Get the simple slopes of a SEM model — simple

This function calculates simple slopes (predicted values of the outcome variable) at user-specified values of the focal predictor (x) and moderator (z) in a structural equation modeling (SEM) framework. It supports interaction terms (xz), computes standard errors (SE), and optionally returns confidence or prediction intervals for these predicted values. It also provides p-values for hypothesis testing. This is useful for visualizing and interpreting moderation effects or to see how the slope changes at different values of the moderator.

Usage

simple_slopes(
  x,
  z,
  y,
  model,
  vals_x = -3:3,
  vals_z = -1:1,
  rescale = TRUE,
  ci_width = 0.95,
  ci_type = "confidence",
  relative_h0 = TRUE,
  standardized = FALSE,
  xz = NULL,
  ...
)

Arguments

x: The name of the variable on the x-axis (focal predictor).
z: The name of the moderator variable.
y: The name of the outcome variable.
model: An object of class modsem_pi, modsem_da, modsem_mplus, or a lavaan object. This should be a fitted SEM model that includes paths for y ~ x + z + x:z.
vals_x: Numeric vector of values of x at which to compute predicted slopes. Defaults to -3:3. If rescale = TRUE, these values are taken relative to the mean and standard deviation of x. A higher density of points (e.g., seq(-3, 3, 0.1)) will produce smoother curves and confidence bands.
vals_z: Numeric vector of values of the moderator z at which to compute predicted slopes. Defaults to -1:1. If rescale = TRUE, these values are taken relative to the mean and standard deviation of z. Each unique value of z generates a separate regression line y ~ x | z.
rescale: Logical. If TRUE (default), x and z are standardized according to their means and standard deviations in the model. The values in vals_x and vals_z are interpreted in those standardized units. The raw (unscaled) values corresponding to these standardized points will be displayed in the returned table.
ci_width: A numeric value between 0 and 1 indicating the confidence (or prediction) interval width. The default is 0.95 (i.e., 95% interval).
ci_type: A string indicating whether to compute a "confidence" interval for the predicted mean (i.e., uncertainty in the regression line) or a "prediction" interval for individual outcomes. The default is "confidence". If "prediction", the residual variance is added to the variance of the fitted mean, resulting in a wider interval.
relative_h0: Logical. If TRUE (default), hypothesis tests for the predicted values (predicted - h0) assume h0 is the model-estimated mean of y. If FALSE, the null hypothesis is h0 = 0.
standardized: Should coefficients be standardized beforehand?
xz: The name of the interaction term (x:z). If NULL, it will be created by combining x and z with a colon (e.g., "x:z"). Some backends may remove or alter the colon symbol, so the function tries to account for that internally.
...: Additional arguments passed to lower-level functions or other internal helpers.

Value

A data.frame (invisibly inheriting class "simple_slopes") with columns:

vals_x, vals_z: The requested grid values of x and z.
predicted: The predicted value of y at that combination of x and z.
std.error: The standard error of the predicted value.
z.value, p.value: The z-statistic and corresponding p-value for testing the null hypothesis that predicted == h0.
ci.lower, ci.upper: Lower and upper bounds of the confidence (or prediction) interval.

An attribute "variable_names" (list of x, z, y) is attached for convenience.

Details

Computation Steps

The function extracts parameter estimates (and, if necessary, their covariance matrix) from the fitted SEM model (model).
It identifies the coefficients for x, z, and x:z in the model's parameter table, as well as the variance of x, z and the residual variance of y.
If xz is not provided, it will be constructed by combining x and z with a colon (":"). Depending on the approach used to estimate the model, the colon may be removed or replaced internally; the function attempts to reconcile that.
A grid of x and z values is created from vals_x and vals_z. If rescale = TRUE, these values are transformed back into raw metric units for display in the output.
For each point in the grid, a predicted value of y is computed via (beta0 + beta_x * x + beta_z * z + beta_xz * x * z) and, if included, a mean offset.
The standard error (std.error) is derived from the covariance matrix of the relevant parameters, and if ci_type = "prediction", adds the residual variance.
Confidence (or prediction) intervals are formed using ci_width (defaulting to 95%). The result is a table-like data frame with predicted values, CIs, standard errors, z-values, and p-values.

Examples

# \dontrun{
library(modsem)

m1 <- "
# Outer Model
  X =~ x1 + x2 + x3
  Z =~ z1 + z2 + z3
  Y =~ y1 + y2 + y3

