Study how something varies across people — fit

Estimates a person-varying quantity, tests whether it genuinely varies, sorts people by it, and describes who sits at the extremes.

Usage

fit_heterogeneity(
  data,
  y,
  x,
  id,
  target = c("cate", "error", "gain"),
  treatment = NULL,
  model = c("linear", "ridge", "tree"),
  estimator = "native",
  time = NULL,
  num_splits = 100L,
  prop_aux = 0.5,
  n_groups = 4L,
  clan = NULL,
  split = c("person", "occasion"),
  conf_level = 0.95,
  ...
)

Arguments

data: Data frame.
y: Outcome column name.
x: Predictors: names, numeric positions, a:b range, formula, or data frame.
id: Person/unit ID column.
target: What varies across people: "cate", "error", or "gain".
treatment: Binary treatment column. Required when target = "cate".
model: Candidate models for the proxy. The winner is chosen by how well it detects heterogeneity (see learners()), not by prediction error.
estimator: Backend for the proxy models. See fit_ml().
time: Optional ordering column.
num_splits: Number of random splits. More splits, less seed-dependence.
prop_aux: Share of the sample used to learn the proxy in each split.
n_groups: Number of sorted groups.
clan: Person-level columns to describe the extreme groups with. Defaults to the predictors.
split: "person" (persons are the independent units) or "occasion" (split rows within each person). gain requires "occasion", since a person needs rows in both halves to have a model of their own.
conf_level: Confidence level.
...: Passed to the proxy models.

Value

An idiographic_heterogeneity object. See heterogeneity(), clan(), and learners().

Details

What varies is chosen by target:

cate: How much a treatment helped. Needs treatment.
error: How predictable each person is. Sorted groups run from the people the model serves best to the people it fails.
gain: How much a person-specific model beats a pooled one for this person – for whom idiographic modelling actually pays off. Positive means modelling them alone helped.

The reported quantities, for any target:

average: The quantity, averaged over everyone. For cate this is the ATE.
group:g1..gK: Sorted groups, from the lowest value of the quantity to the highest.
group:top-bottom: The gap between the extremes. If its interval excludes zero, the quantity genuinely differs across people.
heterogeneity: The slope of the held-out scores on the proxy. A significant slope means the variation is real and predictable, not noise.

Inference follows the paper: the data are split many times, each split is analysed separately, and results are aggregated by median with a conservative interval and a doubled p-value. A single split is seed-dependent, which is the problem this design exists to solve. Standard errors are clustered on the person throughout.

Note that these splits are random, not time-ordered. The question here is whether a quantity varies across people, not whether the future can be forecast; fit_rolling() is the verb for the latter.

References

Chernozhukov, V., Demirer, M., Duflo, E., & Fernandez-Val, I. (2020). Generic Machine Learning Inference on Heterogeneous Treatment Effects in Randomized Experiments. arXiv:1712.04802.

Examples

set.seed(1)
d <- data.frame(id = rep(1:10, each = 30), day = rep(1:30, 10),
                x1 = rnorm(300), x2 = rnorm(300))
d$drug <- rbinom(300, 1, 0.5)
d$mood <- 2 * d$drug * (d$x1 > 0) + 0.5 * d$x1 + rnorm(300, sd = 0.5)

het <- fit_heterogeneity(d, y = "mood", x = c("x1", "x2"), id = "id",
                         target = "cate", treatment = "drug",
                         num_splits = 20)
heterogeneity(het)
#>   target model           effect   estimate std_error   conf_low conf_high
#> 1   cate  tree          average 1.04035991 0.1119039  0.7357513 1.3449685
#> 2   cate  tree    heterogeneity 0.93966622 0.1134357  0.5916619 1.2880932
#> 3   cate  tree         group:g1 0.03954251 0.1381655 -0.3460203 0.4249075
#> 4   cate  tree         group:g2 0.18144586 0.1774303 -0.3046805 0.6478898
#> 5   cate  tree         group:g3 1.66341355 0.2812181  0.8943487 2.5374715
#> 6   cate  tree         group:g4 2.20589914 0.2151240  1.6270498 2.8758411
#> 7   cate  tree group:top-bottom 2.09155128 0.2361300  1.5546881 2.7754934
#>        p_value   n n_people splits
#> 1 0.0013997455 150        5     20
#> 2 0.0034196399 150        5     20
#> 3 0.5241434951 150        5     20
#> 4 0.7718019897 150        5     20
#> 5 0.0090585589 150        5     20
#> 6 0.0008237084 150        5     20
#> 7 0.0017107797 150        5     20
clan(het)
#>   target model variable    estimate std_error   conf_low conf_high      p_value
#> 1   cate  tree       x1  1.41249841 0.1187707  1.1037501  1.760570 0.0005504121
#> 2   cate  tree       x2 -0.02888505 0.1712446 -0.4815505  0.477836 1.0000000000
#>    n n_people splits
#> 1 75        5     20
#> 2 75        5     20