Sensitivity of Latent Trait Analysis to Highly Skewed Ability Distributions

• Activity Number: 12
• Type: Topic Contributed
• Date/Time: Sunday, August 6, 2006 : 2:00 PM to 3:50 PM
• Sponsor: Social Statistics Section
• Author(s): David Dailey*+ and Elena Erosheva
• Companies: Woodcock-Munoz Foundation and University of Washington
• Keywords: latent trait analysis ; skewed ability distributions ; marginal maximum likelihood estimation ; two-parameter logistic model ; simulation study ; parameter estimates

Abstract

In this simulation study, we explore parameter estimation sensitivity to characteristics of the generating ability distribution and choices of the fitting distribution. Using marginal maximum likelihood estimation for the two-parameter logistic response model, we examine the usual choice of the standard normal, a double gamma for a bimodal case, and an exponential for a highly skewed case. We obtain simulated data under these distributions, varying test length and sample size. We examine effects of using incorrect fitting distributions by analyzing recovery of item parameters and item ranking, as well as goodness-of-fit. We find that the exponential distribution has a high impact on parameter estimates. Thus, it is important not to use the normal fitting distribution with exponential-generated data or the exponential fitting distribution with normal-generated data.