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Cross-National Educational Achievement Data for MAIHDA

Source: R/maihda_country_data.R
maihda_country_data.Rd

A cross-national dataset for demonstrating how Multilevel Analysis of Individual Heterogeneity and Discriminatory Accuracy (MAIHDA) can be used to compare intersectional inequality across a higher-level grouping variable (here, country) with compare_maihda_groups and maihda. Each row is a 15-year-old student; the intersectional strata are formed by gender and socioeconomic status (ses), and the outcome is the PISA mathematics score.

Usage

maihda_country_data

Format

A data frame with 3,600 rows (600 students in each of 6 countries) and 7 variables:

country

Factor; one of Finland, Germany, United Kingdom, Italy, Japan, Mexico. The higher-level grouping variable.

gender

Factor; student gender (female/male). A stratum dimension.

ses

Factor; socioeconomic status as global tertiles (Low/Medium/High) of escs, computed on the pooled sample so a band means the same in every country. A stratum dimension.

escs

Numeric; the PISA index of economic, social and cultural status (the continuous measure underlying ses).

math

Numeric; PISA mathematics score (first plausible value). The primary outcome.

reading

Numeric; PISA reading score (first plausible value).

low_math

Factor; "Yes" if math is below 420 (PISA proficiency Level 2 baseline), else "No". A binary outcome for logistic examples.

Source

Derived from the OECD Programme for International Student Assessment (PISA) 2018 student questionnaire data (OECD (2019), PISA 2018 Database), accessed and cleaned via the learningtower R package (MIT licensed), https://CRAN.R-project.org/package=learningtower. A balanced random subsample of 600 complete-case students per country was taken (seed 2026). The data preparation script is in data-raw/maihda_country_data.R.

Details

Intersectional inequality (the between-stratum share of variance, VPC/ICC) in mathematics achievement differs across the six countries, which is what makes the dataset a useful showcase for the group-comparison workflow.

The intersectional strata are gender:ses (2 x 3 = 6 strata). A canonical MAIHDA "null" model is math ~ 1 + (1 | gender:ses); comparing its VPC across countries quantifies how much joint gender-by-class inequality in achievement varies between countries.

Note

This is a teaching/illustration dataset only. It uses a single PISA plausible value for each score and does not carry the PISA survey weights or complex sampling design, so results are not survey-representative and should not be used for substantive cross-national inference. (For your own survey data, the package supports design-weighted MAIHDA via the sampling_weights argument of fit_maihda / maihda.)

Examples

# \donttest{
data(maihda_country_data)

# Compare intersectional (gender x SES) inequality across countries
analysis <- maihda(
  math ~ 1 + (1 | gender:ses),
  data = maihda_country_data,
  group = "country"
)
#> boundary (singular) fit: see help('isSingular')
#> maihda(): added the additive main effect(s) of the stratum dimension(s) gender, ses to the adjusted model; the null model excludes them. List them in the formula to specify the adjusted model explicitly.
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
#> boundary (singular) fit: see help('isSingular')
analysis
#> MAIHDA Analysis
#> ===============
#> 
#> Null formula:    math ~ (1 | stratum)
#> Adjusted formula:math ~ (1 | stratum) + gender + ses
#> Engine: lme4 | Family: gaussian
#> VPC/ICC (null): 0.1493
#> PCV (null -> adjusted): 1.0000
#> Between-stratum variance: 1124.7631 (null) -> 0.0000 (adjusted)
#>   ~100.0% of the between-stratum variance is additive (the dimensions' main
#>   effects); the remainder is the between-stratum variance remaining after the
#>   additive main effects -- a model-dependent quantity
#> Strata: 6
#> Intersectional interactions: 0 of 6 strata flagged (95% interval, BH-adjusted)
#> 
#> Group comparison by 'country':
#> MAIHDA Group Comparison
#> =======================
#> 
#> Group variable: country 
#> Engine: lme4  | Family: gaussian  | Strata: shared/global 
#> 
#>           group   n n_strata     vpc var_between var_other var_residual pcv
#>         Finland 600        6 0.10994       785.8         0         6361   1
#>         Germany 600        6 0.14448      1271.6         0         7529   1
#>           Italy 600        6 0.11890      1065.3         0         7895   1
#>           Japan 600        6 0.13344      1032.3         0         6704   1
#>          Mexico 600        6 0.13649       771.5         0         4881   1
#>  United Kingdom 600        6 0.06011       470.5         0         7357   1
#>  var_between_adjusted var_between_adjusted_ml status
#>             0.000e+00               0.000e+00     ok
#>             0.000e+00               0.000e+00     ok
#>             0.000e+00               0.000e+00     ok
#>             3.782e-12               3.022e-12     ok
#>             0.000e+00               0.000e+00     ok
#>             0.000e+00               0.000e+00     ok
#> 
#> Use summary() for variance components and plot(type = ...) for figures.
#> 
plot(analysis, type = "group_vpc")

# }