Fitting item response theory models in complex survey data using Mplus: A practical, empirical example

Mplus offers a powerful framework for examining a variety of statistical models, including item response theory (IRT) models. Mplus' strengths include the ability to estimate models incorporating complex sample designs and weights. IRT models see increasing use in health outcomes research, large scale epidemiological surveys, and other public health settings. Failure to include design information can lead to biased standard errors and inadequate tests of IRT model fit, leading analysts to a number of inappropriate and inaccurate conclusions. Mplus recently added the ability to include design information. Methodologists and statisticians may be unfamiliar with Mplus generally and this feature particularly. Using data from the National Epidemiologic Survey of Alcohol and Related Conditions (NESARC), a large (n = 43,903) representative sample of the civilian US that utilized a complex sample design and provides weighted data, the presentation demonstrates the use of Mplus to fit an IRT model for a set of items assessing Nicotine Dependence. The presentation describes estimating IRT models in Mplus, the incorporation of complex sampling information, and provides an example of the program language used to generate the IRT model. Results compare a model incorporating design information to one failing to include this information, empirically demonstrating and describing the deleterious effects of this information failure on standard error estimates and tests of model fit. Discussion emphasizes program output and interpretation.