Causal Rasch Models

Abstract

Rasch's unidimensional models for measurement show how to connect object measures (e.g., reader abilities), measurement mechanisms (e.g., machine-generated cloze reading items), and observational outcomes (e.g., counts correct on reading instruments). Substantive theory shows what interventionsInterventions or manipulations to the measurement mechanism can be traded off against a change to the object measure to hold the observed outcome constant. A Rasch modelRasch model integrated with a substantive theory dictates the form and substance of permissible interventionsInterventions. Rasch analysis, absent construct theoryConstruct theory and an associated specification equation, is a black box in which understanding may be more illusory than not. Finally, the quantitative hypothesis can be tested by comparing theory-based trade-off relations with observed trade-off relations. Only quantitative variables (as measured) support such trade-offs. Note that to test the quantitative hypothesis requires more than manipulation of the algebraic equivalencies in the Rasch model or descriptively fitting data to the model. A causal Rasch modelRasch model involves experimental intervention/manipulation on either reader ability or text complexity or a conjoint interventionInterventions on both simultaneously to yield a successful prediction of the resultant observed outcome (count correct). We conjecture that when this type of manipulation is introduced for individual reader text encounters and model predictions are consistent with observations, the quantitative hypothesis is sustained.