Zero and One Inflated Item Response Theory Models for Bounded Continuous Data

Bounded continuous data are encountered in many applications of item response theory, including the measurement mood, personality, and times analyses summed scores. Although different theory models exist to analyze such bounded data, most assume be an open interval cannot accommodate a closed interval. As result, ad hoc transformations needed prevent scores on bounds observed variables. To motivate present study, we demonstrate real simulated that this practice fitting can majorly affect parameter estimates even cases with only 5% responses one address problem, propose zero inflated modeling framework for We illustrate how four existing from literature accommodated framework. The resulting studied simulation study application investigate recovery, model fit, consequences incorrect distribution data. find neglecting nature biases parameters misspecification exact may results depending generating model.