<p> Latent growth curve modeling is an increasingly popular approach for evaluating longitudinal data. Researchers tend to focus on overall model fit information or component model fit information when evaluating a latent growth curve model (LGCM). However, there is also an interest in understanding a given individual's level and pattern of change over time, specifically an interest in identifying observations with aberrant patterns of change. Thus it is also important to examine model fit at the level of the individual. Currently there are several proposed approaches for evaluating person level fit information from a LGCM including factor score based approaches (Bollen &amp; Curran, 2006; Coffman &amp; Millsap, 2006) and person log-likelihood based approaches (Coffman &amp; Millsap, 2006; McArdle, 1997). Even with multiple methods for evaluating person-level information, it is unusual for researchers to report any examination of the person level fit information. Researchers may be hesitant to use person level fit indices because there are very few studies that evaluate how effective these person level fit indices are at identifying aberrant observations, or what criteria to use with the indices. In order to better understand which approaches for evaluating person level information will perform best for LGCMs, this research uses simulation studies to examine the application of several person level fit indices to the detection of three types of aberrant observations including: extreme trajectory aberrance, extreme variability aberrance, and functional form aberrance. Results indicate that examining factor score estimates directly can help to identify extreme trajectory aberrance, while approaches examining factor score residuals or examining a person log-likelihood are better at identifying extreme variability aberrance. The performance of these approaches improved with more observation times and higher communality. All of the factor score estimate approaches were able to identify functional form aberrance, as long as there were a sufficient number of observation times and either higher communality or a greater difference between the functional forms of interest.</p>

<p> The Next Generation Science Standards (NGSS Lead States, 2013) define performance targets which will require assessment tasks that can integrate discipline knowledge and cross-cutting ideas with the practices of science. Complex computerized tasks will likely play a large role in assessing these standards, but many questions remain about how best to make use of such tasks within a psychometric framework (National Research Council, 2014). This dissertation explores the use of a more extensive cognitive modeling approach, driven by the extra information contained in action data collected while students interact with complex computerized tasks. Three separate papers are included. In Chapter 2, a mixture IRT model is presented that simultaneously classifies student understanding of a task while measuring student ability within their class. The model is based on differentially scoring the subtask action data from a complex performance. Simulation studies show that both class membership and class-specific ability can be reasonably estimated given sufficient numbers of items and response alternatives. The model is then applied to empirical data from a food-web task, providing some evidence of feasibility and validity. Chapter 3 explores the potential of using a more complex cognitive model for assessment purposes. Borrowing from the cognitive science domain, student decisions within a strategic task are modeled with a Markov decision process. Psychometric properties of the model are explored and simulation studies report on parameter recovery within the context of a simple strategy game. In Chapter 4 the Markov decision process (MDP) measurement model is then applied to an educational game to explore the practical benefits and difficulties of using such a model with real world data. Estimates from the MDP model are found to correlate more strongly with posttest results than a partial-credit IRT model based on outcome data alone.</p>