Assessment of Latent Constructs: a joint application of generalizability theory and covariance modelling with an emphasis on inference and structure

For the conceptually oriented researcher it appears that much can be gained by approaching models that reflect high interpretability of latent factors combined with high generalizability of linear composites representing the factors. The present study demonstrates how perspectives from covariance structural modelling (CSM) and generalizability theory (G‐theory) can be combined for a comprehensive assessment of latent constructs. This integration is implemented by a modelling procedure where a generalizability‐theory‐oriented component (GTC) model is specified in a covariance‐modelling framework. The GTC model is applied to a one‐facet person by indicator crossed design and to a two‐facet person by indicator within a construct design in the present paper. This model can be applied to a large variety of different measurement designs. By appropriate prespecification of the model matrices, the GTC model can estimate generalizability‐study (G‐study) or decision‐study (D‐study) variance components. If a proper rationale can be established, further decomposition of the G‐ and the D‐study variance components is possible. The potentiality of the present GTC model suggests that the validity of inferences reflecting both the interpretability of latent factors and the generalizability of the corresponding observed linear composites can be improved by taking into account a covariance‐modelling framework.