Bayesian Dimensionality Assessment for the Multidimensional Nominal Response Model
This article introduces Bayesian estimation and evaluation procedures for the multidimensional nominal response model. The utility of this model is to perform a nominal factor analysis of items that consist of a finite number of unordered response categories. The key aspect of the model, in comparis...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Frontiers Media S.A.
2017-06-01
|
| Series: | Frontiers in Psychology |
| Subjects: | |
| Online Access: | http://journal.frontiersin.org/article/10.3389/fpsyg.2017.00961/full |
| _version_ | 1811284040452407296 |
|---|---|
| author | Javier Revuelta Carmen Ximénez |
| author_facet | Javier Revuelta Carmen Ximénez |
| author_sort | Javier Revuelta |
| collection | DOAJ |
| description | This article introduces Bayesian estimation and evaluation procedures for the multidimensional nominal response model. The utility of this model is to perform a nominal factor analysis of items that consist of a finite number of unordered response categories. The key aspect of the model, in comparison with traditional factorial model, is that there is a slope for each response category on the latent dimensions, instead of having slopes associated to the items. The extended parameterization of the multidimensional nominal response model requires large samples for estimation. When sample size is of a moderate or small size, some of these parameters may be weakly empirically identifiable and the estimation algorithm may run into difficulties. We propose a Bayesian MCMC inferential algorithm to estimate the parameters and the number of dimensions underlying the multidimensional nominal response model. Two Bayesian approaches to model evaluation were compared: discrepancy statistics (DIC, WAICC, and LOO) that provide an indication of the relative merit of different models, and the standardized generalized discrepancy measure that requires resampling data and is computationally more involved. A simulation study was conducted to compare these two approaches, and the results show that the standardized generalized discrepancy measure can be used to reliably estimate the dimensionality of the model whereas the discrepancy statistics are questionable. The paper also includes an example with real data in the context of learning styles, in which the model is used to conduct an exploratory factor analysis of nominal data. |
| first_indexed | 2024-04-13T02:22:40Z |
| format | Article |
| id | doaj.art-061403694ee14996bdd97238a74ca487 |
| institution | Directory Open Access Journal |
| issn | 1664-1078 |
| language | English |
| last_indexed | 2024-04-13T02:22:40Z |
| publishDate | 2017-06-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Psychology |
| spelling | doaj.art-061403694ee14996bdd97238a74ca4872022-12-22T03:06:53ZengFrontiers Media S.A.Frontiers in Psychology1664-10782017-06-01810.3389/fpsyg.2017.00961243933Bayesian Dimensionality Assessment for the Multidimensional Nominal Response ModelJavier RevueltaCarmen XiménezThis article introduces Bayesian estimation and evaluation procedures for the multidimensional nominal response model. The utility of this model is to perform a nominal factor analysis of items that consist of a finite number of unordered response categories. The key aspect of the model, in comparison with traditional factorial model, is that there is a slope for each response category on the latent dimensions, instead of having slopes associated to the items. The extended parameterization of the multidimensional nominal response model requires large samples for estimation. When sample size is of a moderate or small size, some of these parameters may be weakly empirically identifiable and the estimation algorithm may run into difficulties. We propose a Bayesian MCMC inferential algorithm to estimate the parameters and the number of dimensions underlying the multidimensional nominal response model. Two Bayesian approaches to model evaluation were compared: discrepancy statistics (DIC, WAICC, and LOO) that provide an indication of the relative merit of different models, and the standardized generalized discrepancy measure that requires resampling data and is computationally more involved. A simulation study was conducted to compare these two approaches, and the results show that the standardized generalized discrepancy measure can be used to reliably estimate the dimensionality of the model whereas the discrepancy statistics are questionable. The paper also includes an example with real data in the context of learning styles, in which the model is used to conduct an exploratory factor analysis of nominal data.http://journal.frontiersin.org/article/10.3389/fpsyg.2017.00961/fullmultidimensional nominal response modelmultidimensional item response theorystandardized generalized discrepancy measureWAICCLOOBayesian inference |
| spellingShingle | Javier Revuelta Carmen Ximénez Bayesian Dimensionality Assessment for the Multidimensional Nominal Response Model Frontiers in Psychology multidimensional nominal response model multidimensional item response theory standardized generalized discrepancy measure WAICC LOO Bayesian inference |
| title | Bayesian Dimensionality Assessment for the Multidimensional Nominal Response Model |
| title_full | Bayesian Dimensionality Assessment for the Multidimensional Nominal Response Model |
| title_fullStr | Bayesian Dimensionality Assessment for the Multidimensional Nominal Response Model |
| title_full_unstemmed | Bayesian Dimensionality Assessment for the Multidimensional Nominal Response Model |
| title_short | Bayesian Dimensionality Assessment for the Multidimensional Nominal Response Model |
| title_sort | bayesian dimensionality assessment for the multidimensional nominal response model |
| topic | multidimensional nominal response model multidimensional item response theory standardized generalized discrepancy measure WAICC LOO Bayesian inference |
| url | http://journal.frontiersin.org/article/10.3389/fpsyg.2017.00961/full |
| work_keys_str_mv | AT javierrevuelta bayesiandimensionalityassessmentforthemultidimensionalnominalresponsemodel AT carmenximenez bayesiandimensionalityassessmentforthemultidimensionalnominalresponsemodel |