Detecting Causal Relations Among Indicators with the CTA Test: Simulations and Applications

In the context of using structural equation modelling to develop economic and social indicators, a debate regarding the choice of measurement modes for theoretical constructs is becoming a very important issue, with conceptual and practical implications. The nature of each construct, which can be defined as reflective or formative, is mainly based on theoretical considerations, but confirmatory tetrad analysis (CTA) can support decisions about the model specification. One flexible approach to carrying out CTA involves multiple hypothesis testing, which also provides relevant information on empirical data to guide the construction of composite indicators. This prompts a deeper investigation of the effects of correction methods on decisions derived from tests, with special attention to error control and statistical power. In this study, we explore the properties of six procedures, in particular the well-known Bonferroni and Benjamini–Hochberg corrections, using various simulation scenarios and real applications. We find that, with respect to the Benjamini–Hochberg, the Bonferroni correction is too conservative and has lower power, especially with small sample sizes and many manifest variables.