Multitudinal Analysis

In my recent essay, Once Upon a Time Series, I’d titled one of the sections “Multitudinal”. It was a playful portmanteau of “multitude” and “longitudinal”.

Would Merriam-Webster approve? They define “multitudinal” as:

1. including a multitude of individuals : populous (e.g., the multitudinous city)
2. existing in a great multitude (e.g., multitudinous opportunities)
3. existing in or consisting of innumerable elements or aspects (e.g., multitudinous applause)

But different versions of the same person can also comprise a multitude!

I am large, I contain multitudes. — Walt Whitman

A self that goes on changing is a self that goes on living. — Virginia Woolf

But what is contemporary technology if not a mechanism for the containment of multitudes? — Taylor Fang

Repeated measurements taken on that person would thereby comprise a sample from this “population-of-one” (Daza, 2018)—or what we might call a “multitudinal population”. Such data are commonly called longitudinal because they are repeatedly collected over time for every study participant.

Used in this way, the term “multitudinal” certainly satisfies my penchant for puns. But it also accurately describes the analyses used in n-of-1 trials and studies.

In these typical esametric studies, the estimands are stable, recurring quantities—like the average correlation between how long the (sole) study participant sleeps, and how stressed they feel, on any given day. And this participant is measured repeatedly throughout the study period.

I therefore propose two new terms:

1. A multitudinal study is a research design that collects longitudinal data with the goal of estimating, inferring, or predicting participant-specific recurring average quantities (i.e., at the participant level). It may involve only one study participant. Typical examples include n-of-1 trials and studies, single-case experimental and observational designs, and multiple baseline designs.
2. A multitudinal analysis is a statistical analysis of multitudinal study data. A typical example is multivariate partitioned time series analysis (multilevel for more than one study participant).

These terms follow the statistics naming convention of describing a type of study or analysis based on its target population’s structure and main outcomes. For example: longitudinal analysis, time series analysis, and survival analysis.

What do you think? Would you describe your n-of-1 study analysis as multitudinal?