htmt: Assessing Discriminant Validity using Heterotrait-Monotrait...

In semTools: Useful Tools for Structural Equation Modeling

Assessing Discriminant Validity using Heterotrait–Monotrait Ratio

Description

This function assesses discriminant validity through the heterotrait-monotrait ratio (HTMT) of the correlations (Henseler, Ringlet & Sarstedt, 2015). Specifically, it assesses the arithmetic (Henseler et al., ) or geometric (Roemer et al., 2021) mean correlation among indicators across constructs (i.e. heterotrait–heteromethod correlations) relative to the geometric-mean correlation among indicators within the same construct (i.e. monotrait–heteromethod correlations). The resulting HTMT(2) values are interpreted as estimates of inter-construct correlations. Absolute values of the correlations are recommended to calculate the HTMT matrix, and are required to calculate HTMT2. Correlations are estimated using the lavaan::lavCor() function.

Usage

htmt(model, data = NULL, sample.cov = NULL, missing = "listwise",
  ordered = NULL, absolute = TRUE, htmt2 = TRUE)

Arguments

model	lavaan lavaan::model.syntax() of a confirmatory factor analysis model where at least two factors are required for indicators measuring the same construct.
data	A data.frame or data matrix
sample.cov	A covariance or correlation matrix can be used, instead of ⁠data=⁠, to estimate the HTMT values.
missing	If "listwise", cases with missing values are removed listwise from the data frame. If "direct" or "ml" or "fiml" and the estimator is maximum likelihood, an EM algorithm is used to estimate the unrestricted covariance matrix (and mean vector). If "pairwise", pairwise deletion is used. If "default", the value is set depending on the estimator and the mimic option (see details in lavaan::lavCor()).
ordered	Character vector. Only used if object is a data.frame. Treat these variables as ordered (ordinal) variables. Importantly, all other variables will be treated as numeric (unless is.ordered in ⁠data=⁠). See also lavaan::lavCor().
absolute	logical indicating whether HTMT values should be estimated based on absolute correlations (default is TRUE). This is recommended for HTMT but required for HTMT2 (so silently ignored).
htmt2	logical indicating whether to use the geometric mean (default, appropriate for congeneric indicators) or arithmetic mean (which assumes tau-equivalence).

Value

A matrix showing HTMT(2) values (i.e., discriminant validity) between each pair of factors.

Author(s)

Ylenio Longo (University of Nottingham; [e-mail])

Terrence D. Jorgensen (University of Amsterdam; [e-mail])

References

Henseler, J., Ringle, C. M., & Sarstedt, M. (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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s11747-014-0403-8")}

Roemer, E., Schuberth, F., & Henseler, J. (2021). HTMT2—An improved criterion for assessing discriminant validity in structural equation modeling. Industrial Management & Data Systems, 121(21), 2637–2650. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1108/IMDS-02-2021-0082")}

Voorhees, C. M., Brady, M. K., Calantone, R., & Ramirez, E. (2016). Discriminant validity testing in marketing: An analysis, causes for concern, and proposed remedies. Journal of the Academy of Marketing Science, 44(1), 119–134. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s11747-015-0455-4")}

Examples

HS.model <- ' visual  =~ x1 + x2 + x3
              textual =~ x4 + x5 + x6
              speed   =~ x7 + x8 + x9 '

dat <- HolzingerSwineford1939[, paste0("x", 1:9)]
htmt(HS.model, dat)

## save covariance matrix
HS.cov <- cov(HolzingerSwineford1939[, paste0("x", 1:9)])
## HTMT using arithmetic mean
htmt(HS.model, sample.cov = HS.cov, htmt2 = FALSE)

semTools documentation built on April 3, 2025, 9:23 p.m.