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The presented journal article formatted dissertation investigated the performance of two models for hierarchical-structured item response data (i.e., Kamata's MLIRT model, and Multiple Regression IRT model) and discussed an application of the multilevel IRT modeling, i.e., a longitudinal multilevel logistic regression model for DIF analyses. Study I compared the estimates of abilities and IRT difficulty parameters of the two models for multilevel-structured IRT data. Bias and RMSE were compared under 8 conditions (2 test lengths, 4 intraclass correlation coefficients, i.e., ICC). Study II sought to learn the causes of DIF, specifically investigating if DIF arises through higher-level clusters, such as different schools, and longitudinal sources, such as multiple time points of test (e.g., beginning v.s. end of year). The accuracies of DIF detection at each level were evaluated under 48 conditions (2 test lengths, 2 percentages of DIF items at school-level, 2 percentages of DIF items of time-level, 3 sample sizes, 2 magnitude of DIF) by power and Type I error rate. Findings of Study I provided guidelines for model selection between MLIRT and MR-IRT model. Results indicated more accurate estimates of school abilities but less accurate estimates of student abilities with MLIRT model. MR-IRT was found more appropriate to use when sample size was small. For both the MLIRT and MR-IRT models, the longer test length resulted in more accurate estimates. ICC played an important role in estimating the school variances of abilities. Study II examined the power and Type I error of DIF detection with the proposed model. Results showed an overall powerful DIF detection. Type I error rates at each level roughly fell into the liberal range of Bradley (1978), 0.025 to 0.075. Consistent with previous study, the magnitude of DIF at each level and the sample was found to be the most important factors for a powerful DIF detection. In general, the time-level detection had higher power than the school-level. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/155505
Rapid technological advances in devices used for data collection have led to the emergence of a new class of longitudinal data: intensive longitudinal data (ILD). Behavioral scientific studies now frequently utilize handheld computers, beepers, web interfaces, and other technological tools for collecting many more data points over time than previously possible. Other protocols, such as those used in fMRI and monitoring of public safety, also produce ILD, hence the statistical models in this volume are applicable to a range of data. The volume features state-of-the-art statistical modeling strategies developed by leading statisticians and methodologists working on ILD in conjunction with behavioral scientists. Chapters present applications from across the behavioral and health sciences, including coverage of substantive topics such as stress, smoking cessation, alcohol use, traffic patterns, educational performance and intimacy. Models for Intensive Longitudinal Data (MILD) is designed for those who want to learn about advanced statistical models for intensive longitudinal data and for those with an interest in selecting and applying a given model. The chapters highlight issues of general concern in modeling these kinds of data, such as a focus on regulatory systems, issues of curve registration, variable frequency and spacing of measurements, complex multivariate patterns of change, and multiple independent series. The extraordinary breadth of coverage makes this an indispensable reference for principal investigators designing new studies that will introduce ILD, applied statisticians working on related models, and methodologists, graduate students, and applied analysts working in a range of fields. A companion Web site at www.oup.com/us/MILD contains program examples and documentation.
This edited volume gives a new and integrated introduction to item response models (predominantly used in measurement applications in psychology, education, and other social science areas) from the viewpoint of the statistical theory of generalized linear and nonlinear mixed models. It also includes a chapter on the statistical background and one on useful software.
