A simulated long-format (one row per person-occasion) panel for demonstrating
longitudinal / growth-curve MAIHDA (fit_maihda(id =, time =) and
maihda(decomposition = "longitudinal")). 600 individuals are each
measured over five waves on a continuous wellbeing score, within 12
intersectional strata defined by gender x ethnicity x education. The
between-stratum trajectory differences are constructed to be mostly
additive (each dimension's main effect on the baseline level and on the rate of
change) with one genuine multiplicative interaction, so the longitudinal PCV –
a high but sub-1 PCV_slope – is demonstrable.
Format
A data frame with 3000 rows (600 persons x 5 waves) and 8 variables:
- id
Person identifier (level 2); repeated across waves.
- wave
Measurement occasion, 0 to 4 (the numeric time variable).
- gender
Gender (
Women/Men); a stratum dimension.- ethnicity
Ethnicity (
EthA/EthB/EthC); a stratum dimension.- education
Education (
Low/High); a stratum dimension.- age
Baseline age in years, a time-invariant covariate.
- wellbeing
Continuous wellbeing outcome (the growth-curve response).
- low_wellbeing
Binary companion outcome (1 = bottom 40% of wellbeing), for the logistic longitudinal path.
Source
Simulated for the purpose of the MAIHDA package. The growth structure follows the longitudinal MAIHDA of Bell, Evans, Holman & Leckie (2024) doi:10.1016/j.socscimed.2024.116955 .
Examples
data(maihda_long_data)
# \donttest{
# Time-varying VPC from a 3-level growth model:
m <- fit_maihda(wellbeing ~ wave + (1 | gender:ethnicity:education),
data = maihda_long_data, id = "id", time = "wave")
#> Warning: Model failed to converge with max|grad| = 0.00213664 (tol = 0.002, component 1)
#> See ?lme4::convergence and ?lme4::troubleshooting.
summary(m)
#> MAIHDA Model Summary
#> ====================
#>
#> Fit diagnostics:
#> Convergence warnings reported by lme4:
#> - Model failed to converge with max|grad| = 0.00213664 (tol = 0.002, component 1)
#> See ?lme4::convergence and ?lme4::troubleshooting.
#>
#>
#> Variance Partition Coefficient (VPC/ICC) at baseline (wave = 0):
#> Estimate: 0.3986
#>
#> Variance Components:
#> component variance sd
#> Between-stratum: intercept (time = 0) 0.407878 0.6387
#> Between-stratum: slope (wave) 0.042860 0.2070
#> Between-stratum: intercept-slope covariance 0.088498 NA
#> Between-individual (id): intercept (time = 0) 0.255609 0.5056
#> Between-individual (id): slope (wave) 0.019360 0.1391
#> Between-individual (id): intercept-slope covariance -0.001107 NA
#> Within (residual) 0.359816 0.5998
#>
#> Time-varying VPC/ICC (between-stratum share over wave):
#> range 0.3986 to 0.6629 across wave in [0, 4].
#> The between-stratum variance is a function of time (random intercept +
#> slope), so the VPC varies; it depends on where time is zeroed. See
#> plot(type = "vpc_trajectory") for the full curve.
#>
#> Fixed Effects:
#> term estimate
#> (Intercept) 4.986466
#> wave -0.006306
#>
#> Stratum baseline (intercept) deviations (first 10):
#> stratum stratum_id label random_effect se lower_95 upper_95
#> 1 1 Men × EthB × Low -0.63796 0.08953 -0.81344 -0.4625
#> 2 2 Women × EthB × Low -0.06459 0.08595 -0.23305 0.1039
#> 3 3 Men × EthA × High 0.86072 0.07783 0.70819 1.0133
#> 4 4 Men × EthB × High 0.09121 0.10260 -0.10988 0.2923
#> 5 5 Women × EthA × High 0.93602 0.08804 0.76345 1.1086
#> 6 6 Women × EthC × High 0.35851 0.13545 0.09302 0.6240
#> 7 7 Men × EthC × High -0.11460 0.13287 -0.37503 0.1458
#> 8 8 Men × EthA × Low -0.32848 0.07050 -0.46667 -0.1903
#> 9 9 Women × EthA × Low 0.15992 0.07326 0.01633 0.3035
#> 10 10 Men × EthC × Low -0.82710 0.13287 -1.08753 -0.5667
#> ... and 2 more strata
#> (random slope not shown; use predict(type = "strata") for the per-stratum intercept and slope, or plot(type = "trajectories")).
# Additive-vs-multiplicative PCV (null vs adjusted growth model):
a <- maihda(wellbeing ~ wave + (1 | gender:ethnicity:education),
data = maihda_long_data, id = "id", time = "wave",
decomposition = "longitudinal")
#> Warning: Model failed to converge with max|grad| = 0.00213664 (tol = 0.002, component 1)
#> See ?lme4::convergence and ?lme4::troubleshooting.
a$pcv
#> Longitudinal PCV (additive vs. multiplicative intersectionality)
#> ================================================================
#>
#> Baseline (wave = 0) variance: 0.4079 (null) -> 0.0332 (adjusted)
#> PCV_intercept: 91.9% of the baseline between-stratum inequality is additive.
#> Slope (wave) variance: 0.0429 (null) -> 0.0058 (adjusted)
#> PCV_slope: 86.6% of the *trajectory* between-stratum inequality is additive
#> (the remainder is the multiplicative/interaction part).
#>
#> The PCV is the share of the null model's between-stratum (trajectory) variance
#> explained by the dimensions' additive main effects and their time interactions;
#> a high PCV_slope means trajectory inequalities are 'mostly additive'.
#>
# }