterized by latent variables or random effects, such as individuals in measurement models or schools in multilevel models and “unit” refers to the elementary entity such as an item in measurement. Cluster-level endogeneity problems can arise in a number of settings, including unobserved confounding of causal effects, measurement error, retrospective sampling, informative cluster sizes, missing data, and heteroskedasticity. Severely inconsistent estimation can result if these challenges are ignored.

A system approach to calculating the width of pedestrian communications in transportation hubs

Introduction. Pedestrian communications are not a single (elementary) entity; first, they are a set of elements that are interconnected, interact with each other and the external environment, have one common goal and measurable result, that is, width. Moreover, whether it is a large transport hub, a small stopping point within a land-based urban passenger transport system, or even a pedestrian path along a motor road, its space-planning solution must comply with three basic rules. They are safety, comfort and accessibility. Pedestrian communications are a set of elements whose parameters result from the proper process organization, or represent a system. The approach to the study, management, creation and development of pedestrian communications must be akin to the one applicable to a system. The purpose of the method is to develop a procedure for calcula­ting the main parameter of pedestrian communications — its total width b, in meters, and identify the conditions for a transition between various types of pedestrian communications. Materials and methods. The system approach allows to represent one complex problem as a set of simple problems that are solved faster and easier using mathematical modelling. Results. Thanks to mathematical modelling, a procedure was developed for calculating the main parameter of pedestrian communications, that is, width, with regard for low-mobility population groups in a pedestrian flow. Conclusions. Low-mobility population groups must be addressed when pedestrian communications are designed to ensure the safe and comfortable operation of transport hubs. This algorithm can also be used to analyze other directed linear pedestrian spaces.