- Multivariate analysis examines several variables at once; the technique is chosen by the decision question, not by whichever statistics package is at hand.
- Regression explains an outcome (satisfaction, purchase intent, spending) through several factors and shows the contribution of each, but it does not prove causation.
- Factor analysis reduces many correlated questions to a few underlying dimensions, useful for building indices and simplifying later analysis.
- Cluster analysis groups respondents by similarity and underpins segmentation; the solution must be checked for stability and profiled on variables not used to form it.
- All three need planned data: suitable scales, an adequate sample and the necessary questions included in the questionnaire from the start.
1. The problem: cross-tabulations are no longer enough
A service company has the results of a survey of 800 customers with 40 questions. The report contains cross-tabulations: satisfaction by age, by region, by type of subscription. Every table is correct, yet management has three questions that no table answers. Which of the 15 service attributes matters most for the intention to stay? What do the 25 brand statements customers rated actually boil down to? And are there distinct groups of customers who should be treated differently? Multivariate analysis is the family of statistical techniques that examine several variables at once and answer questions like these.
This article explains three techniques, regression, factor analysis and cluster analysis, through the decision question each one answers. It is not a statistics course but a guide for whoever commissions data analysis and needs to know what to ask for, what to check and how to read the result.
2. What multivariate analysis is: two families of techniques
Multivariate techniques fall into two families, depending on the structure of the question.
- Dependence techniques start from a variable to be explained (satisfaction, purchase intent, choice of product) and look for the factors that influence it. Regression is the main example; discriminant analysis and logistic regression are the variants for categorical outcomes such as "bought" or "did not buy".
- Interdependence techniques have no variable to explain. They look for structure in the data: which variables go together (factor analysis) or which respondents resemble each other (cluster analysis).
The first question for any multivariate analysis is therefore: do we have an outcome to explain, or are we looking for structure? The answer picks the family, and the type of variables (numeric scales or categories) picks the specific technique.
3. Regression: which factors explain an outcome
Multiple regression estimates how a numeric outcome varies with several factors considered together. In a satisfaction study, the outcome might be the intention to remain a customer, and the factors the ratings of attributes: speed, courtesy, price, clarity of the bill. The coefficients show how much the outcome changes when one factor rises by one unit, holding the others constant, and the coefficient of determination (R squared) shows what share of the variation in the outcome all the factors together explain. This is the basis of the driver analysis described in the guide on customer satisfaction and NPS.
Three cautions decide whether a regression result can be used.
- Association is not causation. Regression shows that two variables move together, controlling for the other factors included. It does not prove that one produces the other. Causal evidence requires an experiment, not a regression on survey data.
- Multicollinearity. When the factors are strongly correlated with each other, for example "friendly staff" and "competent staff", the coefficients become unstable and may change from one sample to the next, and the relative importance of each factor can no longer be established unambiguously. The remedies are to combine closely related factors, often through a prior factor analysis, and to present importance through several measures rather than just one.
- Validation. A model fitted on one sample always fits that sample better than it fits reality. Testing it on a part of the data not used in estimation shows whether the model holds up. Automatic stepwise selection of factors is particularly prone to this problem.
4. Factor analysis: what dimensions lie behind many questions
Image, attitude or workplace climate questionnaires often contain 20-40 statements rated on the same scale. Many of them in fact measure the same thing. Factor analysis identifies these underlying dimensions, called factors: for example, 25 statements about a bank may reduce to four dimensions, such as trust, accessibility, modernity and cost.
The process has several steps that should be reported. First, the data are checked for suitability: the statements must be sufficiently correlated, and the usual tests (Bartlett's test of sphericity and the KMO measure) show whether they are. Next, the number of factors is decided, using criteria such as eigenvalues greater than 1, the scree plot and, above all, interpretability. The factors are rotated to make them easier to interpret, and each one is named after the statements that load strongly on it. The result is then used through factor scores, through simple indices built from each factor's main statements, or by choosing one representative statement per factor for shorter future studies.
As a rule of thumb, the sample should be at least four to five times the number of variables analysed, and in practice more is sought. Naming the factors is an act of interpretation, not an output of the calculation: two analysts may name the same solution differently, so the report must show the statements behind every label.
5. Cluster analysis: what groups of customers exist
Cluster analysis groups respondents so that those in the same group are as similar as possible and the groups as different from each other as possible. It is the core technique of segmentation: customers are grouped by needs, benefits sought, attitudes or behaviour, and each group becomes a segment with its own strategy. The guide on market sizing and segmentation shows how segments are used in decisions; here we are concerned with how they are produced.
