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A Test to Distinguish Monotone Homogeneity from Monotone Multifactor Models.
- Source :
- Psychometrika; Jun2023, Vol. 88 Issue 2, p387-412, 26p
- Publication Year :
- 2023
-
Abstract
- The goodness-of-fit of the unidimensional monotone latent variable model can be assessed using the empirical conditions of nonnegative correlations (Mokken in A theory and procedure of scale-analysis, Mouton, The Hague, 1971), manifest monotonicity (Junker in Ann Stat 21:1359–1378, 1993), multivariate total positivity of order 2 (Bartolucci and Forcina in Ann Stat 28:1206–1218, 2000), and nonnegative partial correlations (Ellis in Psychometrika 79:303–316, 2014). We show that multidimensional monotone factor models with independent factors also imply these empirical conditions; therefore, the conditions are insensitive to multidimensionality. Conditional association (Rosenbaum in Psychometrika 49(3):425–435, 1984) can detect multidimensionality, but tests of it (De Gooijer and Yuan in Comput Stat Data Anal 55:34–44, 2011) are usually not feasible for realistic numbers of items. The only existing feasible test procedures that can reveal multidimensionality are Rosenbaum's (Psychometrika 49(3):425–435, 1984) Case 2 and Case 5, which test the covariance of two items or two subtests conditionally on the unweighted sum of the other items. We improve this procedure by conditioning on a weighted sum of the other items. The weights are estimated in a training sample from a linear regression analysis. Simulations show that the Type I error rate is under control and that, for large samples, the power is higher if one dimension is more important than the other or if there is a third dimension. In small samples and with two equally important dimensions, using the unweighted sum yields greater power. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00333123
- Volume :
- 88
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Psychometrika
- Publication Type :
- Academic Journal
- Accession number :
- 163738800
- Full Text :
- https://doi.org/10.1007/s11336-023-09905-w