The Inductive Subgroup Comparison Approach (‘ISCA’) offers a way to compare groups that are internally differentiated and heterogeneous. It starts by identifying the social structure of a reference group against which a minority or another group is to be compared, yielding empirical subgroups to which minority members are then matched based on how similar they are. The modelling of specific outcomes then occurs within specific subgroups in which majority and minority members are matched. ISCA is characterized by its data-driven, probabilistic, and iterative approach and combines fuzzy clustering, Monte Carlo simulation, and regression Analysis. ISCA_random_assignments() assigns subjects probabilistically to subgroups. ISCA_clustertable() provides summary statistics of each cluster across iterations. ISCA_modeling provides OLS regression results for each cluster across iterations.
You can install the package from this GitHub repository. Be sure to first install the remotes package.
install.packages("remotes")Then install ISCA using the install_github function in
the remotes
package.
remotes::install_github("ldrouhot/ISCA")The functions are demonstrated using a fictitious dataset containing
1,000 observations, which is included in the package. The first function
ISCA_random_assignments() produces a dataset that has one
new column for each probabilistic draw/iteration. The values indicate
the respective cluster assignments. The output is the foundation of the
other two functions in the ISCA-package.
library(ISCA)
data(sim_data)
ISCA_step1 <- ISCA::ISCA_random_assignments(data=sim_data, filter=native, majority_group=1, minority_group=c(0), fuzzifier = 1.5, n_clusters=4, draws=5, cluster_vars= c("female", "age", "education", "income"))head(ISCA_step1)
#> female age education income religiosity discrimination native A1 A2 A3 A4 A5
#> 1 1 74 6 1608 2 2 0 1 1 1 1 1
#> 2 1 69 9 1227 10 4 0 4 4 4 4 4
#> 3 0 21 6 0 2 5 0 3 3 3 3 3
#> 4 1 64 6 2132 10 3 0 2 2 2 2 2
#> 5 1 20 7 1487 2 3 0 1 4 1 1 1
#> 6 1 25 5 1761 9 3 0 1 1 1 1 1The second function result_ISCA_clustertable() gives an
overview of the distribution of the variables of interest per cluster
and across iterations.
result_ISCA_clustertable <- ISCA::ISCA_clustertable(data = ISCA_step1, cluster_vars = c("native", "education", "age", "female", "discrimination", "religiosity"), draws = 5)
print(result_ISCA_clustertable)
#> variable 1 2 3 4
#> 1 assignment 1.0000 2.0000 3.0000 4.0000
#> 2 grand_mean_native 0.5014 0.4214 0.4684 0.4576
#> 3 cluster_error_native 0.0175 0.0122 0.0213 0.0103
#> 4 grand_mean_education 5.0306 5.0152 5.0688 5.0278
#> 5 cluster_error_education 0.0443 0.0426 0.0410 0.0448
#> 6 grand_sd_education 1.3002 1.3807 1.2700 1.3782
#> 7 grand_mean_age 47.4305 46.2335 47.5678 49.5852
#> 8 cluster_error_age 0.3652 0.5450 0.3787 0.2581
#> 9 grand_sd_age 18.9128 18.2450 17.5107 17.9565
#> 10 grand_mean_female 0.4802 0.4777 0.4976 0.4795
#> 11 cluster_error_female 0.0072 0.0112 0.0033 0.0091
#> 12 grand_mean_discrimination 3.9587 4.0172 3.9800 3.9644
#> 13 cluster_error_discrimination 0.0401 0.0392 0.0141 0.0231
#> 14 grand_sd_discrimination 1.1245 1.2439 1.2637 1.2664
#> 15 grand_mean_religiosity 4.8027 4.8783 4.7865 4.8623
#> 16 cluster_error_religiosity 0.0914 0.0761 0.0860 0.0705
#> 17 grand_sd_religiosity 2.9023 2.8570 2.8655 2.8037
#> 18 grand_mean_count 232.4000 188.4000 252.8000 326.4000
#> 19 cluster_error_count 8.0808 3.4351 13.6638 10.5024The third function ISCA_clustertable() runs OLS
regressions for each cluster across iterations. The output is a list
storing the regression estimates and adjusted R Squared values.
ISCA_modeling_res <- ISCA::ISCA_modeling(data= ISCA_step1, model_spec="religiosity ~ native + female + age + education + discrimination", draws = 5, n_clusters = 4)
#> `mutate_if()` ignored the following grouping variables:
#> • Column `cluster`
print(ISCA_modeling_res[1])
#> [[1]]
#> # A tibble: 30 × 5
#> # Groups: cluster [5]
#> cluster term mean_coefficients mean_std.error mean_p_value
#> <fct> <chr> <dbl> <dbl> <dbl>
#> 1 1 (Intercept) 4.09 0.482 0.0012
#> 2 1 age 0.0007 0.0036 0.784
#> 3 1 discrimination 0.206 0.0873 0.267
#> 4 1 education 0.0283 0.047 0.765
#> 5 1 female 0.623 0.191 0.130
#> 6 1 native -1.16 0.182 0.0048
#> 7 2 (Intercept) 4.23 0.537 0.0009
#> 8 2 age -0.0067 0.0066 0.504
#> 9 2 discrimination 0.190 0.0649 0.285
#> 10 2 education 0.131 0.0692 0.417
#> # ℹ 20 more rows
print(ISCA_modeling_res[2])
#> [[1]]
#> mean.fit.cluster1 mean.fit.cluster2 mean.fit.cluster3 mean.fit.cluster4
#> 1 0.03939277 0.03813129 0.05497081 0.09119341
#> pooled.model
#> 1 0.06104137Check out the ISCA vignette for more in-depth explanations.
# browseVignettes("ISCA")Please cite the package as follows:
Drouhot, Lucas G., and Marion Späth. 2024. ISCA: Compare Heterogeneous Social Groups. R package version 0.1.0.