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Simulate Latent Growth-Curve Data

Source: R/simulate_multilevel.R
simulate_growth.Rd

Generate longitudinal data from a linear latent growth-curve model. Each subject draws a random intercept and slope from a bivariate normal with specified means, standard deviations, and correlation, then $$y_{it} = b_{0i} + b_{1i} \, t + e_{it},$$ with time coded 0..(n_time - 1). The result is returned in long format. Designed so that the mean per-subject slope recovers slope_mean and the spread of per-subject intercepts recovers intercept_sd at large n.

Usage

simulate_growth(
  n = 200,
  n_time = 5,
  intercept_mean = 0,
  slope_mean = 1,
  intercept_sd = 1,
  slope_sd = 0.5,
  intercept_slope_cor = 0,
  residual_sd = 1,
  seed = NULL
)

Arguments

n

Integer. Number of subjects. Default: 200.

n_time

Integer >= 2. Number of measurement occasions per subject. Default: 5.

intercept_mean

Numeric. Mean of subject intercepts \(b_{0i}\). Default: 0.

slope_mean

Numeric. Mean of subject slopes \(b_{1i}\). Default: 1.

intercept_sd

Positive numeric. Standard deviation of subject intercepts. Default: 1.

slope_sd

Positive numeric. Standard deviation of subject slopes. Default: 0.5.

intercept_slope_cor

Numeric in [-1, 1]. Correlation between subject intercepts and slopes. Default: 0.

residual_sd

Positive numeric. Level-1 (occasion) residual standard deviation \(\sigma_e\). Default: 1.

seed

Integer or NULL. Random seed.

Value

A saqr_sim object with:

$data

long-format data.frame with columns subject (factor), time (numeric, 0..n_time-1), and y (numeric).

$params

list with means (intercept/slope), sds (intercept/slope), correlation, residual_sd, n_time, subject_intercepts (true \(b_{0i}\)), and subject_slopes (true \(b_{1i}\)).

Examples

r <- simulate_growth(n = 300, n_time = 6, slope_mean = 2,
                     intercept_sd = 1.5, seed = 1)
print(r)
#> saqr_sim [growth]  1800 x 3  (seed=1)
#>   params: means, sds, correlation, residual_sd, n_time, subject_intercepts, subject_slopes 
#>   cols:   subject, time, y 
head(r)
#>   subject time         y
#> 1       1    0 -1.280748
#> 2       1    1  3.009581
#> 3       1    2  4.482301
#> 4       1    3  6.943021
#> 5       1    4  8.710993
#> 6       1    5 10.157770

# Correlated intercepts and slopes
r2 <- simulate_growth(n = 250, intercept_slope_cor = 0.5, seed = 42)
r2$params$correlation
#> [1] 0.5