When Conditioning Causes Bias: Endogeneity in Time-Augmented Item Response Models

Response time and other forms of process data are increasingly incorporated into psychometric models. A frequently overlooked challenge is that response time is often treated as exogenous, even though time use plausibly depends on latent ability. This paper investigates how causal relationships among ability, response time, and response accuracy can bias parameter estimation when conditioning directly on observed time or accuracy without modeling how time is generated. Using causal graphs, we show that when response time depends on latent ability, conditioning on response time can bias both item and person parameter estimates, while conditioning on accuracy can induce spurious associations between time and ability. Simulation results under an explicit data-generating process demonstrate that naive one-step estimation treating response time as exogenous yields systematic distortion in item parameter estimates. To address this problem, we propose a two-step estimation strategy that first estimates ability from response accuracy alone and then fits a time-augmented item response model conditional on these estimates. This approach substantially reduces estimation bias. An empirical analysis of TIMSS data provides evidence of endogeneity in response times and illustrates both the risks of naive conditioning and the value of diagnostic analyses based on structured patterns of time use.