In structural equation modeling software, either limited-information (bivariate proportions) or full-information item parameter estimation routines could be used for the 2PL IRT model. Limited-information methods assume the continuous variable underlying an item response is normally distributed. For skewed and platykurtic latent variable distributions, three methods were compared in Mplus: limited-information, full-information integrating over a normal distribution, and full-information integrating over the known underlying distribution. For the most discriminating easy or difficult items, limited-information estimates of both parameters were considerably biased. Full-information estimates obtained by integrating over a normal distribution were somewhat biased. Full-information estimates obtained by integrating over the true latent distribution were essentially unbiased. For the a-parameters, standard errors were larger for the limited-information estimates when the bias was positive but smaller when the bias was negative. For the b-parameters, standard errors were generally similar for the limited- and full-information estimates. Sample size did not substantially impact the differences between the estimation methods; limited-information did not gain an advantage for smaller samples.
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DeMars, C. E. (2010, May). A comparison of limited-information and full-information methods in Mplus for estimating IRT parameters for non-normal populations. Paper presented at the annual meeting of the National Council on Measurement in Education, Denver.