What Is Discriminant? How to Read Discriminant Validity in SmartPLS
What is discriminant validity
In a quantitative thesis, discriminant usually appears in the phrase discriminant validity. It answers a practical question: are the constructs in your model genuinely different, or are they measuring almost the same thing.
For example, your model may contain two latent variables, Service Quality and Satisfaction. Discriminant validity is supported when the indicators of Service Quality concentrate on that construct and do not overlap excessively with the indicators of Satisfaction. You check this as part of the measurement model, before interpreting path coefficients or testing hypotheses.
In SmartPLS, you will usually see tables or outputs named Discriminant Validity, HTMT, Cross Loadings or Fornell-Larcker Criterion. At a general level, discriminant validity reflects the difference between the variance a construct explains in its own indicators and the variation it shares with other constructs. Under the Fornell-Larcker criterion, the square root of a construct's AVE is compared with the correlations between that construct and the remaining constructs (Fornell and Larcker, 1981).
You also need to distinguish discriminant validity from what is a scale. A scale is a set of indicators used to measure a construct. Discriminant validity is a group of criteria used to check whether different scales overlap too much.
Why discriminant validity matters in quantitative research
Discriminant validity helps you decide whether constructs can remain separate in the model or whether the measurement scales need to be reviewed. If two constructs are too highly correlated, interpreting the separate effect of each construct on the dependent variable becomes difficult to justify. A path coefficient may then reflect overlapping scale content rather than a clear theoretical relationship.
In PLS-SEM, you normally assess the measurement model first and then move to the structural model. This two-step approach, checking the measurement model before the structural model, follows the procedure described by (Anderson and Gerbing, 1988). Within the measurement model, discriminant validity is assessed alongside reliability and convergent validity. A scale can have good Cronbach's Alpha or CR and still fail discriminant validity if it is too similar to another construct.
Discriminant validity also helps you answer a question from your supervisor or the committee: “Why are these two concepts treated as two separate independent variables in the model?” You need to show that the HTMT, Fornell-Larcker or cross-loadings results support a measurement-level distinction between the constructs. If you cite only the theory and omit the discriminant validity results, the scale assessment remains incomplete.
Do not confuse discriminant validity with discriminant analysis. Discriminant analysis is a classification or prediction technique that usually asks which group an observation belongs to. Discriminant validity assesses the quality of measurement scales in an SEM model. The two terms contain the word “discriminant”, but their objectives, input data and output tables are different.
What value of discriminant validity is acceptable
Do not look at one number and make an immediate decision. SmartPLS usually provides several checks, and HTMT is widely used to assess discriminant validity. According to (Henseler et al., 2015), HTMT should be below 0.85, or below 0.90 when the constructs are conceptually close. The Fornell-Larcker criterion requires the square root of a construct's AVE to be greater than its correlations with the other constructs (Fornell and Larcker, 1981).
The table below summarises common thresholds and the sources you can cite in your thesis. These thresholds are reference criteria for the research context. They are not an automatic reason to delete an indicator when a result is outside the preferred range.
| Criterion in the output | Common level | Interpretation | Canonical source |
|---|---|---|---|
| HTMT between two constructs | < 0.85 | Discriminant validity is supported under the strict threshold | (Henseler et al., 2015) |
| HTMT between conceptually close constructs | < 0.90 | May be accepted when the concepts are close, but the theoretical basis must be explained | (Henseler et al., 2015) |
| Square root of AVE | Greater than the correlation with another construct | The construct is distinct from the remaining constructs under Fornell-Larcker | (Fornell and Larcker, 1981) |
| Outer loading of an indicator | ≥ 0.70 | The indicator has a strong association with its construct | (Chin, 1998) |
| AVE | ≥ 0.50 | The construct explains a sufficient share of the average indicator variance | (Fornell and Larcker, 1981) |
| Cross-loadings | Highest loading is on the expected construct | The indicator does not load more strongly on another construct | (Chin, 1998) |
This table does not mean that HTMT below 0.85 is the only condition that matters. Review the indicator content, theoretical model, outer loadings and related statistics together. In current PLS-SEM reporting, HTMT is often the main check, while Fornell-Larcker and cross-loadings can provide additional evidence (Hair et al., 2019).
How to read discriminant validity in the output
Suppose you open SmartPLS 4, run PLS Algorithm and select the results for your constructs. The Discriminant Validity table may display an HTMT matrix. The following is illustrative output, not the result of an actual study.
| Construct pair | HTMT | Reference threshold | Illustrative conclusion |
|---|---|---|---|
| CLDV - HAILONG | 0.742 | < 0.85 | Acceptable |
| CLDV - GIATRI | 0.861 | < 0.90 if the concepts are close | Contextual explanation needed |
| HAILONG - TRUNGTAM | 0.934 | < 0.90 | Not acceptable |
| GIATRI - HAILONG | 0.803 | < 0.85 | Acceptable |
In this example, CLDV - HAILONG has an HTMT value of 0.742, which is below 0.85. This supports discriminant validity under the strict criterion. The HAILONG - TRUNGTAM pair has a value of 0.934, exceeding even 0.90. You should not immediately delete an indicator because this value is high. First determine whether the two constructs are genuinely close in content.
When reading the Fornell-Larcker table, the diagonal usually contains the square root of AVE. For example, suppose CLDV has a square root of AVE of 0.812, while its correlation with HAILONG is 0.742 and its correlation with GIATRI is 0.615. The criterion is supported because 0.812 is greater than both related correlations. If an off-diagonal value is greater than the diagonal value for a construct, that is a signal that you need to investigate further.
