In a cross-cultural study, it is crucial to understand whether items and the factorial structure of a survey instrument are equivalent across different cultural groups, because items might mean differently to different population groups, and thus the factorial structure of the measurement instrument might not hold across groups. The purpose of this study was to investigate the measurement invar...

The analysis of measurement invariance of latent constructs is important in research across groups, or across time. By establishing whether factor loadings, intercepts and residual variances are equivalent in a factor model that measures a latent concept, we can assure that comparisons that are made on the latent variable are valid across groups or time. Establishing measurement invariance invo...

In this paper we define the concept of a profile, which is a characteristic clause set, corresponding to an LK-proof in first-order logic, which is invariant under rule permutations. It is shown (via cutelimination) that the profile is even invariant under a large class of proof transformations (called “simple transformations”), which includes transformations to negation normal form. As proofs ...

The paper discusses the invariance view of reality: a view inspired by the relativity and quantum theory. It is an attempt to show that both versions of Structural Realism (epistemological and ontological) are already embedded in the invariance view but in each case the invariance view introduces important modifications. From the invariance view we naturally arrive at a consideration of symmetr...

Information fit indexes such as Akaike Information Criterion, Consistent Akaike Information Criterion, Bayesian Information Criterion, and the expected cross validation index can be valuable in assessing the relative fit of structural equation models that differ regarding restrictiveness. In cases in which models without mean restrictions (i.e., saturated mean structure) are compared to models ...

This paper concerns measurement invariance analysis for situations with many groups or time points. A BSEM (Bayesian Structural Equation Modeling) approach is proposed for detecting non-invariance that is similar to modification indices with maximum-likelihood estimation, but unlike maximum-likelihood is applicable also for high-dimensional latent variable models for categorical variables. Unde...

We address the question of equivalence between modeling results obtained on intra-individual and inter-individual levels of psychometric analysis. Our focus is on the concept of measurement invariance and the role it may play in this context. We discuss this in general against the background of the latent variable paradigm, complemented by an operational demonstration in terms of a linear state...