Larry Hoyle

Standard Errors and Confidence Intervals from Bootstrapping for Ramsay-Curve Item Response Theory Model Item Parameters.

Ramsay-curve item response theory (RC-IRT) is a nonparametric procedure that estimates the latent trait using splines, and no distributional assumption about the latent trait is required (Woods & Thissen, 2006). Description of this procedure can be found, for example, in the technical manual of RCLOG v.2, software for RC-IRT (Woods, 2006b). For item parameters of the twoparameter logistic (2-PL), three-parameter logistic (3-PL), and polytomous IRT models, RC-IRT can provide more accurate estimates than the commonly used marginal maximum likelihood estimation (MMLE) when the latent trait is not normally distributed (Woods, 2006a, 2007, 2008). However, standard errors (SEs) for the item parameter estimates have not been developed in RC-IRT as no analytical solution is readily available (Woods, 2006a, 2007, 2008; Woods & Lin, 2009). In such cases, bootstrapping provides an alternative way to estimate SEs. Using bootstrapping, the observed sample is treated as the pseudopopulation from which n repeated random samples are drawn with replacement. The same estimation procedure is employed on each random sample and the point estimates are retained. Then, the SE of a particular parameter estimate is the standard deviation of the retained estimates, and the associated confidence interval (CI) can be determined by two percentiles. For example, a 95% CI can be determined by the range between the 2.5th and 97.5th percentiles. In this research, bootstrapping was utilized to estimate SEs and CIs for item parameters in the 2-PL model, and the performance of bootstrapping was compared with that of MMLE.