With the Cross Loadings table, check whether each indicator has its highest outer loading on the construct for which it was originally designed. For example, CLDV3 has a loading of 0.781 on CLDV, 0.422 on HAILONG and 0.365 on GIATRI. This pattern is consistent with the intended measurement. If CLDV3 loads 0.612 on CLDV but 0.744 on HAILONG, review the wording, coding or assignment of the indicator to the construct.
You can also review outliers when you suspect that unusual rows are increasing the correlation between two constructs. An outlier is not a convenient reason to delete data. You need a checking criterion and a record of the decision you made.
What to do when discriminant validity is not supported
EFA or PLS-SEM rarely produces a completely clean result on the first run. When HTMT exceeds the selected threshold, work from the easiest causes to check toward larger changes in the model.
Check the variable coding and input data
Open the .csv or .sav file and check variable names, coding direction, missing values and reverse-coded indicators. A reverse-coded indicator that was not recoded can reduce correlations within a construct or create an unusual loading pattern. In SmartPLS 4, make sure every indicator has been assigned to the correct construct and has not been placed in a similarly named construct by mistake.
Read the indicator wording again
Place the two constructs with high HTMT side by side and read every item wording. If the indicators for “intention to use” and “intention to continue using” are asking almost the same thing, the problem may be in the scale design. Compare the scale source, research context and construct definitions before changing the data.
Check cross-loadings and outer loadings
Look for an indicator with a low loading on its intended construct or a high loading on another construct. Deleting an indicator is defensible when it has a statistical problem and a clear content-based reason. After each deletion, rerun the model and save the previous result so you can explain the decision to your supervisor or the committee.
Delete an indicator for a reason, not to reach a target number
If an indicator has ambiguous wording, cross-loads on another construct and can be removed without destroying the construct's content, you may consider deleting it. Do not delete several indicators in succession simply to push HTMT below 0.85. That can remove important content from the scale and leave you with a result that is difficult to defend.
Review whether constructs should be combined or separated
When two constructs repeatedly have high HTMT and their content is almost identical, the issue may be in the conceptual model. You may need to discuss combining the constructs, separating dimensions or retaining the model while explaining its limitation. A model change made after seeing the results must be recorded as a research decision. Do not present it as though it had been specified from the beginning.
Discriminant validity and convergent validity
Convergent validity and discriminant validity are both part of measurement model assessment, but they answer different questions. Convergent validity asks whether indicators intended to measure the same construct actually converge on that construct. The statistics commonly reviewed include outer loading, AVE and CR. AVE of 0.50 or above and CR of 0.70 or above are commonly used reference points (Fornell and Larcker, 1981).
Discriminant validity asks whether one construct is different from another construct. You normally review HTMT, Fornell-Larcker and cross-loadings. A construct can meet the AVE requirement and still have a high HTMT with another construct. Meeting convergent validity requirements is therefore not enough to conclude that the scale has adequate validity overall.
You also need to keep discriminant validity separate from concepts such as mediator, moderator and moderating. A mediator and a moderator describe a variable's role in a relationship between variables. Discriminant validity describes whether constructs can be distinguished from one another. These are different layers of assessment within a quantitative model.
Common mistakes
The first mistake is writing “HTMT is acceptable” without naming the construct pair, reporting the value or stating the threshold used. In Chapter 4, include the HTMT table or a shortened table showing the important pairs, together with the source (Henseler et al., 2015).
The second mistake is using CFI, TLI, RMSEA or SRMR to conclude that discriminant validity has been established in SmartPLS. These fit indices are commonly associated with CB-SEM under (Hu and Bentler, 1999). They do not replace HTMT in PLS-SEM.
The third mistake is calling discriminant validity discriminant analysis. If you are looking at HTMT, Fornell-Larcker Criterion or Cross Loadings, you are assessing the discriminant validity of the scale. If you are classifying observations into groups, you are dealing with a different problem.
The final mistake is deleting indicators until the table looks “clean”. Every deleted indicator needs both a statistical and a content-based reason, together with a record of the results before and after the change. If a construct is left with too few indicators, stop and review the model instead of continuing to adjust the output.
Frequently asked questions
What is discriminant validity?
Discriminant validity is evidence that different constructs in a model measure different concepts. In SmartPLS, you usually assess it with HTMT, Fornell-Larcker and cross-loadings.
What value of discriminant validity is acceptable?
HTMT below 0.85 is commonly treated as acceptable under the strict threshold. For two constructs that are conceptually close, a threshold below 0.90 may be used as a reference, but you need to explain the theoretical basis clearly (Henseler et al., 2015).
What should I do if HTMT is not acceptable?
Check the coding, reverse-coded indicators, construct assignment, wording and cross-loadings first. Only then consider deleting an indicator with a clear problem or discussing a model adjustment. Do not delete an indicator merely to reduce HTMT.
How are convergent validity and discriminant validity different?
Convergent validity asks whether the indicators of one construct converge on that construct. Discriminant validity asks whether one construct is different from another. A scale can meet convergent validity requirements and still fail discriminant validity.
Do I need to report both HTMT and Fornell-Larcker?
Report the criterion required by your method and supervisor, and you can use the other criterion as additional evidence. HTMT is often prioritised in current PLS-SEM reporting, while Fornell-Larcker allows readers to inspect the correlation structure between constructs as an additional check.
When you return to your own file, open the HTMT table, record each construct pair, compare the values with the selected threshold, and check cross-loadings before changing the model. If you need to rerun the full procedure on your .sav or .csv file, M4 Data Analysis performs this step in SPSS and SmartPLS, keeps the real results and preserves the processing history for Chapter 4.