The Latent Growth Curve Model and Change Over Time

latent-growth-curve-change.R

# Libraries.
library(lavaan)
library(ggplot2)
library(patchwork)

# If not installed, then install as follows:
install.packages(c("lavaan", "ggplot2", "patchwork"))

# Model 1.
#
# Here the mean of the latent quadratic slope factor is fixed to -5. This
# indicates that the average rate of change has a negative acceleration (i.e.,
# it decreases or decelerates over time).
model_1 <- "
    # Add latent growth intercept with 10 waves.
    Intercept =~ 1*x1 + 1*x2 + 1*x3 + 1*x4 + 1*x5 + 1*x6 + 1*x7 + 1*x8 + 1*x9 + 1*x10

    # Add slope with 10 waves.
    Slope =~ 0*x1 + 1*x2 + 2*x3 + 3*x4 + 4*x5 + 5*x6 + 6*x7 + 7*x8 + 8*x9 + 9*x10

    # Add quadratic slope with 10 waves.
    SlopeSquared =~ 0*x1 + 1*x2 + 4*x3 + 9*x4 + 16*x5 + 25*x6 + 36*x7 + 49*x8 + 64*x9 + 81*x10

    # Fix the means of the latent quadratic slope factors (i.e., the average rate of change).
    SlopeSquared ~ -5*1
"

# Model 2.
#
# Here the mean of the latent quadratic slope factor is fixed to 5. This
# indicates that the average rate of change has a positive acceleration (i.e.,
# it increases or accelerates over time).
model_2 <- "
    # Add latent growth intercept with 10 waves.
    Intercept =~ 1*x1 + 1*x2 + 1*x3 + 1*x4 + 1*x5 + 1*x6 + 1*x7 + 1*x8 + 1*x9 + 1*x10

    # Add slope with 10 waves.
    Slope =~ 0*x1 + 1*x2 + 2*x3 + 3*x4 + 4*x5 + 5*x6 + 6*x7 + 7*x8 + 8*x9 + 9*x10

    # Add quadratic slope with 10 waves.
    SlopeSquared =~ 0*x1 + 1*x2 + 4*x3 + 9*x4 + 16*x5 + 25*x6 + 36*x7 + 49*x8 + 64*x9 + 81*x10

    # Fix the means of the latent quadratic slope factors (i.e., the average rate of change).
    SlopeSquared ~ 5*1
"

# Set a seed for reproducibility of the plots below.
set.seed(2024)

# Generate some data for the two models above.
data_model_1 <- simulateData(model_1, sample.nobs = 100, meanstructure = TRUE)
data_model_2 <- simulateData(model_2, sample.nobs = 100, meanstructure = TRUE)

# Reshape the wide data to long format (i.e., for model 1).
data_long_model_1 <- reshape(
    data_model_1,
    varying = list(c("x1", "x2", "x3", "x4", "x5", "x6", "x7", "x8", "x9", "x10")),
    v.names = "x",
    timevar = "time",
    times = 1:10,
    idvar = "id",
    direction = "long"
)

# Reshape the wide data to long format (i.e., for model 2).
data_long_model_2 <- reshape(
    data_model_2,
    varying = list(c("x1", "x2", "x3", "x4", "x5", "x6", "x7", "x8", "x9", "x10")),
    v.names = "x",
    timevar = "time",
    times = 1:10,
    idvar = "id",
    direction = "long"
)

# Plot the data generated according to each time of acceleration (i.e., negative).
plot_data_model_1 <- ggplot(data_long_model_1, aes(x = time, y = x)) +
    geom_jitter(
        alpha = 0.1,
        width = 0.1
    ) +
    stat_summary(
        fun.y = mean,
        geom = "line",
        col = "darkred",
        linewidth = 1
    ) +
    scale_x_continuous(
        breaks = seq(1, 10, 1),
        labels = seq(1, 10, 1)
    ) +
    labs(
        title = "Negative acceleration (i.e., decreasing rate of change)",
        x = "Measurement occasion",
        y = "Observed variable"
    ) +
    theme_bw() +
    theme(
        axis.title.y = element_text(
            margin = margin(t = 0, r = 5, b = 0, l = 0)
        ),
        axis.title.x = element_text(
            margin = margin(t = 15, r = 0, b = 0, l = 0)
        )
    )

# Plot the data generated according to each time of acceleration (i.e., positive).
plot_data_model_2 <- ggplot(data_long_model_2, aes(x = time, y = x)) +
    geom_jitter(
        alpha = 0.1,
        width = 0.1
    ) +
    stat_summary(
        fun.y = mean,
        geom = "line",
        col = "darkred",
        linewidth = 1
    ) +
    scale_x_continuous(
        breaks = seq(1, 10, 1),
        labels = seq(1, 10, 1)
    ) +
    labs(
        title = "Positive acceleration (i.e., increasing rate of change)",
        x = "Measurement occasion",
        y = "Observed variable"
    ) +
    theme_bw() +
    theme(
        axis.title.y = element_text(
            margin = margin(t = 0, r = 5, b = 0, l = 0)
        ),
        axis.title.x = element_text(
            margin = margin(t = 15, r = 0, b = 0, l = 0)
        )
    )

# Show the plots side by side.
plot_data_model_1 / plot_data_model_2

Example of plots produced by the code above.