New Developments in Quantitative Psychology by Roger E. Millsap L. Andries Ark Daniel M. Bolt & Carol M. Woods

Author:Roger E. Millsap, L. Andries Ark, Daniel M. Bolt & Carol M. Woods
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

It is readily apparent from Fig. 1 that the obtained improvement of MNRM on NRM varies considerably by calibration sample; differences in BIC for models calibrated and fit on the same sample range from 7,721 to 18,516. (With 50 additional free parameters, a significant 2, at α = 0.05, is at least 71.4.) The narrow cross-fit ranges suggest that model overfit, or capitalization on chance, is not a large determinant in the obtained improvement; the mean advantage in BIC conferred by MNRM calibration and fit evaluation on the same sample was 380. Instead, calibration on certain data samples resulted in universally better or worse parameter vectors. This pattern could result from local minima in the loglikelihood surface for the model in parameter space, but it might also simply indicate large nearly flat regions in the same surface, over which minimization algorithms do not readily traverse. Either way, the loglikelihood surface is not well suited to minimization. Further evidence toward rotational near-indeterminacy, as suggested by Bolt and Johnson (2009), is provided by comparison of the configurations of loadings of four representative items across two dimensions, as shown in Fig. 2. NRM generated much more consistent patterns of loadings between calibration samples than did MNRM.

Fig. 2Rotational indeterminacy in practice. Obtained factor loading configurations differed more between calibration samples under MNRM than under NRM

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