Confirmatory Factor Analysis (CFA)
A method that tests whether survey items actually measure well the factor structure the researcher specified in advance.
Can job burnout be measured accurately with a handful of survey items? Are emotional exhaustion and cynicism distinct concepts? Can we also check whether the items on professional efficacy really belong to the factor the researcher expected?
In this way, the method that tests whether a factor structure the researcher specified in advance holds up in real data is confirmatory factor analysis (CFA).
Whereas exploratory factor analysis focuses on exploring from the data which factors the items group into, confirmatory factor analysis first fixes the links between items and factors according to theory and then evaluates how well the model explains the observed data. It checks not only the factor loadings but also the overall fit and whether the factors can be told apart.
It is widely used in research that measures latent concepts with survey items, in psychology, organizational and HR studies, education, health, marketing and more. In this article we use a job burnout scale for employees as an example to look at the measurement structure of three factors, factor loadings, model fit, how CFA differs from EFA, and points to watch when reporting results.
What is confirmatory factor analysis (CFA)?
It evaluates whether a measurement structure set in advance fits the data.
Confirmatory factor analysis (CFA) is a method used when a concept that is hard to observe directly is measured with several survey items: the researcher specifies in advance which items measure which factor and then tests how well that structure fits the data.
For example, if job burnout is defined as three dimensions, emotional exhaustion, cynicism and professional efficacy, you can check whether each item is properly linked to its intended dimension.
Why do we need confirmatory factor analysis?
Before using scale scores, you need to check the item structure first.
Grouping survey items a few at a time and averaging them does not automatically make each group measure a single concept. The relationships among items may differ from what was expected, and different factors may turn out to be overly similar.
CFA checks the measurement structure the researcher assumed and provides a basis for judging whether the scale scores to be used later in group comparisons or structural equation analysis are valid.
How does confirmatory factor analysis work?
It checks how much of the covariance among items the specified factor structure explains.
① Link factors and items based on theory
Emotional exhaustion items E1–E3 are linked to the exhaustion factor, cynicism items C1–C3 to the cynicism factor, and efficacy items P1–P3 to the efficacy factor. Cross-loadings on other factors are constrained to 0 in the basic model.
② Estimate the factor loadings and the error for each item
A factor loading shows how closely an item is connected to its latent factor. Each item also retains unique variation that the factor does not explain.
③ Evaluate whether the model reproduces the actual relationships among items
Based on the difference between the observed covariances and the covariances predicted by the model, you check the χ² test and fit indices such as CFI, TLI, RMSEA and SRMR.
④ Interpret loadings, factor correlations and model diagnostics together
Even if the overall fit is good, if a particular item's loading is low or a correlation between factors is too high, the measurement structure needs further review.
Real-world example: validating a job burnout scale for employees
A three-factor model that distinguishes emotional exhaustion, cynicism and professional efficacy.
Suppose 300 employees were asked to answer 9 items. Each item is measured on a scale from 1 (strongly disagree) to 5 (strongly agree). The figures below are hypothetical results for illustration, not the results of analyzing real data.
| Latent factor | Example survey item | Item code |
|---|---|---|
| Emotional exhaustion | I feel emotionally drained when I finish work | E1–E3 |
| Cynicism | I feel less meaning in my work than before | C1–C3 |
| Professional efficacy | I can solve the tasks assigned to me effectively | P1–P3 |
For professional efficacy a higher score is the positive direction, so when combining it as a subfactor of burnout you must be clear about the score direction and the theoretical definition.
How do you interpret factor loadings?
See how well each item reflects its intended factor.
A standardized factor loading expresses the degree of connection between an item and its factor in a form that is easy to compare. Usually, the larger the absolute value, the more strongly the item is related to that factor. However, you should not delete items based only on a one-size-fits-all cutoff.
| Factor | Item | Standardized loading |
|---|---|---|
| Emotional exhaustion | E1 / E2 / E3 | 0.82 / 0.78 / 0.74 |
| Cynicism | C1 / C2 / C3 | 0.80 / 0.76 / 0.71 |
| Professional efficacy | P1 / P2 / P3 | 0.85 / 0.79 / 0.73 |
For example, if E1's standardized loading is 0.82, it can be interpreted as an item strongly linked to emotional exhaustion. In a simplified standard CFA model, it can also be read as the factor explaining about 67% (0.82²) of the item's variance.
What does model fit tell you?
It evaluates the measurement model as a whole, not just individual items.
Model fit tells you how well the factor structure specified by the researcher reproduces the relationships among items seen in the actual responses. Rather than concluding a model fits based on any single index, review several indices together with theoretical plausibility.
| Index | Value in the hypothetical example | How to read it |
|---|---|---|
| χ²(df=24) | 43.2, p = .009 | A test that assumes perfect fit; sensitive to sample size |
| CFI | 0.969 | Fit relatively better than a comparison model |
| TLI | 0.953 | Comparative fit that accounts for model complexity |
| RMSEA | 0.052 | Level of approximation error of the model |
| SRMR | 0.041 | Average size of the standardized residuals |
Values such as CFI 0.90 or 0.95 and RMSEA 0.06 or 0.08 are only rules of thumb often cited in the literature, not absolute pass marks that apply to every study.
Which indicators do you check in CFA results?
Combine information on reliability and validity together with fit.
Standardized factor loadings and error variances
Check which items measure their factor well and how much unmeasured error remains.
Correlations between factors
Emotional exhaustion and cynicism may be highly correlated, but it also matters whether the two factors are actually distinct. An excessively high correlation can suggest a discriminant validity problem.
