A list containing a simulated exposure dataset (df) and the ground-truth parameters
(theta0) used to generate it.
The dataset df contains \(N = 4500\) observations across \(n_{Ind} = 1500\)
individuals, with $n_R = 3$ repeated measures per individual.
exposure_dataA list with 2 components:
A data frame with 4,500 rows and 6 variables (the simulated data).
A list of 11 elements containing the true parameters used for simulation.
Continuous predictor (\(\sim N(0, 1)\)).
Time-like variable (structured around 0, 1, 2).
**Individual ID** (1 to 1500), the grouping factor.
Exposure continuous predictors.
The **Simulated Response Variable** calculated as: \(\bold{Y} = y_{Fe} + y_{Int} + y_{Re} + \epsilon\), where \(\epsilon ~ N(0, 1)\).
The list theta0 holds the true values used to generate Y, including:
Lat: **Categorical Factor** (9 levels), defining the clusters for interaction effects.
beta: True fixed effects for the global intercept and \(\bold{X}\) (i.e., $(3, 2)$).
alphaLat: Vector of 18 coefficients defining the cluster-specific intercepts and slopes for \(\bold{X}\) within the 9 Lat categories.
alphaRE: Vector of 1500 random slopes for the time variable \(\bold{t}\), drawn from $N(0, 1)$.
sigma: Residual standard deviation (1).
The underlying model for the response \(\bold{Y}\) is: $$\bold{Y} = \bold{X}_{Fe}\bold{\beta} + \bold{X}_{Int}\bold{\alpha}_{Lat} + \bold{X}_{Re}\bold{\alpha}_{RE} + \bold{\epsilon}$$