A simulated longitudinal dataset made for growth models. 300 students sit
an achievement test on up to seven occasions (wave 0 to 6). Three kinds of
student follow three trajectories: improving (starts near 48, gains 3.5
points a wave), stable (starts near 62, gains 0.5) and declining
(starts near 58, loses 2.5). Within each kind, students vary around the
trajectory: each has their own start and rate of change (random intercept
SD 4, random slope SD 0.8, correlation -0.3, the same spread in every kind),
with residual SD 3. Motivation, measured once, makes a student more likely
to be improving and less likely to be declining. About 12% of tests were
missed at random, so the panel is unbalanced.
Format
A data frame with 1844 rows (300 students) and 5 columns:
- student
Integer student identifier, 1 to 300. Pass it as
id.- wave
Integer test occasion, 0 to 6. The time variable.
- score
Achievement score.
- motivation
Standardized motivation, constant within student.
- trajectory
Factor,
"improving","stable"or"declining": the student's generating kind. Not for fitting; kept to check recovery.
Details
Because students vary within their kind, a trajectory model without random effects needs more classes than the three that generated the data; a growth mixture model with random intercepts and slopes recovers three.
Examples
descriptives(growth_scores, c("score", "motivation"))
#> variable n n_missing mean sd min max n_distinct
#> 1 score 1844 0 57.57039046 8.909898 24.90 81.20 400
#> 2 motivation 1844 0 0.03240239 1.006345 -3.35 2.82 200
# \donttest{
fit <- mixture_regression(score ~ wave, growth_scores, n_classes = 3,
id = "student", class_level = "group",
random = "wave", random_covariance = "equal",
n_starts = 4, seed = 1)
get_results(fit, "recovery", data = growth_scores, truth = "trajectory")
#> Recovery of a known classification
#>
#> Assigned trajectory Persons Share of assigned
#> -------- ---------- ------- -----------------
#> Class 1 improving 109 0.973
#> Class 2 improving 0 0.000
#> Class 3 improving 6 0.067
#> Class 1 stable 3 0.027
#> Class 2 stable 3 0.030
#> Class 3 stable 82 0.921
#> Class 1 declining 0 0.000
#> Class 2 declining 96 0.970
#> Class 3 declining 1 0.011
# }