Discovering Person Subgroups with find_subgroups() • idiographic

Analytic question

find_subgroups() assigns people to subgroups based on person-specific effects, prediction errors, repeated splits, moderators, or mixtures of regressions. The function takes a repeated-measures regression problem, a method, a group count, and a resampling count. It returns group assignments and assignment stability for each person.

find_subgroups() uses effect clustering here. The method estimates each learner’s regression coefficients and clusters those coefficient vectors. Repeated resamples assess whether each learner returns to the same group. Stability measures reproducibility of the partition. It does not test whether separate populations exist.

Estimate a two-group partition

find_subgroups() clusters efficacy and monitoring effects into two groups. Twenty resamples provide an assignment-stability estimate.

subgroup_result <- find_subgroups(analysis_data, y = "effort", x = c("efficacy", "monitoring"), id = "name", method = "effect_clustering", k = 2, reps = 20, time = "day")
subgroup_result
#> Idiographic Subgroups
#>   Method:      effect_clustering
#>   Subgroups:   2
#>   People:      12
#>   Sizes:       g1=4, g2=8
#>   Stability:   0.82 (how reproducible the partition is --
#>                NOT evidence that the subgroups are real)
#> 
#>   Existence:   not tested. Use test_subgroups() to ask whether any
#>                subgroups exist before trusting this partition.
#> 
#>   Use groups(), test_subgroups(), fit_subgroups()

find_subgroups() returns two groups and reports their sizes. The print method also states that existence was not tested because k = 2 was supplied. A stable forced partition can occur in a population without discrete classes.

Inspect assignments

groups() returns one row per learner with the subgroup, method, stability, and number of assignments. Table 1 sorts through the public sort_by argument.

groups(subgroup_result, sort_by = "subgroup")
#>    subject subgroup            method stability n_assignments
#> 1   Astrid       g1 effect_clustering 0.9833333            20
#> 2    Diana       g1 effect_clustering 0.9500000            20
#> 3   Fatima       g1 effect_clustering 0.9833333            20
#> 4    Frank       g1 effect_clustering 0.9833333            20
#> 5    Aisha       g2 effect_clustering 0.5428571            20
#> 6    Alice       g2 effect_clustering 0.8285714            20
#> 7    Anika       g2 effect_clustering 0.8285714            20
#> 8    Bjorn       g2 effect_clustering 0.8285714            20
#> 9      Bob       g2 effect_clustering 0.8285714            20
#> 10 Charlie       g2 effect_clustering 0.4571429            20
#> 11    Erik       g2 effect_clustering 0.8285714            20
#> 12     Eve       g2 effect_clustering 0.8000000            20

groups() shows which learners share a coefficient pattern in Table 1. Stability values near one indicate consistent reassignment across resamples. Values near the two-group chance level of 0.5 indicate uncertain membership.

Plot assignment stability

plot_subgroups() colours learners by subgroup and draws the chance-level reference. Figure 1 orders learners within subgroup by stability.

plot_subgroups(subgroup_result)

Figure 1. Resampling stability of each learner’s two-group assignment.

Figure 1 identifies learners whose assignments are stable and learners near the chance reference. Uncertain memberships should not be used as fixed labels without sensitivity analysis.

Assumptions and failure checks

find_subgroups() assumes that its feature representation corresponds to the scientific definition of similarity. Effect clustering groups coefficient patterns. Error clustering groups prediction-error patterns. Model trees use person-level moderators. These methods answer different questions and can produce different partitions.

find_subgroups() requires enough people per requested group and enough observations to estimate person features. Coefficient skewness can create apparent classes (Bauer and Curran 2003). k = "auto" delegates the group count to test_subgroups() and can return one population.

When to use which

find_subgroups() is appropriate for estimating assignments after the target representation and group count are justified. test_subgroups() is appropriate for deciding whether more than one population is supported. fit_subgroups() is appropriate for evaluating whether group-specific models improve held-out prediction.

References

Bauer, Daniel J., and Patrick J. Curran. 2003. “Distributional Assumptions of Growth Mixture Models: Implications for Overextraction of Latent Trajectory Classes.” Psychological Methods 8 (3): 338–63. https://doi.org/10.1037/1082-989X.8.3.338.