HTMT2–an improved criterion for assessing discriminant validity in structural equation modeling

Abstract

PurposeOne popular method to assess discriminant validity in structural equation modeling is the heterotrait-monotrait ratio of correlations (HTMT). However, the HTMT assumes tau-equivalent measurement models, which are unlikely to hold for most empirical studies. To relax this assumption, the authors modify the original HTMT and introduce a new consistent measure for congeneric measurement models: the HTMT2.Design/methodology/approachThe HTMT2 is designed in analogy to the HTMT but relies on the geometric mean instead of the arithmetic mean. A Monte Carlo simulation compares the performance of the HTMT and the HTMT2. In the simulation, several design factors are varied such as loading patterns, sample sizes and inter-construct correlations in order to compare the estimation bias of the two criteria.FindingsThe HTMT2 provides less biased estimations of the correlations among the latent variables compared to the HTMT, in particular if indicators loading patterns are heterogeneous. Consequently, the HTMT2 should be preferred over the HTMT to assess discriminant validity in case of congeneric measurement models.Research limitations/implicationsHowever, the HTMT2 can only be determined if all correlations between involved observable variables are positive.Originality/valueThis paper introduces the HTMT2 as an improved version of the traditional HTMT. Compared to other approaches assessing discriminant validity, the HTMT2 provides two advantages: (1) the ease of its computation, since HTMT2 is only based on the indicator correlations, and (2) the relaxed assumption of tau-equivalence. The authors highly recommend the HTMT2 criterion over the traditional HTMT for assessing discriminant validity in empirical studies.

Psychometric Properties of the Wong and Law Emotional Intelligence Scale in a Colombian Manager Sample

“…In addition, the relationship between the variables was assessed as small, medium and large considering correlation coefficients above 0.10, 0.30 and 0.50, respectively ( Cohen 1988 ). On the other hand, the discriminant evidence was collected through two procedures, the heterotrait–monotrait ratio (HTMT2), considering the generic measurement model ( Roemer et al 2021 ), taking as adequate values lower than 0.85 ( Henseler et al 2015 ), and the Fornell and Larcker criterion, which consists of comparing the square root of the AVE and the correlations with the other variables, where the former must be greater than the latter to conclude that there is discriminant evidence ( Fornell and Larcker 1981 ).…”

Progress in partial least squares structural equation modeling use in marketing research in the last decade

“…For example, a higher HTMT threshold, such as 0.9, can be assumed for conceptually similar constructs, whereas the analysis of conceptually distinct constructs should rely on a lower threshold, such as 0.85 (Franke & Sarstedt, 2019; Hair et al, 2022). Roemer et al (2021) recently proposed the HTMT2, which relaxes the original criterion's assumption of equal population indicator loadings. Their simulation study shows that the HTMT2 produces a marginally smaller bias in the construct correlation estimates when the indicator loading patterns are very heterogeneous; that is, when some loadings are 0.55 or lower while others are close to 1.…”

“…Roemer et al (2021) recently proposed the HTMT2, which relaxes the original criterion's assumption of equal population indicator loadings. Their simulation study shows that the HTMT2 produces a marginally smaller bias in the construct correlation estimates when the indicator loading patterns are very heterogeneous; that is, when some loadings are 0.55 or lower while others are close to 1.…”

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“…The discriminant validity of this study in Table 4 uses the HTMT measure and all have met the cut-off value, which is less than 0.900 (Henseler et al , 2015; Henseler, 2017). In addition to using HTMT, it is measured by the latest measure, namely, HTMT 2 according to Roemer et al (2021). The HTMT online calculator (Henseler, 2021) was used with the results, and all of them have met the cut off value, which is less than 0.900.…”