Dealing with Reflection Invariance in Bayesian Factor Analysis.

This paper considers the reflection unidentifiability problem in confirmatory factor analysis (CFA) and the associated implications for Bayesian estimation. We note a direct analogy between the multimodality in CFA models that is due to all possible column sign changes in the matrix of loadings and the multimodality in finite mixture models that is due to all possible relabelings of the mixture components. Drawing on this analogy, we derive and present a simple approach for dealing with reflection in variance in Bayesian factor analysis. We recommend fitting Bayesian factor analysis models without rotational constraints on the loadings-allowing Markov chain Monte Carlo algorithms to explore the full posterior distribution-and then using a relabeling algorithm to pick a factor solution that corresponds to one mode. We demonstrate our approach on the case of a bifactor model; however, the relabeling algorithm is straightforward to generalize for handling multimodalities due to sign invariance in the likelihood in other factor analysis models.

Development and assessment of a composite score for memory in the Alzheimer's Disease Neuroimaging Initiative (ADNI).

We sought to develop and evaluate a composite memory score from the neuropsychological battery used in the Alzheimer's Disease (AD) Neuroimaging Initiative (ADNI). We used modern psychometric approaches to analyze longitudinal Rey Auditory Verbal Learning Test (RAVLT, 2 versions), AD Assessment Schedule - Cognition (ADAS-Cog, 3 versions), Mini-Mental State Examination (MMSE), and Logical Memory data to develop ADNI-Mem, a composite memory score. We compared RAVLT and ADAS-Cog versions, and compared ADNI-Mem to RAVLT recall sum scores, four ADAS-Cog-derived scores, the MMSE, and the Clinical Dementia Rating Sum of Boxes. We evaluated rates of decline in normal cognition, mild cognitive impairment (MCI), and AD, ability to predict conversion from MCI to AD, strength of association with selected imaging parameters, and ability to differentiate rates of decline between participants with and without AD cerebrospinal fluid (CSF) signatures. The second version of the RAVLT was harder than the first. The ADAS-Cog versions were of similar difficulty. ADNI-Mem was slightly better at detecting change than total RAVLT recall scores. It was as good as or better than all of the other scores at predicting conversion from MCI to AD. It was associated with all our selected imaging parameters for people with MCI and AD. Participants with MCI with an AD CSF signature had somewhat more rapid decline than did those without. This paper illustrates appropriate methods for addressing the different versions of word lists, and demonstrates the additional power to be gleaned with a psychometrically sound composite memory score.