Multilevel factor analytic models for assessing the relationship between nurse-reported adverse events and patient safety

We explore health outcomes and nurse staffing data that are multivariate multilevel structured. These data can be used to relate latent constructs such as patient safety to hospital, nursing unit, nurse and patient characteristics by using factor analytic models. It is important that the multilevel nature of the data is taken into account; otherwise it can lead to invalid inferences. We explore the relationship between patient safety and nurse-reported adverse events from the Belgian chapter of the Europe Nurse Forecasting Survey. The data were split into a learning and a validation data set. Since no a priori factor structure has been proposed in the literature, we establish the factor structure by using a frequentist exploratory factor analysis on the learning data set and validate the factor structure proposed by using a Bayesian confirmatory factor analysis on the validation data set. Multivariate analysis-of-variance discrepancy measures were used to assess the need for multilevel factor analysis. We establish that there was substantial between-nursing-unit, but not between-hospital, variability to warrant the use of multilevel factor analyses. The final model was a two-level (nurse level and nursing unit level) factor analytic model with two factors at both levels. The Bayesian approach offers more flexibility in fitting the multilevel confirmatory factor analysis. To avoid double usage of the data the validation and learning data sets were used to fit and assess the goodness of fit of the multilevel confirmatory factor analysis respectively.