Parallelianalyysin

Parallelianalyysin is a proposed statistical framework used in discussions of cross-study data analysis. It aims to identify a shared latent structure that is reproducible across multiple datasets, while allowing for study-specific variation in measurement and sampling. The term is not widely standardized and appears mainly in theoretical or methodological discussions about cross-study replication.

Conceptually, parallelianalyysin extends the idea of parallel analysis beyond a single dataset. For each study, a parallel analysis is performed to estimate the dimensionality of the latent space. The framework then seeks to align these local solutions across studies, using a common rotation or a joint matrix factorization approach, and to assess the degree of cross-study congruence among factor loadings and eigenvalues. A combined null model, built from simulations that preserve study-specific correlation structure, is used to test whether observed cross-study patterns could arise by chance.

Procedure, in brief, involves collecting datasets with comparable constructs, estimating within-study dimensionality, generating cross-study null distributions, and identifying factors that are consistently replicated across studies. Robust factors are those whose loadings show similar patterns and whose eigenvalues exhibit concordant behavior across datasets.

Applications of parallelianalyysin include fields where reproducibility across independent samples is a priority, such as psychology, genomics, education, and ecology. Limitations include the requirement for measurement invariance or at least comparable scales, substantial sample sizes, and considerable computational effort. The approach is related to, but distinct from, meta-analysis, integrative data analysis, and multi-study factor analysis, emphasizing cross-study replication of latent structure rather than single-study results. See also: parallel analysis, factor analysis, integrative data analysis.