Your scale has four dimensions on paper. Do your data agree? Confirmatory factor analysis answers that question by testing a measurement model you specify in advance: which items belong to which construct, and nothing else. In a thesis that uses structural equation modeling, it is the step that must succeed before any hypothesis about paths between constructs can be tested.
This article is part of our guide How to Write a Master’s Thesis by the Mastermind PhD team and relates to our Statistical Analysis service. Sources last checked: November 2026.
This guide shows how to prepare the data, draw and run a confirmatory factor analysis model in IBM SPSS Amos, read the fit indices, assess reliability and validity, and use modification indices without overfitting. The menu names refer to recent versions of AMOS; older versions look very similar.
What is confirmatory factor analysis? It is a form of structural equation modeling that tests whether a hypothesized measurement model fits the observed data. The researcher specifies the number of latent constructs, which observed items load on each construct and which errors, if any, correlate. The software estimates the loadings and reports how well the implied covariance matrix reproduces the observed one.
When do you use confirmatory factor analysis instead of EFA?
Use CFA when theory or previous research already defines the structure of the scale, and you want to test it. Use exploratory factor analysis when the structure is unknown, or when a scale has been newly developed or substantially changed. Running an EFA and a confirmatory factor analysis on the same sample does not provide independent confirmation; if you need both, split the sample.
How do you prepare the data?
- Sample size: confirmatory factor analysis has no fixed minimum, but 200 is often cited as a reasonable starting point for a model of moderate complexity, and more is needed for many constructs or weak loadings (Kline, 2023).
- Missing data: AMOS can estimate with missing values (full information maximum likelihood, by ticking Estimate means and intercepts), but then it will not produce modification indices or bootstrapping. Many students therefore handle missing values in SPSS before opening AMOS, and report how.
- Normality: maximum likelihood assumes multivariate normality. Request Tests for normality and outliers in AMOS and check Mardia’s coefficient; with clear non-normality, use bootstrapping or report robust results.
- Reverse-coded items must be recoded before the analysis.
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How do you draw and run the model in AMOS?
- Open AMOS Graphics and link the SPSS file through File, then Data Files.
- Use the “Draw a latent variable or add an indicator” tool: click once to draw the construct, then click inside it once per item to add indicators with their error terms.
- Drag the item names from List variables in data set onto the rectangles.
- Name the constructs (double-click, Object Properties) and name all error terms with Plugins, then Name Unobserved Variables.
- Draw double-headed arrows (covariances) between every pair of constructs.
- AMOS fixes the first loading of each construct to 1 automatically so the model is identified.
- In View, then Analysis Properties, then Output, tick Standardized estimates, Squared multiple correlations and Modification indices.
- Click Calculate estimates and open Text Output.
Which fit indices should you report in a CFA?
Report several indices from different families, never only one, when you evaluate a confirmatory factor analysis. The cutoffs most often cited come from Hu and Bentler (1999), who stressed that they are guidelines rather than strict rules.
| Index | What it measures | Common cutoff |
|---|---|---|
| χ² with df and p | Exact fit; almost always significant in large samples | Report it, interpret with χ²/df (below about 3 is often used) |
| CFI | Comparative fit against a null model | ≥ .95 good, ≥ .90 acceptable in many studies |
| TLI | Comparative fit with a parsimony penalty | ≥ .95 |
| RMSEA with 90% CI | Approximate error per degree of freedom | ≤ .06 good, ≤ .08 acceptable |
| SRMR | Average standardized residual | ≤ .08 |
SRMR is not in the default AMOS text output. Get it through Plugins, then Standardized RMR, which opens a window you must keep open while running the model.
How do you assess reliability and validity?
Standardized loadings should be significant and ideally .70 or higher; loadings between .50 and .70 are often retained if the construct still meets the criteria below.
Composite reliability (CR) should be at least .70. It is calculated from the standardized loadings and is preferred to Cronbach’s alpha in a CFA context.
