Plot Conditional Effects From a Moderated Mediation Analysis

Draws the conditional effects from a mediation_mbco analysis that declared a moderator: for each moderated pathway effect, the curve tracing how the effect changes over the moderator's range, with a pointwise confidence band, the probed values marked, a dashed reference line at zero, and a rug showing where the moderator was actually observed. The picture answers, at a glance, the questions the table answers row by row: how large is the effect at any given moderator value, where (if anywhere) does its interval exclude zero, and over what part of the moderator's range the data can support either statement.

Usage

plot_mediation_mbco(
  x,
  effects = NULL,
  conf_level = NULL,
  B = 10000,
  from = NULL,
  to = NULL,
  n_grid = 200,
  show_probe_values = TRUE,
  show_rug = TRUE,
  palette = c("okabe_ito", "tableau"),
  xlab = NULL,
  ylab = NULL,
  title = NULL,
  seed = NULL
)

Arguments

x: A dmar_mediation_mbco object returned by mediation_mbco with a moderator. An object fit without a moderator has no conditional effects to draw, and the function says so.
effects: Character vector naming which moderated effects to draw, using the base effect names from the result table (e.g., "indirect_via_m", "total_effect"). Defaults to all moderated effects. Unmoderated effects are flat lines and are not drawn.
conf_level: Confidence level for the band. Defaults to the level used when the object was fit.
B: Number of Monte Carlo draws behind the band. Defaults to 10000.
from, to: Range of moderator values to draw. Defaults to the observed range of the moderator. Values outside the observed range are extrapolation; the rug makes that visible.
n_grid: Number of grid points along the moderator at which the curve and band are evaluated. Defaults to 200.
show_probe_values: Logical. If TRUE (default), mark the probed moderator values (the _at_ rows of the result table) as points on each curve.
show_rug: Logical. If TRUE (default), draw a rug of the observed moderator values along the horizontal axis.
palette: Character string naming the color palette. Defaults to "okabe_ito", base R's colorblind-safe Okabe-Ito palette; "tableau" is also available.
xlab, ylab, title: Optional axis labels and title. The defaults name the moderator on the horizontal axis and describe the vertical axis as the conditional effect of x on y.
seed: Optional integer seed for the Monte Carlo band, used locally (the caller's random number generator state is restored on exit). Default NULL leaves the random number generator state alone.

Value

A ggplot2 object. Its data contains one row per effect and grid value with columns effect_label, w_value, estimate, band_lower, and band_upper, so the numbers behind the picture are recoverable from the object itself.

Details

What is drawn, and where it comes from. A pathway effect in a model with interactions is a polynomial in the moderator: a straight line when the pathway is moderated in one place (its slope is the index of moderated mediation), a curve when it is moderated in more than one. mediation_mbco derives each polynomial symbolically and stores it with the result, so this function evaluates the same quantity the table probes, just everywhere in the moderator's range instead of at two or three values. The marked points are exactly the table's _at_ rows.

The band is pointwise. At each grid value of the moderator, the band is a conf_level Monte Carlo confidence interval for the conditional effect at that one value: the path coefficients are drawn from their joint normal approximation (MacKinnon, Lockwood, & Williams, 2004), each draw's polynomial is evaluated along the grid, and the band connects the pointwise quantiles. Read vertically at a single moderator value of interest, it is an ordinary confidence interval. Read horizontally, the moderator values where the band crosses zero estimate the Johnson-Neyman boundaries (Johnson & Neyman, 1936; Preacher, Rucker, & Hayes, 2007), the values separating "interval excludes zero" from "interval includes zero". That horizontal reading scans many intervals at once, so the pointwise band understates the uncertainty of the boundary locations themselves; treat the crossing points as estimates, not as sharp cutoffs, and lean on the table's moderation and constancy tests for the formal question of whether the effect depends on the moderator at all.

The rug guards against extrapolation. The curve can be evaluated at any moderator value, but the data only inform it where the moderator was observed. The rug shows that support directly; a confident-looking band in a region with no rug beneath it is arithmetic, not evidence.

The band and the table may differ slightly. The band is always Monte Carlo, whichever ci_method the table used. At a probed value, a Monte Carlo band and a profile likelihood or Wald interval agree closely in large samples but are not the same construction; small discrepancies between the band and an _at_ row's interval are expected, not a defect.

The plot is an ordinary ggplot2 object, so any further customization (themes, additional layers, institutional color scales) can be added to the returned value with +.

Note

Requires ggplot2 (listed in Suggests).

References

Johnson, P. O., & Neyman, J. (1936). Tests of certain linear hypotheses and their application to some educational problems. Statistical Research Memoirs, 1, 57–93.

MacKinnon, D. P., Lockwood, C. M., & Williams, J. (2004). Confidence limits for the indirect effect: Distribution of the product and resampling methods. Multivariate Behavioral Research, 39(1), 99–128. doi:10.1207/s15327906mbr3901_4

Preacher, K. J., Rucker, D. D., & Hayes, A. F. (2007). Addressing moderated mediation hypotheses: Theory, methods, and prescriptions. Multivariate Behavioral Research, 42(1), 185–227. doi:10.1080/00273170701341316

Tofighi, D., & Kelley, K. (2020). Improved inference in mediation analysis: Introducing the model-based constrained optimization procedure. Psychological Methods, 25(4), 496–515. doi:10.1037/met0000259

Author

Ken Kelley kkelley@nd.edu

Examples

# First-stage moderated mediation: the effect of x on m depends on
# w, so the indirect effect of x on y is a line in w; the direct
# effect is unmoderated and is not drawn.
set.seed(113)
n <- 300
x <- rnorm(n)
w <- rnorm(n)
m <- 0.5 * x + 0.3 * w + 0.4 * x * w + rnorm(n)
y <- 0.5 * m + 0.2 * x + 0.1 * w + rnorm(n)
d_mod <- data.frame(x = x, w = w, m = m, y = y)

# Neither the fit nor the plot is run here: every probed effect costs
# its own constrained null model fit in OpenMx, and the band draws B
# coefficient vectors from their joint normal approximation. The Wald
# interval and the two probe values keep a hand run of these lines
# quick; the default probe values are the moderator's mean and one
# standard deviation either side, and the curve and its band cover
# the whole range of w either way. The calls are:
# res <- mediation_mbco("m ~ x + w + x:w \n y ~ m + x + w",
#                       data = d_mod, x = "x", y = "y",
#                       moderator = "w", ci_method = "wald",
#                       probe_values = c(low = -1, high = 1))
# plot_mediation_mbco(res, seed = 113)

# Only the indirect pathway, over a chosen moderator range:
# plot_mediation_mbco(res, effects = "indirect_via_m",
#                     from = -2, to = 2, seed = 113)