Pace or Inverse Error Provide Facile Observational-Level Approximations to Logarithmic Response Time Residuals and Response Time in the Analysis of Computerized Assessments

Abstract

Network analysis of assessment data suggested a close conjoint relationship of pace and QTI to response time, independent of person speed. Theoretical consideration indicated that this was a necessary consequence of the relationship of pace and its inverse error to the cumulative distribution function, assuming a normal dependent variable and linear approximations. Simulation supported this speculation. With empirical data, it was confirmed that pace and erf.inv were linearly related to the residuals of logarithmic RT (correlations >0.95). Importantly, response times in either their logarithmic transform or raw metric (seconds), were also well predicted. Thus, pace or erf.inv provide approximations to response time residuals in assessments and in conjunction with QTI can also predict assessment RT. Pace or inverse error can therefore be considered as facile alternatives to RT residuals for the process analysis of assessments.