Ordinal Convergent Validity
Ordinal Convergent Validity Assessment · Also known as: OCV, convergent validity for ordinal scales, polychoric convergent validity, ordinal AVE
Ordinal convergent validity assesses the degree to which indicators of the same latent construct correlate strongly with each other when those indicators are measured on ordinal (e.g., Likert-type) scales. It adapts standard convergent validity procedures — factor loadings, average variance extracted, and HTMT ratios — to account for the discrete, bounded nature of ordinal response categories using polychoric correlations and ordinal-appropriate estimation methods.
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When to use it
Use ordinal convergent validity assessment when your scale items use ordinal response formats (Likert, rating scales with five or fewer categories) and you want to confirm that items intended to measure the same construct do indeed cohere. It is the correct approach whenever item-level skewness, ceiling or floor effects, or fewer than six response categories make the assumption of continuous normality untenable. Do not use the standard (Pearson-based) convergent validity procedure in these situations, as it can produce misleading loadings and AVE values. Ordinal convergent validity is also inappropriate when items are genuinely continuous and approximately normally distributed, in which case the standard ML-based CFA is simpler and equally valid.
Strengths & limitations
- Corrects for attenuation bias introduced by treating ordinal responses as continuous, yielding more accurate factor loadings and AVE estimates.
- Polychoric correlations and ordinal estimators (DWLS/WLSMV) are robust to non-normality, making them appropriate for the skewed distributions common in survey data.
- Provides a principled, quantitative summary of item coherence (AVE) and a direct comparison between within- and across-construct correlations (HTMT).
- Integrates naturally into a full ordinal CFA workflow, enabling simultaneous assessment of model fit, reliability (ordinal omega), and both convergent and discriminant validity.
- Software implementations (lavaan, Mplus, R packages polycor and psych) make the procedure accessible without requiring custom programming.
- Polychoric correlation estimation requires sufficiently large samples (commonly at least 200–300 observations) to be stable; small samples can produce non-positive-definite matrices.
- The 0.50 AVE threshold is a rule of thumb, not a fixed criterion; borderline values (e.g., 0.45–0.49) require contextual judgment and should not be mechanically rejected.
- DWLS/WLSMV estimators lose efficiency relative to ML when data are genuinely continuous, so mis-specifying the data type in the other direction also introduces error.
- Polychoric correlations assume bivariate normality of the underlying continuous variables; violations of this assumption can distort the estimated correlations.
Frequently asked
Why does it matter whether I use polychoric or Pearson correlations for convergent validity?
Pearson correlations applied to ordinal items are attenuated relative to the true association between the underlying continuous variables. This attenuation lowers estimated factor loadings and AVE, which can make a genuinely valid scale appear to fail the convergent validity threshold. Polychoric correlations correct for this attenuation, providing an unbiased basis for the factor model.
Which estimator should I use for ordinal CFA?
DWLS (also called WLS with a diagonal weight matrix) or its mean-and-variance-adjusted form WLSMV are the most widely recommended for ordinal data because they do not require multivariate normality and produce well-calibrated standard errors and fit statistics. WLSMV is the default in Mplus for categorical indicators and is also available in lavaan via estimator = 'WLSMV'.
What AVE value is sufficient for convergent validity?
The commonly cited threshold is AVE >= 0.50, meaning the latent factor accounts for at least half the variance in its indicators. Values slightly below 0.50 may be defensible if composite reliability (omega) is high (above 0.60) and the overall pattern of loadings is strong, but the case must be made explicitly rather than the threshold being ignored.
How does HTMT complement AVE in ordinal convergent validity?
AVE measures how much variance a factor captures from its own items. HTMT assesses whether items measuring the same construct correlate more strongly with each other than with items from other constructs. Used together on the polychoric matrix, AVE confirms adequate within-construct convergence while HTMT guards against insufficient between-construct discrimination, providing a more complete picture of construct validity.
Can I use ordinal convergent validity with binary items?
Yes. Binary items use tetrachoric rather than polychoric correlations, but the logic and procedure are identical. Most software that supports polychoric correlations also handles tetrachoric as a special case when items have exactly two categories.
Sources
- Rhemtulla, M., Brosseau-Liard, P. E., & Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. Psychological Methods, 17(3), 354–373. DOI: 10.1037/a0029315 ↗
- Flora, D. B., & Curran, P. J. (2004). An empirical evaluation of alternative methods of estimation for confirmatory factor analysis with ordinal data. Psychological Methods, 9(4), 466–491. DOI: 10.1037/1082-989X.9.4.466 ↗
How to cite this page
ScholarGate. (2026, June 3). Ordinal Convergent Validity Assessment. ScholarGate. https://scholargate.app/en/psychometrics/ordinal-convergent-validity
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Confirmatory factor analysisPsychometrics↔ compare
- Convergent ValidityPsychometrics↔ compare
- Discriminant ValidityPsychometrics↔ compare
- Measurement InvariancePsychometrics↔ compare
- Ordinal CFAPsychometrics↔ compare
- Ordinal Reliability AnalysisPsychometrics↔ compare