The quality of a segmentation is settled by a few technical choices. Clustering variables are chosen according to the logic of the decision, not thrown "all into the model". Variables measured on different scales are standardised, and outliers are examined, because they can form artificial groups. Hierarchical methods help choose the number of groups, and non-hierarchical methods (k-means type) refine the solution. The number of groups has no single statistical answer: it is chosen on statistical criteria, interpretability and usefulness, because a marketing plan can work with four or five segments, not twelve.
6. How the techniques combine in a real project
In real projects the techniques are used together, in a logical order. A typical segmentation study starts with factor analysis of the attitude statements, reducing 30 correlated variables to 5-6 dimensions; continues with cluster analysis on those dimensions to identify the segments; and ends with profiling the segments and, possibly, a regression or discriminant analysis that shows which short questions can assign a new customer to a segment. A satisfaction study may use factor analysis to merge closely related attributes and regression to establish which of the resulting dimensions matters most.
Other multivariate techniques answer more specialised questions: conjoint analysis measures how much each feature of an offer is worth and is central to pricing research, while multidimensional scaling produces perceptual maps of competing brands. The principle stays the same: the question chooses the technique.
7. What multivariate analysis needs from the data
Most of the problems in a multivariate analysis are born before the analysis, in the study design. Four requirements must be settled before the questionnaire.
- The necessary variables are in the questionnaire. A regression cannot include a factor that was never measured. The list of possible factors is built from qualitative research or the team's experience, and the guide on questionnaire design shows how to word them.
- The scales are suitable. Regression, factor analysis and distance-based cluster analysis need numeric variables or scales with enough points, applied consistently. Yes/no or categorical questions call for other variants of the techniques.
- The sample is large enough. For factor analysis, at least four to five times the number of variables; for regression, large relative to the number of factors; for segmentation, large enough for the smallest useful segment to have a workable base.
- Weighting and design are taken into account. If the data are weighted or the sample is clustered, standard errors and significance tests must be calculated accordingly, as the article on weighting survey data explains.
8. The three techniques compared
| Technique | Decision question | Data it needs | What it delivers | Typical mistake |
|---|---|---|---|---|
| Regression | Which factors explain an outcome, and how much does each matter? | A numeric outcome and factors measured in the same survey | Coefficients, R squared, a ranking of factors | Reading coefficients as causes; ignoring multicollinearity |
| Factor analysis | What dimensions lie behind many questions? | Many correlated variables on the same scale | Factors, loadings, scores or indices | Unfounded factor names; too small a sample |
| Cluster analysis | What distinct groups of respondents exist? | Clustering variables chosen for the decision, standardised | Segments, each with its profile | Accepting an unchecked solution; too many segments |
9. Common errors and how to spot them in a report
The first warning sign is a report that presents results without diagnostics: a regression with no R squared and no check of the correlations between factors, a factor analysis with no criterion for the number of factors, a segmentation with no stability check. The second is causal language on correlational data: "price drives satisfaction" instead of "price is the factor most strongly associated with satisfaction". The third is apparent precision that ignores the sample: rankings of factors separated by tiny differences, presented as if they were certain. The fourth, perhaps the most expensive, is a statistically elegant segmentation that cannot be applied, because the segments cannot be identified in the customer base or do not differ on anything marketing can influence.
Good multivariate analysis is recognisable by the clarity of its translation: every statistical result ends with a sentence about what it means for the decision and how certain it is.
10. What to ask the agency
- The decision question for each analysis and the proposed technique, agreed before the questionnaire.
- The list of variables the analysis needs and confirmation that they are included, with suitable scales.
- A justification of the sample size for the planned techniques and for the smallest group to be analysed.
- For regression: R squared, a multicollinearity check, validation on separate data, and wording free of causal claims.
- For factor analysis: the suitability tests, the criterion for the number of factors and the table of loadings.
- For segmentation: the stability check, segment profiles on external variables and a rule for classifying new customers.
- A translation of every result into implications for the decision, with its degree of certainty.
- The dataset and the analysis syntax, so the analysis can be repeated in later waves.
Multivariate analysis is not a technical extra added at the end but the part of a study that turns data into priorities, dimensions and segments. Planned from the start, it makes the difference between a report full of tables and one that says what to do. Our market research and segmentation and decision support teams can help you choose the analysis that fits your question.
See also: Data analysis and desk research Market research and segmentation Decision support Market sizing and segmentation Customer satisfaction and NPS Weighting survey data
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