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Practical Formulations of the Latent Growth Item Response Model


Growth modeling using longitudinal data seems to be a promising direction for improving the methodology associated with the accountability movement. Longitudinal modeling requires that the measurements of ability are comparable over time and on the same scale. One way to create the vertical scale is through concurrent estimation with identification of groups (Bock & Zimowski, 1997). However, there are concerns about how well this vertical scale will function using longitudinal data with few common items between years (Briggs et al., 2008). Other concerns about the adequacy of this and other vertical scaling strategies arise when the common items shift over time. This study explores these two practical issues in application of a Latent Growth Item Response model (LG-IRM). To illustrate how psychological constructs could be tracked over time, an application to psychological data is also included.

Since the number of common items between years can be few, it is important to ensure that the growth modeling procedure can produce good estimations in this situation. A concurrent estimation procedure of the scales is examined. To verify the estimability of the growth model using concurrent estimation, a simulation study is conducted. The LG-IRM is then applied to real data from the LSAY. A study of item shifts over time is also included. Models that do not consider item shifts are compared to those that do. An extended version of the Latent Growth Item Response Model is proposed in which estimates growth parameters are produced while allowing for item shift over time.

Item Response Theory (IRT) has been applied extensively to research in education. Its use in modeling achievement and student ability has been demonstrated using various IRT model formulations. To a lesser degree IRT has also been applied to personality research. Although the conceptualization of the domain, the item types, and the measurement goals are often different in personality research, IRT tools can still provide valuable information. The LG-IRM also provides a way to explore questions in personality research. For instance, it can provide information on the stability of self-esteem in the Black population over time. In this study the Latent Growth Item Response Model is extended to include polytomous item types. The LGIRM is then applied to data from a longitudinal study of Black Self-Esteem.

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