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Reflective Measurement Model
Reflective Measurement Model
It is a measurement model specification, in which it is assumed that the indicators are caused by the underlying construct.
Convergent Validity
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
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 signifiÂcant. 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.
Outer Loading Relevance Testing
Outer Loading Relevance Testing
Indicator 2: Average Variance Extracted (AVE)
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).
AVE is equivalent to the communality of a construct. An AVE value of 0.50 or higher indicates that the construct explains more than half of the variance of its indicators.
AVE of less than 0.50 indicates that more error remains in the items than the variance explained by the construct.
If AVE < 0.50, then item with the lowest factor loading for that particular construct should be deleted.
Indicator 3: Internal Consistency Reliability
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:
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.
If CR < 0.70, then item with the lowest factor loading for that particular construct should be considered to be deleted.
CR of 0.60 to 0.70 are acceptable in exploratory research, while in more advanced stages of research, values between 0.70 and 0.90 can be regarded as satisfactory (Nunally & Bernstein, 1994).
Values above 0.90 (and definitely> 0.95) are not desirable because they indicate that all the indicator variables are measuring the same phenomenon and are therefore unlikely to be a valid measure of the construct
Discriminant Validity
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
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).
Limitation of Fornell & Larcker Criterion
Limitation of Fornell & Larcker Criterion
Performs very poorly when indicator loadings of the construct differ only slightly (e.g., between 0.6 & 0.8). If the loadings vary more strongly, its performance improves, but is still rather poor overall (Hair et al., 2017; Henseler et al., 2015; Voorhees et al., 2016)
Cross-Loading
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
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)
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
- HTMT.90 (Gold et al., 2001): More than 0.90 indicates a lack of discriminant validity
- Using bootstrapping to test whether HTMT is significantly different from 1 (HTMTinference). Does the 90% bootstrap confidence interval of HTMT include 1? If yes, no discriminant validity. If No, discriminant validity is satisfactory.
Summary
Summary
Is the measurement model valid?
Is the measurement model valid?
- No, then refine and improve measures, and design new study.
- Yes, Proceed to test structural model
Sources
Sources
- Click here for convergent validity calculator.
Exercise
Exercise
Exercise 1: Manufacturing Strategy. Please download data-set here, and draw the model below.
Further Reading
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.
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