Convergent Validity

The extent to which the items of the specific construct converge together.

Reflects correlation between items measuring the same construct.

Indicator 1: Outer Loading

• High outer loadings of measurement items indicate that the items converge together on a common construct.

All indicators' outer loadings should be statistically signifi­cant. Because a significant outer loading could still be fairly weak, a common rule of thumb is that the (standardized) outer loadings should be 0.708 or higher. The rationale behind this rule is that square of the outer loading (R-square) should be higher than 0.50.

Indicator 2: Average Variance Extracted (AVE)

• Indicates how much variation in the multiple items is explained by the latent variable.

• Is comparable to the proportion of variance explained in factor analysis.

• Value ranges from 0 and 1.

• AVE should exceed 0.5 to suggest adequate convergent validity (Bagozzi & Yi, 1988; Fornell & Larcker, 1981).

Indicator 3: Internal Consistency Reliability

Indicates consistency of measurement items to measure a common construct.

The traditional criterion for internal consistency is Cronbach's alpha, which provides an estimate of the reliability based on the inter-correlations of the observed indicator variables.

Limitation of Cronbach's Alpha:

• It assumes that all indicators are equally reliable (i.e., all the indicators have equal outer loadings on the construct).

• It is sensitive to the number of items in the scale & generally tends to underestimate the internal consistency reliability.

To overcome the limitations of Cronbach's Alpha, Composite Reliability (CR) is suggested as a replacement of the traditional criterion.

Discriminant Validity

Indicates the uniqueness of a construct from other constructs.

A latent variable should explain better the variance of its own indicators than the variance of other latent variables.

Fornell & Larcker Criterion

The square root of AVE of a latent variable should be higher than the correlations between the latent variable and all other variables (Chin, 2010; Chin 1998b; Fornell & Larcker, 1981).

Cross-Loading

The loadings of an item on its assigned latent variable should be higher than its loadings on all other latent variables.

Limitation of cross loading

Fails to indicate a lack of discriminant validity when 2 constructs are perfectly correlated, which renders this criterion ineffective for empirical research (Hair et al., 2017; Henseler et al., 2015).

Heterotrait-Monotrait Ratio (HTMT)

Average heterotrait-heteromethod correlations relative to the average monotrait-heteromethod correlation (Hair et al., 2017; Henseler et al., 2015).

HTMT values close to 1 indicate a lack of discriminant validity

Threshold value:

• HTMT_.85 (Kline, 2011): More than 0.85 indicates a lack of discriminant validity. This threshold is used when the variables are conceptually dissimilar.

• HTMT_.90 (Gold et al., 2001): More than 0.90 indicates a lack of discriminant validity. This threshold is used when the variables are conceptually similar.

• If HTMT is greater than 0.9, then use bootstrapping to test whether HTMT is significantly different from 1 (HTMT_inference). Does the 90% bootstrap confidence interval of HTMT include 1? If yes, discriminant validity is not satisfactory. If No, discriminant validity is satisfactory, then the researcher can proceed with analysis.

Things to take note

1. If more than one item in a construct do not achieve the threshold value of outer loading, the researcher should only delete the item one at a time for that particular construct, starting form the item with lowest loading. After that, the model should be re-estimated.

2. Items with loading lower than 0.708 can be kept when the AVE is more than 0.50.

3. If negative value of outer loading is found in a construct, then the researcher should check if the reversed coded items have been addressed. If the negative value still remains, the item should be deleted.

4. Caveat: the researcher should not delete more than 20% of the indicators in the model (Hair, Babin, & Krey, 2017; Hair et al., 2014). Otherwise, the whole research moves into EFA rather than CFA. In addition, the credibility of the research instrument us very much questionable.

Is the measurement model valid?

• No, then refine and improve measures, and design new study.

• Yes, Proceed to test structural model

Sources

• Click here for convergent validity calculator.

Exercise 1

Manufacturing Strategy: Please download data-set here, and draw the model below.

Exercise 2

Smartphone Addiction: Please download data-set here, and draw the model below.

Exercise 3

Please download the data HERE.

Further Reading

Nawanir, G., Fernando, Y., & Teong, L. K. (2018). A second-order model of lean manufacturing implementation to leverage production line productivity with the importance-performance map analysis. Global Business Review, 19(3_suppl), S114-S129. Click here.

Nawanir, G., Lim, K. T., Othman, S. N., & Adeleke, A. Q. (2018). Developing and validating Lean manufacturing constructs: An SEM approach. Benchmarking: An International Journal, 25(5), 1382-1405. Click here.