Multilevel and multidimensional item response models are two commonly used examples as extensions of the conventional item response models. In this dissertation, I investigate extensions and applications of multilevel and multidimensional item response models, with a primary focus on longitudinal item response data that include students' school switching, classification of examinees into latent classes based on multidimensional aspects, and measurement models for complicated learning progressions. In the first paper, multilevel item response models for longitudinal data are extended to the crossed-classified models (Rasbash & Goldstein, 1994; Raudenbush, 1993) and multiple membership models (Hill & Goldstein, 1998; Rasbash & Browne, 2001) to incorporate students' school mobility. If students switch school over time in longitudinal studies, the data structure is not strictly hierarchical; therefore, conventional multilevel models are not applicable. In this study, two types of school mobility and corresponding models are specified. Furthermore, this study investigates the impacts of misspecification of school membership in the analysis of longitudinal data. In the second and third paper, mixture models and measurement models based on multidimensional item response models are presented respectively. The second paper investigates possible usefulness of the mixture random weights linear logistic test model (MixRWLLTM) as a means to identify subgroups of examinees as well as to improve interpretations of differences between latent classes. In the proposed MixRWLLTM, examinees are classified with respect to their multidimensional aspects, a general propensity (intercept) and random coefficients of the item properties. In the third paper, a structured constructs model (SCM) for the continuous latent trait is developed to deal with complicated learning progressions, in which relations between levels across multiple constructs are assumed in advance. Based on the multidimensional Rasch model, discontinuity parameters are incorporated to model the hypothesized relations as the advantage or disadvantage for respondents belonging into a certain level in one construct to reach a level in another construct.
Previous research has demonstrated that DIF methods that do not account for multilevel data structure could result in too frequent rejection of the null hypothesis (i.e., no DIF) when the intraclass correlation coefficient ([rho]) of the studied item was the same as [rho] of the total score. The current study extended previous research by comparing the performance of DIF methods when [rho] of the studied item was less than [rho] of the total score, a condition that may be observed with considerable frequency in practice. The performance of two frequently used simple DIF methods that do not account for multilevel data structure, the Mantel-Haenszel test (MH) and Logistic Regression (LR), was compared to a less frequently used complex DIF method that does account for multilevel data structure, Hierarchical Logistic Regression (HLR). HLR and LR performed equivalently in terms of significance tests under most generated conditions, and MH was conservative across all conditions. Effect size estimates of HLR, LR and MH were more accurate and consistent under the Rasch model than under the 2 parameter item response theory model. The results of the current study provide evidence to help researchers further understand the comparative performance between complex and simple modeling for DIF detection under multilevel data structure.
This book provides a new analytical approach for dynamic data repeatedly measured from multiple subjects over time. Random effects account for differences across subjects. Auto-regression in response itself is often used in time series analysis. In longitudinal data analysis, a static mixed effects model is changed into a dynamic one by the introduction of the auto-regression term. Response levels in this model gradually move toward an asymptote or equilibrium which depends on covariates and random effects. The book provides relationships of the autoregressive linear mixed effects models with linear mixed effects models, marginal models, transition models, nonlinear mixed effects models, growth curves, differential equations, and state space representation. State space representation with a modified Kalman filter provides log likelihoods for maximum likelihood estimation, and this representation is suitable for unequally spaced longitudinal data. The extension to multivariate longitudinal data analysis is also provided. Topics in medical fields, such as response-dependent dose modifications, response-dependent dropouts, and randomized controlled trials are discussed. The text is written in plain terms understandable for researchers in other disciplines such as econometrics, sociology, and ecology for the progress of interdisciplinary research.
Logistic Regression Models presents an overview of the full range of logistic models, including binary, proportional, ordered, partially ordered, and unordered categorical response regression procedures. Other topics discussed include panel, survey, skewed, penalized, and exact logistic models. The text illustrates how to apply the various models t
An overview of the theory and application of linear and nonlinear mixed-effects models in the analysis of grouped data, such as longitudinal data, repeated measures, and multilevel data. The authors present a unified model-building strategy for both models and apply this to the analysis of over 20 real datasets from a wide variety of areas, including pharmacokinetics, agriculture, and manufacturing. Much emphasis is placed on the use of graphical displays at the various phases of the model-building process, starting with exploratory plots of the data and concluding with diagnostic plots to assess the adequacy of a fitted model. The NLME library for analyzing mixed-effects models in S and S-PLUS, developed by the authors, provides the underlying software for implementing the methods presented. This balanced mix of real data examples, modeling software, and theory makes the book a useful reference for practitioners who use, or intend to use, mixed-effects models in their data analyses. It can also be used as a text for a one-semester graduate-level applied course.