Multiple options to calculate influence values

[wlangera]

Efron & Tibshirani (1994)

See also boot package

[wlangera]

boot:::empinf.reg

Section 2.7 of Davison and Hinkley (1997)

Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.

[wlangera]

boot:::empinf.reg

Section 2.7 of Davison and Hinkley (1997)

Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.

This is not based on jackknifing, so the jackknife argument should have another name (infl_type?).

We will also need a separate function. I propose a general function calculate_acceleration() with if statements:

if (jackknife == "reg") {
  # ...

else {
  jackknife_df <- perform_jackknifing(
      data_cube = data_cube,
      fun = fun,
      ...,
      grouping_var = grouping_var,
      ref_group = ref_group,
      progress = progress)
  
  influence_df <- jackknife_df %>%
      dplyr::left_join(bootstrap_samples_df %>%
                         dplyr::distinct(!!dplyr::sym(grouping_var),
                                         .data$est_original),
                       by = dplyr::join_by(!!grouping_var)) %>%
      dplyr::mutate(n = dplyr::n(),
                    .by = dplyr::all_of(grouping_var)) %>%
      dplyr::rowwise() %>%
      dplyr::mutate(intensity = ifelse(
        jackknife == "usual",
        (.data$n - 1) * (.data$est_original - .data$jack_rep),
        (.data$n + 1) * (.data$jack_rep - .data$est_original)
      )
      ) %>%
      dplyr::ungroup()
}

acceleration_df <- influence_df %>%
  dplyr::summarise(
    numerator = sum(.data$intensity^3),
    denominator = 6 * sum(.data$intensity^2)^1.5,
    acceleration = .data$numerator / .data$denominator,
    .by = dplyr::all_of(grouping_var)
)

[wlangera]

All methods give the same results, so this might not be necessary option to add?
However, the jackknife methods take some time, perhaps regression is faster for bigger datasets?

library(boot)

mean.fun <- function(d, i) mean(d$dist[i])
air.boot <- boot(cars, mean.fun, R = 999)

# regression
start.time <- Sys.time()
empinf(air.boot, type = "reg")  
#>      1      1      1      1      1      1      1      1      1      1      1 
#> -40.98 -32.98 -38.98 -20.98 -26.98 -32.98 -24.98 -16.98  -8.98 -25.98 -14.98 
#>      1      1      1      1      1      1      1      1      1      1      1 
#> -28.98 -22.98 -18.98 -14.98 -16.98  -8.98  -8.98   3.02 -16.98  -6.98  17.02 
#>      1      1      1      1      1      1      1      1      1      1      1 
#>  37.02 -22.98 -16.98  11.02 -10.98  -2.98 -10.98  -2.98   7.02  -0.98  13.02 
#>      1      1      1      1      1      1      1      1      1      1      1 
#>  33.02  41.02  -6.98   3.02  25.02 -10.98   5.02   9.02  13.02  21.02  23.02 
#>      1      1      1      1      1      1 
#>  11.02  27.02  49.02  50.02  77.02  42.02
end.time <- Sys.time()
time.taken <- end.time - start.time
time.taken
#> Time difference of 0.03990698 secs

# negative jackknife (usual)
start.time <- Sys.time()
empinf(air.boot, type = "jack") 
#>  [1] -40.98 -32.98 -38.98 -20.98 -26.98 -32.98 -24.98 -16.98  -8.98 -25.98
#> [11] -14.98 -28.98 -22.98 -18.98 -14.98 -16.98  -8.98  -8.98   3.02 -16.98
#> [21]  -6.98  17.02  37.02 -22.98 -16.98  11.02 -10.98  -2.98 -10.98  -2.98
#> [31]   7.02  -0.98  13.02  33.02  41.02  -6.98   3.02  25.02 -10.98   5.02
#> [41]   9.02  13.02  21.02  23.02  11.02  27.02  49.02  50.02  77.02  42.02
end.time <- Sys.time()
time.taken <- end.time - start.time
time.taken
#> Time difference of 0.004027128 secs

# positive jackknife
start.time <- Sys.time()
empinf(air.boot, type = "pos")
#>  [1] -40.98 -32.98 -38.98 -20.98 -26.98 -32.98 -24.98 -16.98  -8.98 -25.98
#> [11] -14.98 -28.98 -22.98 -18.98 -14.98 -16.98  -8.98  -8.98   3.02 -16.98
#> [21]  -6.98  17.02  37.02 -22.98 -16.98  11.02 -10.98  -2.98 -10.98  -2.98
#> [31]   7.02  -0.98  13.02  33.02  41.02  -6.98   3.02  25.02 -10.98   5.02
#> [41]   9.02  13.02  21.02  23.02  11.02  27.02  49.02  50.02  77.02  42.02
end.time <- Sys.time()
time.taken <- end.time - start.time
time.taken
#> Time difference of 0.003934145 secs

^{Created on 2025-03-26 with reprex v2.1.1}

[wlangera]

• added separate function to calculate acceleration in Calc acceleration #31
• change jackknife argument name in Calc acceleration #31

leave this issue open for potential new ways to calculate influence values