What Is Convergent Validity? How to Read AVE, Outer Loading, and CR

What Is Convergent Validity

Convergent validity is the extent to which items measure and converge on the latent variable they were designed to measure. For example, the four items in a Satisfaction scale should consistently reflect the same concept rather than measuring four unrelated aspects.

In quantitative research, you usually assess convergent validity using three groups of indicators: the outer loading of each item, Composite Reliability, usually abbreviated as CR, and Average Variance Extracted, abbreviated as AVE. In PLS-SEM, these indicators appear in SmartPLS output tables. With CB-SEM or CFA run in AMOS, the reporting format may differ, but the underlying question remains the same: do the items genuinely represent the same construct?

AVE indicates the average proportion of variance in the items that is explained by the latent variable. At a general level, you can represent the formula as follows:

AVE = sum of squared outer loadings / number of items.

You do not need to calculate AVE manually when the software has already produced the result. Your task is to check the indicator, compare it with a sourced threshold, and then examine outer loading and CR together. Looking at one AVE value and declaring the scale acceptable is not enough.

If you are checking related concepts, see what is construct validity and the Statistics topic to place convergent validity within the full measurement assessment process.

Why Convergent Validity Matters in Quantitative Research

Convergent validity answers a specific question: do the items in the same scale genuinely reflect the same latent variable? This is part of measurement model assessment, which is usually carried out before you interpret relationships between variables in the structural model.

When convergent validity is adequate, you have a stronger basis for using latent variable scores in hypothesis testing. For example, when the Service Quality scale has acceptable AVE and outer loading values, you can continue to examine whether Service Quality affects Satisfaction. When the items do not converge, the path coefficient may be difficult to interpret because the input construct has not been measured consistently.

Convergent validity does not prove that a scale measures only one concept. It shows that the items within the same construct have an acceptable degree of convergence. You still need to assess discriminant validity using HTMT, Fornell-Larcker, or cross-loading. This is why AVE should not be reported separately from the rest of the measurement model.

In PLS-SEM, the procedure usually has two parts: assess the measurement model first, then assess the structural model. This two-step approach is presented in (Anderson and Gerbing, 1988), and the current PLS-SEM procedure is presented in (Hair et al., 2022). For reflective scales, outer loading, CR, and AVE are usually examined together.

What Level of Convergent Validity Is Acceptable

The commonly used benchmarks are AVE of 0.5 or above and CR of 0.7 or above. According to (Fornell and Larcker, 1981), AVE of 0.5 indicates that the latent variable explains at least half of the average variance in the items. The same source indicates that CR of 0.7 or above is generally suitable for composite reliability.

An outer loading of 0.7 or above is a commonly used benchmark in PLS-SEM according to (Chin, 1998) and (Hair et al., 2022). However, a loading below 0.7 does not automatically mean that you must delete the item. You need to examine AVE, CR, the theoretical content of the item, and the effect of removing it.

You may find a scale with AVE of 0.48, CR of 0.82, and several loadings at acceptable levels. In that situation, examine the context, item content, and your supervisor's requirements before deciding. Do not alter the data simply to push AVE above 0.5.

Treat these benchmarks as reference points rather than automatic rules. They help you make a defensible decision, but they do not replace reading the model and checking the scale content. In your thesis, state the source of each benchmark instead of writing only that it meets the usual standard.

How to Read Convergent Validity in the Output

If you run PLS-SEM, open the results in SmartPLS and review the Outer Loadings, Construct Reliability and Validity, or an equivalent section, depending on the version. SmartPLS 4 may arrange the interface differently from SmartPLS 3, but the main indicator groups still include loading, Cronbach's Alpha, rho_A, CR, and AVE.

The table below is illustrative output, not the result of a real study. The column names follow a common output format so that you know which values to find.

Read each row in order. First, check the CR and AVE for each construct. In this example, all three constructs have CR of 0.7 or above and AVE of 0.5 or above. Then open Outer Loadings to see whether any item has an unusually low loading.

For example, the Outer Loadings table may display rows like these:

CLDV3 has a loading of 0.681, below the 0.7 benchmark. You should not delete the item just because you see that number. Run the analysis with and without CLDV3, compare AVE and CR, and check whether the item has important theoretical content. If deleting it removes a necessary aspect of the scale, retaining it and explaining the decision may be more defensible.

If you use SPSS, you will not see an AVE and outer loading table in the same format as SmartPLS. SPSS is commonly used to run Cronbach's Alpha and EFA, where you check Corrected Item-Total Correlation, KMO and Bartlett's Test, Total Variance Explained, and Rotated Component Matrix. You can also see AVE in SPSS to understand the limits of referring to AVE within an SPSS workflow.

What to Do When Convergent Validity Is Not Adequate

Work through the issue in order, starting with the data, then the items, the measurement model, and finally the reporting. The goal is to identify an explainable cause, not to rerun the model repeatedly until a convenient number appears.

Check the Data and Coding

Open the .sav or .csv file and check variable names, data types, missing values, and reverse-coded items. A reverse-coded item that has not been recoded can sharply reduce the correlations between items in the same scale. Also check whether the Likert scale was entered incorrectly, such as one item ranging from 1 to 5 while another was entered from 1 to 7.

Review Each Outer Loading and the Item Content

Identify the item with the lowest loading, then read its wording again in the questionnaire. It may measure a different aspect, have been translated inaccurately, or have been understood differently by respondents. Do not delete a group of items in one step when you have not established what each item contributes to the construct.

