Applying the General Diagnostic Model to Proficiency Data from a National Skills Survey

Abstract

Large-scale educational surveys (including NAEP, TIMSS, PISA) utilize item-response-theory (IRT) calibration together with a latent regression model to make inferences about subgroup ability distributions, including subgroup means, percentiles, as well as standard deviations. It has long been recognized that grouping variables not included in the latent regression model can produce secondary bias in estimates of group differences (Mislevy, RJ, Psychometrika 56:177–196, 1991). To accommodate the ever-increasing number of background variables collected and required for reporting purposes, a principal component analysis based on the background variables (von Davier M, Sinharay S, Oranje A, Beaton AE, The statistical procedures used in national assessment of educational progress: recent developments and future directions. In: Rao CR, Sinharay S (eds) Handbook of statistics: vol. 26. Psychometrics. Elsevier B.V, Amsterdam, pp 1039–1055, 2007; Moran R, Dresher A, Results from NAEP marginal estimation research on multivariate scales. Paper presented at the annual meeting of the National Council on Measurement in Education, Chicago, 2007; Oranje A, Li D, On the role of background variables in large scale survey assessments. Paper presented at the annual meeting of the National Council on Measurement in Education, New York, NY, 2008) is utilized to keep the number of predictors in the latent regression models within a reasonable range. However, even this approach often results in the inclusion of several hundred variables, and it is unknown whether the principal component approach or similar approaches (such as latent-class approaches) are able to generate consistent estimates for individual subgroups (e.g., Wetzel E, Xu X, von Davier M, Educ Psychol Meas 75(5):1–25, 2014). The primary goal of the current study is to provide an exemplary application of diagnostic models for large-scale-assessment data. Specifically, a latent-class structure is used for covariates while continuing to use IRT models for item responses in the analytic model. Previous applications focused on adult literacy data (von Davier M, Yamamoto K, A class of models for cognitive diagnosis. Paper presented at the 4th Spearman invitational conference, Philadelphia, PA, 2004), as well as large-scale English-language testing programs (von Davier M; A general diagnostic model applied to language testing data (Research report no. RR-05-16). Educational Testing Service, Princeton, 2005, von Davier M, The mixture general diagnostic model. In: Hancock GR, Samuelsen KM (eds) Advances in latent variable mixture models. Information Age Publishing, Charlotte, pp 255–274, 2008), while the current application uses diagnostic modeling approaches on data from NAEP.