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Measurement is a fundamental component of educational and psychological research, and this study focused on developing a novel modeling perspective for measuring constructs. The novel approach utilizes testing response time as information on the degree of measurement error observed in a response. The approach joins response process knowledge with psychometric modeling tools to enhance the use of available information. In this study, I examine how measurement error in discrete responses can be directly incorporated into the measurement of constructs. Using NAEP data, the novel modeling approach is demonstrated, and measurement features—e.g., reliability—depend heavily on how available information is incorporated into the measurement model. Implications for constructing scales, the validity of interpretation, and finding evidence of reliability are discussed.