| Title | Limited information goodness-of-fit testing in multidimensional contingency tables |
| Publication Type | Journal Article |
| Year of Publication | 2006 |
| Authors | Maydeu-Olivares, A, Joe, H |
| Journal | Psychometrika |
| Volume | 71 |
| Pagination | 713-732 |
| Date Published | DEC |
| Type of Article | Article |
| ISSN | 0033-3123 |
| Keywords | categorical data analysis, Composite likelihood, item response theory, Lisrel, multivariate discrete data, multivariate multinomial distribution |
| Abstract | We introduce a family of goodness-of-fit statistics for testing composite null hypotheses in multidimensional contingency tables. These statistics are quadratic forms in marginal residuals up to order r. They are asymptotically chi-square under the null hypothesis when parameters are estimated using any asymptotically normal consistent estimator. For a widely used item response model, when r is small and multidimensional tables are sparse, the proposed statistics have accurate empirical Type I errors, unlike Pearson's X-2. For this model in nonsparse situations, the proposed statistics are also more powerful than X-2. In addition, the proposed statistics are asymptotically chi-square when applied to subtables, and can be used for a piecewise goodness-of-fit assessment to determine the source of misfit in poorly fitting models. |
| DOI | 10.1007/s11336-005-1295-9 |
