Construction of the average variance extracted index for construct validation in structural equation models with adaptive regressions

• Published in: Communications in statistics. Simulation and computation Vol. 52; no. 4; pp. 1639 - 1650
• Main Authors: dos Santos, Patricia Mendes, Cirillo, Marcelo Ângelo
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 03.04.2023; Taylor & Francis Ltd
• Subjects: Adaptive regression; Error analysis; Kurtosis; Monte Carlo simulation; Multivariate statistical analysis; Outliers; Outliers (statistics); Structural equation model; Structural equation modeling; Structural models; Variance
• ISSN: 0361-0918; 1532-4141
• DOI: 10.1080/03610918.2021.1888122

A range of indicators, such as the average variance extracted (AVE), is commonly used to validate constructs. In statistics, AVE is a measure of the amount of variance that is captured by a construct in relation to the amount of variance due to measurement error. These conventional indices are formed by factor loadings resulting from estimated least squares or maximum likelihood regressions. Thus, a new proposition that provides new factor loadings may result in a more informative AVE index. Consequently, this study consists of the improvement of the index by using adaptive regressions. A Monte Carlo simulation study was performed considering different numbers of outliers generated by distributions with symmetry deviations and excess kurtosis and sample sizes defined as n = 50, 100, and 200. The conclusion was that, in formative structural models, the adaptive linear regression (ALR) method showed good efficiency for correctly specified models. The results obtained from the ALR method for models with specification errors showed low efficiency, as expected.