Mapping the Patterns You Cannot Average: Multiple Correspondence Analysis for Categorical Course-Evaluation Data

In brief

A lot of course-evaluation data is categorical, not numeric: programme, delivery mode, year of study, a "yes/no/not applicable" answer, or which open-text theme a student raised. Averaging these makes no sense, and factor analysis assumes continuous variables. Multiple correspondence analysis (MCA) is the method built for exactly this case. It takes a table of categorical responses and places every category — and every student — as a point on a low-dimensional map, so that categories answered by the same people sit close together. The result is a picture of how response patterns cluster: which student groups, delivery modes and complaint themes travel together, all without imposing a rating scale on data that never had one.

What the research says

MCA is the multivariable generalisation of simple correspondence analysis, itself a geometric technique for cross-tabulated categorical data developed in the French analyse des données tradition of Jean-Paul Benzécri. The standard reference collection is Michael Greenacre and Jörg Blasius (Eds.), Multiple Correspondence Analysis and Related Methods (Greenacre & Blasius, 2006, Chapman & Hall/CRC, ISBN 1584886285), which assembles both the theory and worked social-science applications and is self-contained enough to serve as a primer.

The clearest applied treatment is Brigitte Le Roux and Henry Rouanet, Multiple Correspondence Analysis (Le Roux & Rouanet, 2010, Sage, Quantitative Applications in the Social Sciences series, No. 163). They frame MCA as geometric data analysis: the analysis produces a Euclidean cloud of categories and a cloud of individuals, and interpretation is about distances and directions in that space. Two categories are close when the same individuals tend to choose both; an individual sits near the categories they endorsed. The principal axes are ordered by how much variance (inertia, in this literature) they explain, much as principal components are.

A compact technical summary is Hervé Abdi and Dominique Valentin's Multiple Correspondence Analysis (Abdi & Valentin, 2007, in N. Salkind, Ed., Encyclopedia of Measurement and Statistics, Sage, pp. 651–657), which lays out the indicator-matrix and Burt-matrix computations and the well-known caveat that raw MCA eigenvalues understate the variance explained, so corrected inertia (the Benzécri or Greenacre adjustment) should be reported.

MCA is distinct from the pattern-finding tools already in the corpus. Latent profile analysis is a model-based clustering of (usually continuous) indicators into latent classes; network psychometrics estimates partial-correlation edges among items; parallel analysis governs how many continuous factors to retain. MCA is none of these — it is an assumption-light, exploratory geometric map of categorical associations, and it is often the right first look before any model is imposed.

Why it matters for course evaluation in practice

Evaluation datasets are full of categorical structure that current reporting flattens. MCA turns that structure into an interpretable map.

• Segment discovery without a model. Plotting categories such as first-year, online mode, raised the "feedback too slow" theme and disagreed that assessment was fair reveals whether these travel together — that is, whether a specific complaint concentrates in a specific student group and mode. This is the exploratory complement to the model-based segmentation in latent profile analysis, and it is far more honest about categorical data than dummy-coding it into a factor analysis.
• Reading open-text themes structurally. Once open comments are coded into themes (Koji does this automatically), MCA can map which themes co-occur with which respondent characteristics — showing, for instance, that "workload" and "unclear expectations" cluster among a distinct cohort rather than being spread evenly. That complements frequency-based approaches like aspect-based sentiment analysis.
• Communicating to non-statisticians. A single MCA map is often more persuasive to a teaching committee than a page of cross-tabs. Proximities on the plane are intuitive: "these students, this mode and this complaint are all in the same corner."

Crucially, MCA respects the measurement level of the data. Where the ordinal-vs-interval debate warns against averaging Likert categories, MCA sidesteps it entirely by treating categories as categories.

A concrete example makes the payoff tangible. Imagine an MCA of a large first-year cohort in which the categories online mode, evening timetable, raised the pace-too-fast theme and disagreed that support was adequate all land in the same quadrant, while on-campus, daytime and praised approachability cluster in the opposite corner. No single cross-tabulation would have made that structure obvious, and averaging the satisfaction scores would have hidden it entirely, because the two groups partly cancel each other out. The map turns a diffuse dataset into a testable hypothesis — that a particular delivery configuration is generating a particular complaint in a particular population — which a follow-up confirmatory model or a targeted consultation can then pursue.

