Multilevel SEM with random slopes in discrete data using the pairwise maximum likelihood

A correlated traits correlated (methods - 1) multitrait-multimethod model for augmented round-robin data

We didactically derive a correlated traits correlated (methods - 1) [CTC(M - 1)] multitrait-multimethod (MTMM) model for dyadic round-robin data augmented by self-reports. The model is an extension of the CTC(M - 1) model for cross-classified data and can handle dependencies between raters and targets by including reciprocity covariance parameters that are inherent in augmented round-robin designs. It can be specified as a traditional structural equation model. We present the variance decomposition as well as consistency and reliability coefficients. Moreover, we explain how to evaluate fit of a CTC(M - 1) model for augmented round-robin data. In a simulation study, we explore the properties of the full information maximum likelihood estimation of the model. Model (mis)fit can be quite accurately detected with the test of not close fit and dynamic root mean square errors of approximation. Even with few small round-robin groups, relative parameter estimation bias and coverage rates are satisfactory, but several larger round-robin groups are needed to minimize relative parameter estimation inaccuracy. Further, neglecting the reciprocity covariance-structure of the augmented round-robin data does not severely bias the remaining parameter estimates. All analyses (including data, R scripts, and results) and the simulation study are provided in the Supporting Information. Implications and limitations are discussed.