This study investigated the item parameter recovery of two methods of factor analysis. The methods researched were a traditional factor analysis of tetrachoric correlation coefficients and an IRT approach to factor analysis which utilizes marginal maximum likelihood estimation using an EM algorithm (MMLE-EM). Dichotomous item response data was generated under the 2-parameter normal ogive model (2PNOM) using PARDSIM software. Examinee abilities were sampled from both the standard normal and uniform distributions. True item discrimination, a, was normal with a mean of .75 and a standard deviation of .10. True b, item difficulty, was specified as uniform [-2, 2]. The two distributions of abilities were completely crossed with three test lengths (n= 30, 60, and 100) and three sample sizes (N = 50, 500, and 1000). Each of the 18 conditions was replicated 5 times, resulting in 90 datasets. PRELIS software was used to conduct a traditional factor analysis on the tetrachoric correlations. The IRT approach to factor analysis was conducted using BILOG 3 software. Parameter recovery was evaluated in terms of root mean square error, average signed bias, and Pearson correlations between estimated and true item parameters. ANOVAs were conducted to identify systematic differences in error indices. Based on many of the indices, it appears the IRT approach to factor analysis recovers item parameters better than the traditional approach studied. Future research should compare other methods of factor analysis to MMLE-EM under various non-normal distributions of abilities.

Thesis advisor: Zhushan Mandy Li / Differential item functioning (DIF) occurs when examinees of equal ability from different groups have different probabilities of correctly responding to certain items. DIF analysis aims to identify potentially biased items to ensure the fairness and equity of instruments, and has become a routine procedure in developing and improving assessments. This study proposed a DIF detection method using regularization techniques, which allows for simultaneous investigation of all items on a test for both uniform and nonuniform DIF. In order to evaluate the performance of the proposed DIF detection models and understand the factors that influence the performance, comprehensive simulation studies and empirical data analyses were conducted. Under various conditions including test length, sample size, sample size ratio, percentage of DIF items, DIF type, and DIF magnitude, the operating characteristics of three kinds of regularized logistic regression models: lasso, elastic net, and adaptive lasso, each characterized by their penalty functions, were examined and compared. Selection of optimal tuning parameter was investigated using two well-known information criteria AIC and BIC, and cross-validation. The results revealed that BIC outperformed other model selection criteria, which not only flagged high-impact DIF items precisely, but also prevented over-identification of DIF items with few false alarms. Among the regularization models, the adaptive lasso model achieved superior performance than the other two models in most conditions. The performance of the regularized DIF detection model using adaptive lasso was then compared to two commonly used DIF detection approaches including the logistic regression method and the likelihood ratio test. The proposed model was applied to analyzing empirical datasets to demonstrate the applicability of the method in real settings. / Thesis (PhD) — Boston College, 2019. / Submitted to: Boston College. Lynch School of Education. / Discipline: Educational Research, Measurement and Evaluation.

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Item Response Theory (IRT) Models, like the one parameter, two parameters, or normal Ogive, have been discussed for many years. These models represent a rich area of investigation due to their complexity as well as the large amount of data collected in relationship to model parameter estimation. Here we propose a new way of looking at IRT models using I-projections and duality. We use convex optimization methods to derive these models. The Kullback-Leibler divergence is used as a metric and specific constraints are proposed for the various models. With this approach, the dual problem is shown to be much easier to solve than the primal problem. In particular when there are many constraints, we propose the application of a projection algorithm for solving these types of problems. We also consider re-framing the problem and utilizing a decomposition algorithm to solve for parameters as well. Both of these methods will be compared to the Rasch and 2-Parameter Logistic models using established computer software where estimation of model parameters are done under Maximum Likelihood Estimation framework. We will also compare the appropriateness of these techniques on multidimensional item response data sets and propose new models with the use of I-projections.

This study was performed to show advantages of Item Response THeory (IRT) over Classical Test Theory (CTT). Item Response THeory is a complex theory with many applications. This study used one application, test analysis. Ten items from a social psychology midterm were analyzed in order to show how IRT is more accurate than CTT, because IRT has the ability to add and delete individual items. Also, IRT features the Item Characteristic Curve (ICC) to give an easy to read interpretation of the results. The results showed the levels of the three indexes, item discrimination, difficulty, and guessing. The results indicated in which area each item was weak or strong. With this information, suggestions can be made to improve the item and ultimately improve the measurement accuracy of the entire test. Classical Test Theory cannot do this on individual item basis without changing the accuracy of the entire test. The results of this study confirm that IRT can be used to analyze individual items and allow for the improvement or revision of the item. This means IRT can be used for test analysis in a more efficient and accurate manner than CTT. This study provides an introduction to Item Response Theory in the hopes that more research will be performed to establish IRT as a commonly used tool for improving testing measurement.

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