Limitations and honest caveats

• Exploratory, not confirmatory. MCA produces a map, not a test. It suggests patterns; it does not establish that they are statistically reliable or would replicate. Bootstrap or stability checks, and out-of-sample confirmation, are needed before acting.
• Eigenvalues mislead if uncorrected. Raw MCA inertias badly understate explained variance because of the indicator-matrix structure; reporting uncorrected percentages (Abdi & Valentin, 2007) makes the solution look far weaker than it is. Use Benzécri or Greenacre adjusted inertias.
• Interpretation is subjective. Naming the axes and deciding which categories "define" a dimension involves judgement. Two analysts can read the same map differently, so contribution statistics (how much each category contributes to each axis) should discipline the narrative.
• Low-frequency categories distort. Rare categories can be thrown to the edges of the map and dominate an axis despite representing few students; they often need to be merged or treated as passive/supplementary points.
• Not a substitute for a model. If the goal is prediction, class membership probabilities or hypothesis testing, MCA is a first look, not the analysis. It pairs well with, but does not replace, latent-class or regression models.

How Koji incorporates this

Koji generates precisely the mixed categorical dataset — structured choices plus automatically themed open text plus respondent metadata — that MCA is designed to explore.

• Clean categorical capture. Koji's single_choice, multiple_choice, yes_no and ranking question types produce well-defined categorical variables, and respondent attributes (programme, mode, year) are stored consistently — the exact indicator structure MCA consumes, with no lossy conversion to a fake interval scale.
• Automatic thematic coding as MCA input. Koji's automatic thematic analysis turns open-text feedback into categorical theme tags. Those tags become variables in an MCA, letting an institution map how qualitative complaints co-locate with student segments and delivery modes.
• Segment-first reporting. Koji's reporting is built to surface who is saying what, not just an overall average, which is the same question MCA answers geometrically; the platform's structured exports drop directly into MCA-capable tools (R's FactoMineR, for example).
• Honest exploratory framing. Koji presents pattern findings as leads to investigate rather than confirmed effects, matching MCA's exploratory status and steering committees away from over-reading a suggestive cluster.

Koji's core research platform at koji.so uses the same structured-plus-thematic data model for product and customer research, where correspondence analysis and perceptual mapping are long-standing tools for segmenting categorical survey data.

The honest framing: MCA is a lens, not a verdict. Koji supplies the clean categorical and themed data that make the lens usable and keeps the interpretation exploratory — the reliability check and any downstream modelling remain the analyst's responsibility.

Frequently asked questions

When should I use MCA instead of factor analysis?

Use MCA when your variables are genuinely categorical — programme, mode, yes/no answers, coded themes — rather than continuous. Factor analysis assumes interval-level indicators; forcing categorical data into it via dummy coding distorts the result. MCA is built for categories.

How is MCA different from latent profile analysis?

Latent profile analysis is a model-based method that assigns respondents to latent classes, usually from continuous indicators, and gives membership probabilities. MCA is an assumption-light geometric map of categorical associations with no latent-class model. MCA is often the exploratory first step; LPA is a confirmatory-style model.

Why do people say MCA eigenvalues are misleading?

Because of the indicator-matrix structure, raw MCA inertias understate the variance explained. Report Benzécri- or Greenacre-adjusted inertias, or your solution will look far weaker than it is.

Can I map open-text feedback with MCA?

Yes, once the text is coded into categorical themes. The theme tags become variables, and MCA shows which themes co-occur with which student groups and modes. Koji produces those theme tags automatically.

Is an MCA result something I can act on directly?

Treat it as exploratory. MCA suggests patterns; confirm them with stability checks and, where decisions are at stake, a confirmatory model before acting.

References

• Greenacre, M., & Blasius, J. (Eds.). (2006). Multiple Correspondence Analysis and Related Methods. Chapman & Hall/CRC. ISBN 1584886285.
• Le Roux, B., & Rouanet, H. (2010). Multiple Correspondence Analysis (Quantitative Applications in the Social Sciences, No. 163). Sage.
• Abdi, H., & Valentin, D. (2007). Multiple correspondence analysis. In N. Salkind (Ed.), Encyclopedia of Measurement and Statistics (pp. 651–657). Sage.

Related resources

• Latent Profile Analysis for Course-Evaluation Segments
• Network Psychometrics: Items as a Network, Not a Hidden Factor
• Parallel Analysis for Factor Retention
• The Dimensionality Debate for Student Ratings
• Latent Transition Analysis: How Segments Move Between Waves
• Aspect-Based Sentiment Analysis of Open-Text Feedback