A brand tracker asks 30 attribute questions. A personality questionnaire has 50 statements. Reading 30 or 50 columns one at a time is slow, and many of them say nearly the same thing. Factor analysis is the standard way to find out which ones belong together, and the choice of method depends on whether you are exploring, testing or simply summarizing.
Key takeaways
- Factor analysis explains the correlations among many survey items using a few unobserved factors, and the three types usually discussed are exploratory, confirmatory and principal component analysis.
- Use exploratory factor analysis to find which items group together, and confirmatory factor analysis to test a structure you specified in advance.
- PCA is a related summarizing method, not strictly factor analysis, and structural equation modeling is a broader framework that contains confirmatory factor analysis.
- Check the data first with the KMO measure, where below about 0.6 is a warning, then use a scree plot to choose how many factors.
- Items loading above about 0.4 define a factor, and factor analysis groups variables, while cluster analysis groups respondents.
What is factor analysis?
Factor analysis starts from a simple observation: when people answer several questions in a similar way, something shared may be driving those answers. That shared thing cannot be measured directly, so it is called a latent variable or a factor. Someone who thinks a brand is good value will tend to agree with “fair prices”, “worth what I pay” and “good value for money”, and the correlations among those three items are the evidence.
The method works from the correlation matrix of your items. It asks how many underlying factors are needed to reproduce those correlations, and how strongly each item is tied to each factor. That tie is the factor loading. The output is a short list of named dimensions you can report, trend and use in other analysis, in place of a long list of items.
Factor analysis groups variables, not people. If you want to group respondents, you want cluster analysis, covered below.
What are the three types of factor analysis?
Most introductions, including our earlier version of this article, name three. Two of them are true factor analysis. The third needs a caveat.
Exploratory factor analysis (EFA)
EFA is for when you do not know the structure in advance. You give it the items, it proposes how many factors there are and which items load on which, and you interpret the result. Use it on a new battery of attributes, a draft questionnaire, or any time you want to find out which items belong together.
Confirmatory factor analysis (CFA)
CFA is for when you already have a structure, from theory or from an earlier EFA, and want to test it. You specify in advance which items load on which factors, and the analysis reports how well that model fits the data. Use it to validate a scale before you trend it across waves, or to check that a questionnaire measures the same dimensions in two markets.
Principal component analysis (PCA)
PCA is the third member of the usual trio, and it is the one that causes confusion. It is a related technique, not strictly factor analysis. PCA builds components, which are weighted combinations of your items, so that the first captures as much total variance as possible, the second as much of what is left, and so on.
It does not assume latent causes. It is a way of summarizing data, and statistical software often puts it next to factor analysis for that reason. Our guide to principal component analysis covers it in more depth.
Where does structural equation modeling fit?
An older version of this article listed structural equation modeling (SEM) as the third type. That grouping was wrong, and we have corrected it. SEM is a broader modeling framework that tests relationships among latent variables and observed ones. CFA is the measurement part of that framework.
So SEM contains confirmatory factor analysis rather than sitting beside it as a separate kind of factor analysis. SEM is also not exploratory in the way EFA is: you specify a model first, then test it. If you need to test whether one latent factor drives another, SEM is the right tool. If you need to find or confirm the factors themselves, use EFA or CFA.
| Method | Question it answers | Model required first? | Typical use |
|---|---|---|---|
| EFA | Which items group together? | No | New attribute battery, draft questionnaire |
| CFA | Do items load on the factors I expect? | Yes | Validating a scale before trending it |
| PCA | How do I summarize many correlated items in a few scores? | No | Reducing predictors before regression |
| SEM | Do my latent factors relate to each other as I hypothesize? | Yes | Testing causal pathways |
What is factor analysis in psychology?
Factor analysis began in psychology. Charles Spearman used it in 1904 to argue that scores on different mental tests were correlated because they shared a general ability, which he called g. Since then the method has been a workhorse for measuring things nobody can observe directly: personality traits, attitudes, intelligence, anxiety.
The logic is the one described above. A psychologist writes many questionnaire statements, gives them to a sample, and runs an EFA to see how many dimensions emerge. The familiar five-factor model of personality, with traits such as extraversion and neuroticism, was developed largely through this kind of analysis. Later studies use CFA to check that a published scale holds up in a new sample or population.
Market research uses the same machinery. A brand perception battery is a questionnaire, and “innovative”, “modern” and “ahead of its time” play the role of personality items. The skill transfers directly.
How do you run a factor analysis?
The steps are the same whether the items are about personality or about toothpaste.
- Check the data suit the method. Items should be on a comparable scale, usually a rating scale, and correlate with each other. Two common checks are Bartlett’s test of sphericity and the Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy. A KMO below about 0.6 is usually read as a warning.
- Decide how many factors to keep. Plot the eigenvalues in a scree plot and look for the elbow where the curve flattens. Eigenvalues above 1 are a common starting rule, not a law. Interpretability has the last word.
- Extract the factors. Common choices are principal axis factoring and maximum likelihood. Maximum likelihood also gives fit statistics, which helps if you later move to CFA.
- Rotate. The raw solution is hard to read, so you rotate it until each item loads mainly on one factor. Use an orthogonal rotation such as varimax if you want uncorrelated factors, or an oblique rotation such as oblimin if you expect the factors to correlate, as they often do in attitude data.