Convergent validity: the average variance extracted (AVE) should be at least .50, meaning the construct explains more than half of its items’ variance (Fornell & Larcker, 1981).
Discriminant validity: two common tests.
- Fornell-Larcker criterion: the square root of each construct’s AVE is larger than its correlations with other constructs.
- HTMT ratio: values below .85 (strict) or .90 (lenient) indicate discriminant validity. Henseler, Ringle and Sarstedt (2015) showed that HTMT detects problems the Fornell-Larcker criterion misses.
AMOS does not compute CR, AVE or HTMT by default in a confirmatory factor analysis. Calculate them from the standardized output in a spreadsheet, or use a validated plugin, and state which method you used.
How do you use modification indices responsibly?
Modification indices show how much χ² would drop if a fixed parameter were freed. The most common suggestion is a covariance between two error terms. Correlating errors is defensible only when there is a substantive reason, such as two items with near-identical wording or a shared method, and the errors belong to the same construct. Never correlate errors across constructs to improve fit.
Before freeing anything, look at weak items. Removing an item with a loading below .50 is often cleaner than adding error covariances. Make changes one at a time, re-estimate after each, and report every modification.
How do you report the confirmatory factor analysis?
The following is an illustrative example of the wording, not real results: “A confirmatory factor analysis of the four-factor model was conducted in AMOS using maximum likelihood (N = 386). After removing one item with a standardized loading below .50, the model showed acceptable fit, χ²(146) = 312.45, p < .001, χ²/df = 2.14, CFI = .951, TLI = .943, RMSEA = .054, 90% CI [.046, .063], SRMR = .047. All standardized loadings were significant (.61 to .86); composite reliability ranged from .81 to .89 and AVE from .52 to .64.”
Add a table with each item, its standardized loading, and each construct’s CR and AVE, plus a discriminant validity table, and include the diagram as a figure.
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Frequently asked questions
What if my model fit is poor?
Check the data first: entry errors, reverse coding, outliers and non-normality. Then inspect weak loadings and large standardized residuals. Modify only with a theoretical reason, and report all changes. Sometimes the honest conclusion is that the scale does not behave as expected in your sample.
Do I need CFA if I use SmartPLS?
SmartPLS evaluates a measurement model in its own way (loadings, CR, AVE, HTMT) but is not a covariance-based confirmatory factor analysis and does not rely on the same fit indices. The choice between AMOS and SmartPLS depends on your aims; our comparison of the two explains the differences.
Should I run confirmatory factor analysis for each construct separately?
Testing each construct alone is useful for spotting weak items, but the final model should include all constructs together with their covariances, since discriminant validity can only be judged jointly.
Why are my standardized loadings above 1?
A standardized loading above 1 (a Heywood case) usually signals a problem: too few items on a construct, very high correlation between constructs, a small sample or a misspecified model. Investigate before reporting.
Is Cronbach’s alpha still needed?
Many committees still expect it. Report alpha alongside composite reliability, noting that CR does not assume equal loadings.
Sources
- Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1–55. https://doi.org/10.1080/10705519909540118
- Fornell, C., & Larcker, D. F. (1981). Evaluating structural equation models with unobservable variables and measurement error. Journal of Marketing Research, 18(1), 39–50. https://doi.org/10.2307/3151312
- Henseler, J., Ringle, C. M., & Sarstedt, M. (2015). A new criterion for assessing discriminant validity in variance-based structural equation modeling. Journal of the Academy of Marketing Science, 43(1), 115–135. https://doi.org/10.1007/s11747-014-0403-8
- Byrne, B. M. (2016). Structural Equation Modeling With AMOS: Basic Concepts, Applications, and Programming (3rd ed.). Routledge.
- Kline, R. B. (2023). Principles and Practice of Structural Equation Modeling (5th ed.). Guilford Press.
Sources last checked: November 2026. This article is general educational guidance and does not replace your university regulations or your supervisor’s instructions. How we prepare our content.