Simulate Data from Growth Mixture Model with Survey Design — simulate_gmm

Generates simulated longitudinal data from a growth mixture model with complex survey design features (stratification, clustering, weights). Useful for testing, validation, and teaching.

Usage

simulate_gmm_survey(
  n_individuals = 1000,
  n_times = 5,
  n_classes = 3,
  time_scores = NULL,
  class_proportions = NULL,
  growth_parameters = NULL,
  residual_sds = NULL,
  design = "stratified_cluster",
  n_strata = 4,
  n_clusters = 100,
  cluster_size = 10,
  weight_type = "inverse_prob",
  missing_rate = 0.1,
  missing_mechanism = "MCAR",
  covariates = TRUE,
  seed = NULL
)

Arguments

n_individuals: Number of individuals to generate (default: 1000)
n_times: Number of time points (default: 5)
n_classes: Number of latent classes (default: 3)
time_scores: Numeric vector of time scores (default: 0:(n_times-1))
class_proportions: Numeric vector of class proportions (must sum to 1)
growth_parameters: List of lists, each containing intercept and slope for each class. If NULL, reasonable defaults are generated.
residual_sds: Numeric vector of residual standard deviations by class
design: Character string: "srs" (simple random sample), "stratified", "cluster", or "stratified_cluster" (default)
n_strata: Number of strata if stratified design (default: 4)
n_clusters: Number of clusters (PSUs) if cluster design (default: 100)
cluster_size: Average cluster size (default: 10)
weight_type: Character: "none", "inverse_prob", or "calibrated"
missing_rate: Proportion of missing data (default: 0.1)
missing_mechanism: Character: "MCAR" (default), "MAR", or "MNAR"
covariates: Logical, include time-invariant covariates? (default: TRUE)
seed: Random seed for reproducibility (default: NULL)

Value

Data frame in long format with variables:

id: Individual ID
time: Time point
outcome: Observed outcome value
true_class: True latent class (for validation)
stratum: Stratum indicator (if stratified)
psu: Primary sampling unit (if clustered)
weight: Sampling weight (if weighted)
covariates: Additional covariates (if requested)

Details

This function generates data following a growth mixture model:

For individual i in class k: $$y_{it} = (\beta_{0k} + u_{0i}) + (\beta_{1k} + u_{1i}) * t + \epsilon_{it}$$

where:

$\beta_{0k}$, $\beta_{1k}$ are class-specific intercept and slope
$u_{0i}$, $u_{1i}$ are random effects (optional, not yet implemented)
$\epsilon_{it}$ ~ N(0, $\sigma_k^2$) are residuals

Survey design features:

Stratification: Population divided into strata, sampling within strata
Clustering: Individuals nested within PSUs (e.g., schools, neighborhoods)
Weights: Inverse probability weights to account for unequal selection probabilities

The function can generate various missing data patterns to test robustness of analyses.

References

Sterba, S. K. (2014). Fitting nonlinear latent growth curve models with individually varying time points. Structural Equation Modeling, 21(4), 630-647.

Examples

if (FALSE) { # \dontrun{
# Simple 3-class example
sim_data <- simulate_gmm_survey(
  n_individuals = 1000,
  n_times = 5,
  n_classes = 3,
  design = "stratified_cluster",
  seed = 123
)

head(sim_data)
table(sim_data$true_class)

# Fit model to simulated data
fit <- gmm_survey(
  data = sim_data,
  id = "id",
  time = "time",
  outcome = "outcome",
  n_classes = 3,
  strata = "stratum",
  cluster = "psu",
  weights = "weight",
  starts = 100
)

# Compare estimated vs true parameters
summary(fit)
} # }