Estimating the Latent Density in Unidimensional IRT to Permit Non-normality

Authored by: Carol M. Woods

Handbook of Item Response Theory Modeling

Print publication date:  December  2014
Online publication date:  November  2014

Print ISBN: 9781848729728
eBook ISBN: 9781315736013
Adobe ISBN: 9781317565703


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A premise of item response modeling is that observed item responses are indicators of an underlying latent variable (or more than one). Often, for parameter estimation, the latent variable is presumed to be normally distributed. However, many psychological constructs like ambition or dysthymia are unlikely to be normally distributed in the general population. Non-normality could result from the sampling of one or more distinct populations such as those with or without a “disorder” (as defined by contemporary criteria). Alternatively, variables representing symptoms of pathology that are rare in the general population may be skewed because they exist in low levels for most people and in high levels for a few (with other people in between). Simulation studies about item response modeling have shown that when a non-normal latent variable is presumed normal, item parameters and scores for persons can be biased (Abdel-fattah, 1994; Boulet, 1996; Kirisci & Hsu, 1995; Stone, 1992; Woods, 2006a, 2007a, 2007b, 2008a; Woods & Lin, 2009; Woods & Thissen, 2006; Yamamoto & Muraki, 1991; Zwinderman & van den Wollenberg, 1990).

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