A few random notes about plotting, describing, and thinking about trajectories.

# Plotting Trajectories

Imagine we record “affect” ($$Y$$) for five people over 20 time points. ggplot2 produces poor longitudinal trajectories if you only specify time and affect as variables:

library(ggplot2)
library(tidyverse)

plot1 <- ggplot(df1, aes(x = time, y = affect)) +
geom_point() +
geom_line()

plot1 Instead, specify “id” either as the grouping variable:

plot2 <- ggplot(df1, aes(x = time, y = affect, group = id)) +
geom_point() +
geom_line()

plot2 or a color.

plot3 <- ggplot(df1, aes(x = time, y = affect, color = id)) +
geom_point() +
geom_line()

plot3 If you have a data set with too many trajectories then select a random sample to keep dark

df2_sample_ids <- sample(df2\$id, 5)
df2_sample <- df2 %>%
filter(id %in% df2_sample_ids)

and change the color of the background trajectories to a lighter color.

plot5 <- ggplot(df2, aes(x = time, y = affect, group = id)) +
geom_point(color = 'gray85') +
geom_line(color = 'gray85') +

# HERE COMES ADDITIONAL CHANGES

geom_point(data = df2_sample, aes(x = time, y = affect, group = id)) +
geom_line(data = df2_sample, aes(x = time, y = affect, group = id))

plot5 Notice that I had to evoke two additional geom commands and source my new data sample.

# Trajectory Descriptions

## Equilibrium Panel A: Increasing equilibrium level with constant variance.

Panel B: Decreasing equilibrium level with constant variance.

Panel C: Decreasing equilibrium level with increasing variance.

## Latent Growth Intercepts and Slopes Panel A: Between person differences in intercept but no differences in slope.

Panel B: Between person differences in slope but no differences in intercept.

Panel C: Between person differences in intercepts and slopes.

## Between and Within Person Variance Panel A: Between person differences in level (intercept in LGC literature) but no between person differences in variability.

Panel B: No between person differences in level (intercept) or variability, but the amount of variability in these trajectories is greater than Panel A. Panel C: No between person differences in level (intercept) but there are between person differences in variability.

# Main Effects and Interactions (Cross Sectional vs. Over Time)

Imagine we re-test the main and interaction effects from a cross-sectional study several times. If the results are stable across time, what would they look like?

## Main Effect

Group A (difficult, specific goals) higher performance than group B (vague goals). ## Interaction

For males: Group A (difficult, specific goals) higher performance than group B (vague goals). For females: Group B (vague goals) higher performance than group B (difficult, specific goals). ## Interaction and Main Effect Bo$$^2$$m =)