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result(s) for
"Kamata, Akihito"
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Item Analysis by the Hierarchical Generalized Linear Model
The hierarchical generalized linear model (HGLM) is presented as an explicit, two-level formulation of a multilevel item response model. In this paper, it is shown that the HGLM is equivalent to the Rasch model and that, characteristic of the HGLM, person ability can be expressed in the form of random effects rather than parameters. The two-level item analysis model is presented as a latent regression model with person-characteristic variables. Furthermore, it is shown that the two-level HGLM model can be extended to a three-level latent regression model that permits investigation of the variation of students' performance across groups, such as is found in classrooms and schools, and of the interactive effect of person-and group-characteristic variables.
Journal Article
A Note on the Estimator of the Alpha Coefficient for Standardized Variables Under Normality
The asymptotic standard deviation (SD) of the alpha coefficient with standardized variables is derived under normality. The research shows that the SD of the standardized alpha coefficient becomes smaller as the number of examinees and/or items increase. Furthermore, this research shows that the degree of the dependence of the SD on the number of items is a function of the average correlation coefficients. When the average correlation approaches 1, the SD of the alpha coefficient decreases rapidly as the number of items increase, with the order of p . On the other hand, when the items are only weakly correlated, increasing the number of items decreases the SD of the alpha coefficient at a much slower rate.
Journal Article
Elementary teacher’s knowledge of response to intervention implementation
In the USA, many states have adopted response to intervention or multi-tiered systems of supports to provide early intervention. However, there is considerable variability in how states and schools implement RTI. Teachers are responsible for using student data from RTI to inform instructional decisions for students with or at risk for dyslexia, so it is necessary to understand the knowledge they have about the structure of RTI in their individual schools. This study reviews the results of an exploratory factor analysis of a survey aimed at measuring teachers’knowledge about RTI implementation and their understanding of RTI implementation within their school. The 52-item survey was administered online to 139 general and special education teachers. The three final factors from this factor analytic work were (1) Teacher Knowledge about Tier 1 Implementation, (2) Teacher Knowledge about Leadership and School Systems, and (3) Teacher Knowledge about Data-Based Decision Making. Factor determinacy scores demonstrated that the survey had high internal consistency. On average, teachers’ survey scores were higher on the first two factors and slightly lower on the third factor. Implications of the findings for teachers of students with learning disabilities, including dyslexia, and directions for future research were discussed.
Journal Article
Parameter Recovery for the 1-P HGLLM with Non-Normally Distributed Level-3 Residuals
A multilevel Rash model using a hierarchical generalized linear model is one approach to multilevel item
response theory (IRT) modeling and is referred to as a one-parameter hierarchical generalized linear logistic
model (1-P HGLLM). Although it has the flexibility to model nested structure of data with covariates, the
model assumes the normality of the residuals (i.e., abilities) at all its levels. However, in real-world datasets,
the normality assumption of the residuals may not always be sound. This study investigated the parameter
recovery characteristics for the 1-P HGLLM when the normality assumption of higher-level residuals is
violated. Under a three-level 1-P HGLLM, two separate simulation studies were conducted with skewed and
uniformly distributed level-3 residuals. Results from both simulation studies showed that there was not a
dramatic effect of the non-normal level-3 residuals on the parameter estimations. Suggestions for further
research were also provided in the discussion section.
Journal Article
A Multilevel Testlet Model for Dual Local Dependence
The applications of item response theory (IRT) models assume local item independence and that examinees are independent of each other. When a representative sample for psychometric analysis is selected using a cluster sampling method in a testlet-based assessment, both local item dependence and local person dependence are likely to be induced. This study proposed a four-level IRT model to simultaneously account for dual local dependence due to item clustering and person clustering. Model parameter estimation was explored using the Markov Chain Monte Carlo method. Model parameter recovery was evaluated in a simulation study in comparison with three other related models: the Rasch model, the Rasch testlet model, and the three-level Rasch model for person clustering. In general, the proposed model recovered the item difficulty and person ability parameters with the least total error. The bias in both item and person parameter estimation was not affected but the standard error (SE) was affected. In some simulation conditions, the difference in classification accuracy between models could go up to 11%. The illustration using the real data generally supported model performance observed in the simulation study.
Journal Article
Growth Mixture Modeling: Application to Reading Achievement Data From a Large-Scale Assessment
Increasing attention has been paid to growth mixture modeling (GMM) in recent social and behavioral science literature. However, the use of this methodology in educational research is still in its infancy. The purpose of this article is to demonstrate an application of GMM to longitudinal educational data from large-scale reading tests.
Journal Article
Penalized Likelihood Methods for Modeling Count Data
The paper considers parameter estimation in count data models using penalized likelihood methods. The motivating data consists of multiple independent count variables with a moderate sample size per variable. The data were collected during the assessment of oral reading fluency (ORF) in school-aged children. A sample of fourth-grade students were given one of ten available passages to read with these differing in length and difficulty. The observed number of words read incorrectly (WRI) is used to measure ORF. Three models are considered for WRI scores, namely the binomial, the zero-inflated binomial, and the beta-binomial. We aim to efficiently estimate passage difficulty, a quantity expressed as a function of the underlying model parameters. Two types of penalty functions are considered for penalized likelihood with respective goals of shrinking parameter estimates closer to zero or closer to one another. A simulation study evaluates the efficacy of the shrinkage estimates using Mean Square Error (MSE) as metric. Big reductions in MSE relative to unpenalized maximum likelihood are observed. The paper concludes with an analysis of the motivating ORF data.
Paper
The Performance of a Method for the Long-term Equating of Mixed-Format Assessment
The goal of this study was the development of a procedure to predict the equating error associated with the long-term equating method of Tate (2003) for mixed-format tests. An expression for the determination of the error of an equating based on multiple links using the error for the component links was derived and illustrated with simulated data. Expressions relating the equating error for single equating links to relevant factors like the equating design and the history of the examinee population ability distribution were determined based on computer simulation. Use of the resulting procedure for the selection of a long-term equating design was illustrated.
Journal Article