Towards a Logical Framework for Latent Variable Modelling

EasyChair Preprint 196

Abstract

Modelling in psychometrics has become increasingly reliant on computer software; at the same time, many decisions that a researcher makes remain unrecorded and perhaps, unreconciled to anything more than the researcher’s intuition or best guess. The aim of this paper is to set out a logic that accounts for and guides decision procedures, in psychometric research practices. Such a logic is informed by the integration of three systematic viewpoints: i) bounded rationality [6]; ii) axiomatic measurement theory [14-16]; and iii) a constructive mathematics [4]. The integration of these three systems under an overall perspective that is characterised by inference from the best systematisation [13] is reviewed, and compared to current research practices, with particular reference to the problems for psychometric sciences that are revealed in the Reproducibility Project [12] outcomes. Our conclusion for the overall system is that the constraints characterised by constructive mathematics offer unique tools to the researcher in accounting for their decision procedures, and a proposal for a software tool that handles the decision protocol is presented. In characterising the decision procedures, we also explore the way that rough set theory [13] is integrated into decision procedures to provide insight into database fields or variables that hold some import but may otherwise remain hidden in research outcome reporting.

Keyphrases: Constructivism, constraints, systematicity

@booklet{EasyChair:196,
  author    = {Trisha Nowland and Alissa Beath and Simon Boag},
  title     = {Towards a Logical Framework for Latent Variable Modelling},
  doi       = {10.29007/l7g8},
  howpublished = {EasyChair Preprint 196},
  year      = {EasyChair, 2018}}