Confirmatory factor analysis tests whether a factor structure you specified in advance actually fits your data. You state which observed items load on which latent factor before estimating anything, then judge the measurement model against fit indices such as CFI, TLI, RMSEA, and SRMR. It is the standard way to show that a questionnaire measures the constructs you claim it measures.
Why a dissertation needs the confirmatory step at all
Every quantitative hypothesis in a survey-based dissertation rests on an assumption almost nobody states out loud: that the scale scores actually represent the constructs named in the research questions. If a twenty-item questionnaire does not behave as four coherent subscales, a regression run on those four subscale means is testing something other than the theory. Confirmatory factor analysis is where that assumption gets examined rather than assumed.
This is also why examiners ask for it. A committee cannot evaluate your structural findings without first believing your measurement, so construct validity evidence comes before hypothesis testing in the results chapter. Establishing it early has a practical benefit too: a scale that fails at this stage can be revised or dropped while there is still time, instead of undermining every result that follows.
Confirmatory and exploratory analysis answer different questions
The distinction is about whether the structure is an input or an output. In an exploratory factor analysis you let the data suggest how many factors exist and which items belong together; every item is free to load on every factor, and rotation makes the result readable. That is the right approach for a new instrument or an unfamiliar population, and the mechanics are covered in running an exploratory factor analysis in SPSS.
In a confirmatory model the structure is fixed before estimation. Items assigned to Factor 1 are not permitted to load on Factor 2, and every constrained path is a testable claim. Because the model can be wrong, it can also be rejected, which is precisely what makes the evidence worth something. Use exploratory factor analysis when you are discovering a structure and confirmatory factor analysis when you are testing one that theory or prior validation already specifies.
One rule saves a great deal of trouble: do not run both on the same sample and report the confirmatory result as independent evidence. If the structure was derived from these data, confirming it on the same data is circular. Split the sample, or collect a fresh one.
What has to be true before you estimate
A confirmatory model makes real demands of the data, and most failed analyses fail here rather than at estimation.
- Sample size. Maximum likelihood estimation is unstable in small samples. Around 200 cases is a common working minimum, with 10 to 20 cases per estimated parameter as the more honest guide, so a model with more indicators needs more data. Decide this at the design stage using how large a sample the model needs.
- Multivariate normality. Standard maximum likelihood assumes it. When items are skewed, robust estimators such as MLR, or a categorical estimator such as WLSMV for ordinal items, are the correct response. Start with checking normality before estimation.
- Identification. Each factor needs a scale, set either by fixing one loading to 1 or by fixing the factor variance to 1. The model also needs at least as many known values as parameters to be estimated; three indicators per factor is the safe minimum.
- Complete, clean data. Listwise deletion can remove a large share of a survey sample, so full information maximum likelihood is usually the better route. The trade-offs are set out in deciding how to treat missing responses.
Reading the fit indices without cherry-picking
No single number decides whether a measurement model fits. Report a set, and report the same set you planned to report.
- Chi-square. A non-significant value indicates good fit, but it is almost always significant once the sample passes a few hundred cases. Report it for completeness; do not rest a conclusion on it.
- CFI and TLI. Comparative indices where .95 or above is the widely cited threshold for good fit and .90 is often treated as acceptable.
- RMSEA. .06 or below indicates good fit, with values up to about .08 usually described as reasonable. Report the confidence interval alongside it.
- SRMR. .08 or below is the conventional cut-off.
- Factor loadings. Standardised loadings should generally exceed .50, and ideally .70. A low loading is a substantive finding about that item, not a nuisance.
Treat these as guidelines rather than hard rules, because they were derived from simulations under specific conditions. What an examiner will not accept is a model justified by whichever two indices happened to pass.
When the model does not fit
Poor fit is information. The temptation is to add correlated error terms until the indices improve, and that is where a defensible analysis turns into an indefensible one. Every modification has to be theoretically justifiable and reported as a modification.
Work through the plausible causes in order: an item that is double-barrelled or ambiguous and loads weakly; two items with near identical wording, producing genuine shared error variance; a factor that is empirically indistinguishable from another, which shows up as a factor correlation above about .85 and suggests they should be merged; or a structure that simply does not replicate in your population, which is a publishable result rather than a failure. If you modify the model, say so explicitly, give the reasoning, and treat the modified version as exploratory unless you can test it on new data.
Beyond fit: reliability and validity evidence
A model can fit and still describe a weak scale, so pair the fit indices with the evidence a reviewer expects. Composite reliability above .70 indicates the indicators consistently measure their factor, and it is generally preferable to coefficient alpha because it does not assume every item contributes equally. Average variance extracted above .50 supports convergent validity. For discriminant validity, the square root of the average variance extracted for each factor should exceed that factor's correlations with the others. The reliability side of this is covered in scale reliability and internal consistency.
Where the measurement model sits inside SEM
A confirmatory factor analysis is the measurement half of a structural equation model. Estimating it on its own first is deliberate: if the measurement model does not fit, any structural paths estimated on top of it are uninterpretable, and you would not know whether a weak path reflects the theory or the questionnaire. Fit the measurement model, confirm it, then add the structural paths, as set out in modelling the full structural system.
Reporting it so a committee can follow the reasoning
State the hypothesised structure and its source before any numbers appear. Give the software, the estimator, and how missing data were handled. Report the fit indices as a set, then a table of standardised loadings with standard errors, followed by composite reliability and average variance extracted per factor. Disclose every modification and its justification. Finish with a sentence saying plainly whether the structure was supported, because that is the sentence the rest of your results chapter depends on. The formatting conventions are in APA-format reporting of your results.
Measurement validation is the part of a quantitative dissertation that most often sends a student back for corrections, largely because it is attempted last and under time pressure. If you would rather have the model specified and defended properly the first time, our dissertation statistics team takes it on from the questionnaire onward.