htmt {semTools}

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 lavCor function.

Usage

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

Arguments

model

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 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 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. 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. 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. 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)