Heterotrait-monotrait ratio of correlations (HTMT)

The averages run over distinct indicator pairs. Discriminant validity is questioned when the ratio exceeds 0.85 (or the more lenient 0.90); the criterion is a decision, so the tests report a confusion matrix rather than an average.

Usage

Hetero(X, construct_assignment, threshold = 0.85)

Arguments

X: Observations by indicators matrix.
construct_assignment: One construct label per indicator.
threshold: Ratio above which validity is questioned.

Value

List with estimate (largest ratio), htmt, pair_first, flagged, threshold, discriminant_validity, n, method.

Details

Formula: HTMT = mean heterotrait-heteromethod correlation / sqrt(mean within-i correlation * mean within-j correlation).

References

Henseler, Ringle and Sarstedt (2015), A new criterion for assessing discriminant validity in variance-based structural equation modeling, Journal of the Academy of Marketing Science 43(1):115-135, eq. (6). doi:10.1007/s11747-014-0403-8

Examples

set.seed(1)
X <- matrix(rnorm(80), 20, 4)
Hetero(X, construct_assignment = c(1, 1, 2, 2))
#> $estimate
#> [1] 1.046638
#> 
#> $htmt
#> [1] 1.046638
#> 
#> $pair_first
#> [1] 1 2
#> 
#> $flagged
#> [1] 1
#> 
#> $threshold
#> [1] 0.85
#> 
#> $discriminant_validity
#> [1] 0
#> 
#> $n
#> [1] 20
#> 
#> $method
#> [1] "HTMT eq. (6) of Henseler, Ringle & Sarstedt (2015)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"