Skip to contents

Shrink each person's coefficient towards the pooled effect

Source: R/stats_pooling.R
shrink_coefs.Rd

A person measured over few occasions has a noisy coefficient, and taking it at face value overstates how unusual they are. Empirical-Bayes shrinkage pulls each estimate towards the pooled effect by an amount that depends on how well that person was measured:

Usage

shrink_coefs(
  x,
  term = NULL,
  scope = "individual",
  model = NULL,
  subgroup = NULL,
  conf_level = 0.95
)

Arguments

x

An idiographic_fit with individual-scope coefficients.

term

Optional filter on the coefficient name.

scope

Which scope's coefficients to pool. Individual, necessarily.

model, subgroup

Optional filters.

conf_level

Confidence level for the pooled interval.

Value

A data.frame of one row per person per term, with class idiographic_shrunk.

Details

$$\hat\theta_i^{EB} = \bar\theta + \frac{\tau^2}{\tau^2 + v_i} (\hat\theta_i - \bar\theta)$$

weight is that fraction: 1 means the person's own estimate is kept as-is, 0 means it carries no information of its own and is replaced by the pooled value. When tau is zero – no real heterogeneity – every person shrinks all the way to the pooled effect, which is the correct answer.

These are the estimates to cluster on if you cluster at all: clustering raw coefficients finds groups partly in the estimation noise.

Examples

fit <- fit_lm(srl, y = "effort", x = "efficacy", id = "name",
              time = "day", scope = "individual")
shrink_coefs(fit)
#> SHRUNKEN PERSON EFFECTS
#>   People   36
#>   Terms    2
#> 
#>   subject   term              raw      S.E.   weight   shrunken
#> ---------------------------------------------------------------
#>   Aisha     (Intercept)   60.2331    4.5432    0.973    59.6401
#>   Alice     (Intercept)   41.3573    3.2900    0.986    41.3155
#>   Anika     (Intercept)   22.4214    5.0940    0.966    22.9672
#>   Astrid    (Intercept)   57.4470    6.3689    0.948    56.4568
#>   Bjorn     (Intercept)   35.0610    4.5007    0.973    35.1522
#>   Bob       (Intercept)   35.8825    8.5933    0.909    36.1181
#>   Charlie   (Intercept)   29.2662    5.9326    0.954    29.6857
#>   Diana     (Intercept)   74.9567   10.8393    0.862    69.9391
#>   Erik      (Intercept)   25.3872    4.0320    0.978    25.6696
#>   Eve       (Intercept)   28.6605    3.8959    0.980    28.8585
#>   Fatima    (Intercept)   42.0655    7.9466    0.921    41.7816
#>   Frank     (Intercept)   24.7052   10.0727    0.879    26.3709
#> 
#>   ... 60 more rows.
#> 
#>   weight = how much of the person's own estimate is kept