Composite reliability and average variance extracted (AVE)
Composite reliability and AVE can be calculated as supplementary indicators in line with the model and estimation method. Meeting a single criterion does not guarantee the quality of measurement.
| What to check | Meaning |
|---|---|
| Factor loadings | The relationship between items and factors |
| Correlations between factors | Whether the latent factors can be distinguished |
| Reliability such as CR / ω | Consistency of scores across the item set |
| AVE | The average share of item variation explained by the factor |
| Residuals · modification indices | Where the model and the actual data disagree |
How does confirmatory factor analysis differ from exploratory factor analysis (EFA)?
One finds a factor structure; the other tests a structure set in advance.
| Aspect | Exploratory factor analysis (EFA) | Confirmatory factor analysis (CFA) |
|---|---|---|
| Main purpose | Explore possible factor structures in the data | Test a factor structure set in advance |
| Links between items and factors | Estimated during exploration | Specified in advance by the researcher |
| Main results | Number of factors · loading pattern · rotation results | Loadings · model fit · factor relationships |
| When it fits | When the structure is unclear | When checking the structure of an existing theory or scale |
If you are developing a new scale, it is best to carry out exploration and confirmation on independent samples. Claiming to have confirmed a structure after exploring it with the same data repeatedly can overstate the fit.
How does CFA differ from structural equation modeling (SEM)?
It separates testing the measurement structure from analyzing paths of influence between factors.
CFA focuses on the measurement relationships between latent factors and observed items. Structural equation modeling (SEM) can add structural relationships, such as regression paths or mediation paths between latent factors, to such a measurement model.
| Question | Suitable analysis |
|---|---|
| Is job burnout measured by three factors? | CFA |
| How is emotional exhaustion related to turnover intention? | The structural model of SEM or another regression model |
| Can the same item structure be compared across departments? | Multigroup CFA / measurement invariance testing |
Points to watch in confirmatory factor analysis
Do not modify items just to make the model fit look better.
Do not force-delete items to suit the results
When deleting items with low loadings or adding error covariances to improve fit, you need a basis in the item content and theory. The modified model should be re-validated on new data where possible.
Check the response scale and estimation method
Depending on how ordinal Likert items are treated, estimation methods such as ML, robust ML or WLSMV may be appropriate.
Check sample size and missing values
The required sample size depends on the number of factors, number of items, loadings, estimation method and so on. Rather than applying a single minimum-sample rule, review the model's complexity and the state of the data.
Check for high factor correlations and identification problems
If the factors can barely be distinguished or the model is not identified, the estimates can become unstable. You should also check for improper variance estimates and convergence warnings.
Good fit does not mean the scale is fully validated
Beyond the measurement structure, check content validity, relationships with other variables, stability over repeated measurement and so on, as fits your purpose.
What extensions of confirmatory factor analysis are there?
The basic single-group measurement model can be extended to suit the study design.
| Extension | Additional question to check |
|---|---|
| Multigroup CFA / measurement invariance | Is the same structure and unit of measurement maintained across genders and departments? |
| Higher-order factor model | Can the three subfactors be explained by a higher-level burnout factor? |
| Longitudinal CFA | Does the scale keep its meaning across different measurement occasions? |
| Method factor model | Is there a common effect of response format or reverse-worded items? |
| Ordinal CFA | How do the results change when the nature of categorical responses is taken into account? |
As the model becomes more complex, you need sufficient data, clear identification conditions and a theoretical basis.
How do you report confirmatory factor analysis results?
Present the model's composition, estimation method, fit and factor loadings together.
In a paper, it is good to report which items were linked to which factors, the data and estimation method, the overall fit, and the standardized factor loadings and relationships between factors.
To test the three-factor structure of the job burnout scale, a confirmatory factor analysis was conducted on 9 items (N = 300). The fit of the hypothesized measurement model was χ²(24) = 43.20, p = .009, CFI = .969, TLI = .953, RMSEA = .052, SRMR = .041. Standardized factor loadings ranged from .71 to .85, and all items were positively related to their designated factors. These results are broadly consistent with the specified three-factor measurement structure.
The figures and sentences above are a hypothetical reporting example, not actual research results. In a real paper, also describe the estimation method used, standard errors and confidence intervals, the significance of the loadings, correlations between factors and additional diagnostics.
Where can confirmatory factor analysis be used?
It is used in many fields that measure latent concepts with surveys.
| Field | Example use |
|---|---|
| Organizations · HR | Validating job burnout, job satisfaction and organizational commitment scales |
| Psychology | Evaluating the measurement structure of anxiety, depression and personality traits |
| Education | Testing the structure of learning motivation and self-efficacy scales |
| Health · nursing | Validating patient experience, quality of life and job stress scales |
| Marketing | Checking the measurement structure of brand trust, satisfaction and loyalty |
Even for a scale already in use, if the study population, language or survey setting changes, you need to check whether the measurement structure stays the same.
Confirmatory factor analysis is a way to check whether a survey properly measures the concepts it intends to.
Read not only the model fit but also each item's loading, the correlations between factors and the diagnostics from the estimation process.
Confirmatory factor analysis is a method for testing whether survey items properly measure the concepts the researcher intended. In the job burnout example, we set up three factors in advance, emotional exhaustion, cynicism and professional efficacy, and looked at the process of evaluating each item's loading and the overall fit of the model.
A single good fit index does not prove all of a scale's validity. You need to review the correlations between factors, the measurement quality of the items, the characteristics of the data and the estimation method together. When modifying a model, too, put the research theory and the meaning of the items ahead of the goal of improving the numbers.
The core of CFA is testing a factor structure set in advance. Check each item's factor loading together with the overall model fit, and look at whether the factors can be distinguished and whether the data and estimation method are appropriate. Any post hoc modification to improve fit must be theoretically justifiable.