One-Parameter Hierarchical Generalized Linear Logistic Model:
An Application of HGLM to IRT
Akihito Kamata
This paper was presented at the annual meeting of American Educational Research Association, San Diego, CA, April, 1998.
The author brought up two problems of the two-step analysis using item response theory (IRT) models in investigating effects of student characteristics on student abilities. In order to solve the problems, they suggest the hierarchical generalized linear model which the student characteristic variables were included in the IRT model. The HGLM is an extension of the generalized linear model (GLM) to hierarchical data.
The paper explains the formulas of the HGLM in detail. It contains two levels in the model. Level-1 is the item-level model. Level-2 are person-level models. Have those detailed information for the model is helpful for us to write the codes of our own research.
The simulation study was conducted to demonstrate that the reformulated model was able to reproduce item parameter values. However it did not provide some data examples to illustrate the new model is superior to the two-step analysis in that avoids unbiasedness and inconsistency of person parameter estimates, as well as non-random measurement errors of measurement. If the author use take one data as an example, to compare the newly formulated multilevel Rasch model with the former model, it will be more convincing and perfect.
The rest of the paper introduces several extensions of the generalized Rasch model:
a model with a person-level predictor, a DIF model, a three-level model, and a multi- dimensional model. In the model with a person-level predictor and the DIF model, the first level remains the same, and another variable (SES & gender) were added in the second level. In the three-level model, level-1 and level-2 is still the item-level and person-level model. The additional school-level model is added into the model, which enables one to include school-characteristic variables, as well as student-characteristic variables, in the model. The large scale assessment (PISA, ICCS, etc) can be analyzed by this model. The multi- dimensional model contains more than one latent trait parameters in the model which can be applied for confirmatory analysis purposes.
All of the extended models are very useful in the real data analysis. However, if there are some examples to illustrate the efficiency of the model, then it will be more convinced and powerful. The other thing what I am considered about is the complexity of programming for the new model. For now the parameters of the 1-P HGLLM can be analyzed by the HLM program. However I have no idea whether it can do the analysis for the extension models.
No matter what it brings us some new perspective to our own research.
I am still digesting the formulas and need to learn more about the HLM . The reason for the defined parameter and its use is still my confusion.