- Read the loadings and name the factors. Items loading above about 0.4 define a factor. Name each factor from the items that sit on it. Drop items that load on nothing or on two factors at once, then re-run.
- Check reliability and create scores. Test how consistently the items in each factor hang together, then compute a factor score or a simple average of the items for use in reporting and further analysis.
How do six survey items load on two factors?
Here is a small example with illustrative numbers, not real survey data. Imagine six agreement statements about a subscription service, rated 0 to 10 by a sample of customers. An EFA with two factors and a varimax rotation produces these loadings.
| Item | Factor 1 (Value) | Factor 2 (Ease of use) | Communality |
|---|---|---|---|
| Q1 Good value for money | 0.82 | 0.10 | 0.68 |
| Q2 Prices are fair | 0.78 | 0.05 | 0.61 |
| Q3 Worth what I pay | 0.74 | 0.15 | 0.57 |
| Q4 Easy to use | 0.08 | 0.85 | 0.73 |
| Q5 Simple to set up | 0.12 | 0.80 | 0.65 |
| Q6 Intuitive layout | 0.18 | 0.71 | 0.54 |
Read the table across a row first. Q1 loads 0.82 on Factor 1 and only 0.10 on Factor 2, so it belongs to Factor 1. The communality is the share of that item’s variance the two factors explain together. With an orthogonal rotation it is the sum of the squared loadings: for Q1, 0.82 squared is 0.6724 and 0.10 squared is 0.0100, which gives 0.6824, or 0.68 rounded.
Now read down the columns. Q1 to Q3 load strongly on Factor 1 and weakly on Factor 2, so Factor 1 is a value-for-money dimension. Q4 to Q6 do the opposite, so Factor 2 is ease of use. Every item has one clear home, which is what a clean solution looks like.
To see how much each factor explains, add up the squared loadings down its column. Factor 1 gives 0.6724 + 0.6084 + 0.5476 + 0.0064 + 0.0144 + 0.0324 = 1.8816. Factor 2 gives 0.0100 + 0.0025 + 0.0225 + 0.7225 + 0.6400 + 0.5041 = 1.9016.
Together that is 3.7832 out of a possible 6 (one unit of variance per item), so the two factors explain about 63% of the total variance in the six items. Each person now has two scores, value and ease, in place of six answers, and you can report either of them by region or customer type.
How is factor analysis different from PCA and cluster analysis?
Factor analysis and PCA are often run side by side and sometimes give similar answers, but they have different aims. Factor analysis models the variance that items share and treats the rest as unique to each item. PCA uses all the variance and makes no such split.
If you want to name and interpret underlying dimensions, use factor analysis. If you want a compact set of scores for a regression or a chart, PCA is a reasonable choice.
Cluster analysis answers a different question. Factor analysis groups variables, so six items become two factors. Cluster analysis groups respondents, so a thousand people become four segments with similar answers.
Hierarchical clustering builds a tree of nested groups, which is useful when you do not know how many segments to expect, and is explained in our guide to hierarchical clustering. A common sequence is to reduce the items with factor analysis first, then cluster respondents on the factor scores, which gives cleaner segments than clustering on dozens of overlapping questions.
What are the practical uses of factor analysis?
In market research, the main uses are:
- Reducing a 30-attribute brand battery to five drivers a team can actually work with.
- Building composite scores for a tracker, so wave-to-wave movement is easy to read.
- Structuring a segmentation by clustering on factor scores.
- Cleaning a questionnaire by finding items that measure nothing distinct.
- Preparing predictors for driver analysis, where correlated attributes would otherwise cause trouble.
Education researchers use it to study what sits behind test results, such as verbal and numerical ability, and psychologists use it for traits and scales as described above. The wider set of applications, with more examples, is in practical uses of factor analysis.
How do you do this in practice?
Most factor analysis runs in a statistics package, and the output is a set of scores or averages per respondent. After that the work is ordinary survey reporting: cutting each factor by region, age or customer type, weighting to the population, and testing whether differences are real. Halo Reports does that part, with crosstabs and banner tables, weighting and significance testing, charts and interactive report pages. Teams running wide, complex studies and global brand trackers can keep that work in one governed platform for insights and research.
What are the common mistakes?
- Treating PCA as if it were factor analysis. If your goal is to interpret latent dimensions, PCA can overstate how much the items have in common. Choose the method for the question.
- Keeping factors you cannot name. The eigenvalue rule can give you more factors than make sense. If a factor is a grab bag of unrelated items, merge it back or drop it.
- Ignoring cross-loadings. An item loading 0.5 on two factors does not define either one. Rewrite it, remove it, or accept that it measures a blend.
- Using too few respondents or too few items per factor. Solutions from small samples change when you add people. Aim for at least three or four good items per factor.
- Running a CFA on the same data you used to explore. A structure that was found in a sample will always fit that sample well. Confirm it on new data.
- Forcing the analysis on weakly correlated items. If the correlations are low, there is nothing to reduce. Check the correlation matrix before you extract anything.
Start with the data you have. Pull the correlation matrix for one battery of 10 to 20 related questions, check the KMO, and run an exploratory analysis with two to four factors. Name what you find, drop the items that fit nowhere, and write down the structure you end up with.
That written structure is your hypothesis for a confirmatory test the next time you field the survey. If the factors describe how people see your brand, you can then track brand health, consideration, sentiment and competitors continuously.