Rerun the Model After You Have a Reason for Deletion

When there is a clear basis, you may delete one item with a low loading and rerun the model. Record the loading, CR, and AVE before and after deletion. Keeping a record of each round allows you to answer your supervisor when asked why an item was removed.

Retain the Item and Explain the Decision When Its Content Matters

Sometimes a loading is below the reference benchmark but the item is still necessary to cover the construct. You may retain it when the overall indicators and theoretical argument are appropriate, while stating the limitation in the discussion. The decision needs to remain consistent with the scale and the research context.

Collect Data Again Only When the Cause Is the Design or the Sample

If you find a questionnaire error, widespread miscoding, or a sample that does not match the target population, collecting data again may be necessary. Software cannot correct an incorrectly written item or turn an unsuitable sample into a valid one. Discuss the decision with your supervisor before deleting data and collecting responses again, because changing the sample halfway through affects the method description.

Distinguishing Convergent Validity from Discriminant Validity

Convergent validity examines whether items within the same construct converge on the same concept. Discriminant validity examines whether different constructs are sufficiently distinct. The two concepts usually appear next to each other in the measurement assessment chapter, but they answer different questions.

AVE, outer loading, and CR are commonly used to assess convergent validity. HTMT, Fornell-Larcker, and cross-loading are commonly used to examine discriminant validity. You can read separately about what is Fornell-Larcker and what is cross loading if you are reviewing Discriminant Validity tables in SmartPLS.

For example, a Service Quality scale may have high AVE but an excessively high HTMT value with Satisfaction. In that case, the convergent validity of each construct may be acceptable, while the boundary between the two constructs is still unclear. An acceptable AVE therefore cannot be used to conclude that overall discriminant validity is also acceptable.

You also need to distinguish convergent validity from what is face validity. Face validity concerns whether an item appears to fit the concept in an immediately recognizable way, while convergent validity is assessed using quantitative evidence from the data.

Common Errors

Looking Only at AVE and Ignoring Outer Loading

AVE is a construct-level indicator, while outer loading is an item-level indicator. An acceptable AVE does not tell you that every item is equally strong. Report both groups of results and clearly state which items were removed, if any.

Using CB-SEM Thresholds for SmartPLS

CFI, TLI, RMSEA, and other fit indicators are generally associated with CB-SEM, not with the core indicators used to assess PLS-SEM. The thresholds in (Hu and Bentler, 1999) are for CB-SEM. When writing up SmartPLS results, focus on outer loading, CR, AVE, HTMT, VIF, R², f², and Q² according to your analysis design.

Deleting an Item Only to Increase AVE

Deleting an item may increase AVE but narrow the content of the construct. If you remove an item, record its code, the reason, and the indicators before and after removal. You must not directly edit participant responses to make the loading higher.

Confusing CR with Cronbach's Alpha

Cronbach's Alpha assumes a particular reliability structure, while CR is widely used in PLS-SEM assessment. The two indicators are related, but they are not the same indicator. In the results table, use the correct column name and do not replace CR with Alpha when reporting the findings.

How to write this in your thesis

You can adapt the following paragraph to your actual results: “The measurement model assessment shows that the scales have Composite Reliability values ranging from [lowest CR] to [highest CR], all [meeting or not meeting] the 0.7 threshold according to (Fornell and Larcker, 1981). AVE values range from [lowest AVE] to [highest AVE], with [number] scales reaching AVE of 0.5 or above. The outer loadings of the items range from [lowest loading] to [highest loading]. Therefore, the model's convergent validity is [accepted or requires further examination].”

This paragraph is only a writing template. Replace every placeholder with the values in your output, state clearly which items were removed if applicable, and do not use the conclusion “accepted” when an important indicator still fails the criterion you selected.

Frequently asked questions

What is convergent validity, and why do I need to assess it?

Convergent validity indicates whether the items in the same scale reflect the same latent variable. You assess it to establish a basis for using the scale when evaluating the structural model and testing hypotheses.

What level of convergent validity is considered good?

The commonly used benchmarks are AVE of 0.5 or above, CR of 0.7 or above, and outer loading of 0.7 or above. These benchmarks need sources, which can be referenced respectively with (Fornell and Larcker, 1981), (Chin, 1998), and (Hair et al., 2022). When an indicator is below the benchmark, review the full scale and the item content before deciding.

Does AVE below 0.5 mean that I should delete the scale immediately?

You cannot decide that immediately. Check outer loading, CR, the number of items, the input data, and the theoretical content of the scale. If you delete an item, rerun the model, save the results before and after deletion, and explain the decision in your thesis.

Can SPSS run convergent validity analysis?

SPSS can support Cronbach's Alpha and EFA, but it does not produce AVE and outer loading through the PLS-SEM procedure used by SmartPLS. If your study uses PLS-SEM, you will usually prepare a .csv dataset and run the model in SmartPLS. If you use CFA or CB-SEM, AMOS is another option, with a different set of indicators and reporting approach.

How are convergent validity and discriminant validity different?

Convergent validity checks the consistency of items within the same construct. Discriminant validity checks the separation between different constructs, usually through HTMT, Fornell-Larcker, or cross-loading. A scale can have acceptable convergent validity and still have a discriminant validity problem.

Open your SmartPLS or SPSS file now, record the outer loading, CR, and AVE for each construct in a separate table, compare every row with the relevant source, and save the output version before removing any item. If you need to run the analysis on your own .sav or .csv file, see M4 data analysis.