# Inner model
  Y ~ X + Z + X:Z
"
est1 <- modsem(m1, data = oneInt)

# Simple slopes at X in [-3, 3] and Z in [-1, 1], rescaled to the raw metric.
simple_slopes(x = "X", z = "Z", y = "Y", model = est1)
#> 
#> Difference test of Y~X|Z at Z = -1.008 and 1.008:
#> ┌───────────┬───────────┬─────────┬─────────┬───────────────┐
#> │Difference │ Std.Error │ z.value │ p.value │ Conf.Interval │
#> ╞═══════════╪═══════════╪═════════╪═════════╪═══════════════╡
#> │      1.42 │     0.054 │   26.36 │   0.000 │  [1.31, 1.52] │
#> └───────────┴───────────┴─────────┴─────────┴───────────────┘
#> 
#> Effect of Y~X|Z given values of Z:
#> ┌────────┬────────┬───────────┬─────────┬─────────┬────────────────┐
#> │    Y~X │      Z │ Std.Error │ z.value │ p.value │  Conf.Interval │
#> ╞════════╪════════╪═══════════╪═════════╪═════════╪════════════════╡
#> │ -0.033 │  -1.01 │     0.038 │   -0.88 │   0.377 │  [-0.11, 0.04] │
#> │  0.675 │   0.00 │     0.027 │   25.38 │   0.000 │  [ 0.62, 0.73] │
#> │  1.382 │   1.01 │     0.038 │   36.34 │   0.000 │  [ 1.31, 1.46] │
#> └────────┴────────┴───────────┴─────────┴─────────┴────────────────┘
#> 
#> 
#> Predicted Y, given Z = -1.01:
#> ┌───────┬─────────────┬───────────┬─────────┬─────────┬─────────────────┐
#> │     X │ Predicted Y │ Std.Error │ z.value │ p.value │   Conf.Interval │
#> ╞═══════╪═════════════╪═══════════╪═════════╪═════════╪═════════════════╡
#> │ -2.97 │       -0.47 │     0.112 │   -4.17 │   0.000 │  [-0.69, -0.25] │
#> │ -1.98 │       -0.50 │     0.076 │   -6.55 │   0.000 │  [-0.65, -0.35] │
#> │ -0.99 │       -0.53 │     0.043 │  -12.33 │   0.000 │  [-0.62, -0.45] │
#> │  0.00 │       -0.57 │     0.026 │  -21.61 │   0.000 │  [-0.62, -0.51] │
#> │  0.99 │       -0.60 │     0.048 │  -12.56 │   0.000 │  [-0.69, -0.50] │
#> │  1.98 │       -0.63 │     0.081 │   -7.76 │   0.000 │  [-0.79, -0.47] │
#> │  2.97 │       -0.66 │     0.117 │   -5.67 │   0.000 │  [-0.89, -0.43] │
#> └───────┴─────────────┴───────────┴─────────┴─────────┴─────────────────┘
#> 
#> 
#> Predicted Y, given Z = 0:
#> ┌───────┬─────────────┬───────────┬─────────┬─────────┬─────────────────┐
#> │     X │ Predicted Y │ Std.Error │ z.value │ p.value │   Conf.Interval │
#> ╞═══════╪═════════════╪═══════════╪═════════╪═════════╪═════════════════╡
#> │ -2.97 │       -2.00 │     0.079 │  -25.38 │   0.000 │  [-2.16, -1.85] │
#> │ -1.98 │       -1.34 │     0.053 │  -25.38 │   0.000 │  [-1.44, -1.23] │
#> │ -0.99 │       -0.67 │     0.026 │  -25.38 │   0.000 │  [-0.72, -0.62] │
#> │  0.00 │        0.00 │     0.000 │     NaN │     NaN │  [ 0.00,  0.00] │
#> │  0.99 │        0.67 │     0.026 │   25.38 │   0.000 │  [ 0.62,  0.72] │
#> │  1.98 │        1.34 │     0.053 │   25.38 │   0.000 │  [ 1.23,  1.44] │
#> │  2.97 │        2.00 │     0.079 │   25.38 │   0.000 │  [ 1.85,  2.16] │
#> └───────┴─────────────┴───────────┴─────────┴─────────┴─────────────────┘
#> 
#> 
#> Predicted Y, given Z = 1.01:
#> ┌───────┬─────────────┬───────────┬─────────┬─────────┬─────────────────┐
#> │     X │ Predicted Y │ Std.Error │ z.value │ p.value │   Conf.Interval │
#> ╞═══════╪═════════════╪═══════════╪═════════╪═════════╪═════════════════╡
#> │ -2.97 │       -3.54 │     0.120 │  -29.48 │   0.000 │  [-3.78, -3.31] │
#> │ -1.98 │       -2.17 │     0.084 │  -25.94 │   0.000 │  [-2.34, -2.01] │
#> │ -0.99 │       -0.80 │     0.049 │  -16.30 │   0.000 │  [-0.90, -0.71] │
#> │  0.00 │        0.57 │     0.026 │   21.61 │   0.000 │  [ 0.51,  0.62] │
#> │  0.99 │        1.93 │     0.042 │   45.91 │   0.000 │  [ 1.85,  2.02] │
#> │  1.98 │        3.30 │     0.076 │   43.74 │   0.000 │  [ 3.16,  3.45] │
#> │  2.97 │        4.67 │     0.112 │   41.84 │   0.000 │  [ 4.45,  4.89] │
#> └───────┴─────────────┴───────────┴─────────┴─────────┴─────────────────┘
#> 

# If the data or user wants unscaled values, set rescale = FALSE, etc.
simple_slopes(x = "X", z = "Z", y = "Y", model = est1, rescale = FALSE)
#> 
#> Difference test of Y~X|Z at Z = -1.000 and 1.000:
#> ┌───────────┬───────────┬─────────┬─────────┬───────────────┐
#> │Difference │ Std.Error │ z.value │ p.value │ Conf.Interval │
#> ╞═══════════╪═══════════╪═════════╪═════════╪═══════════════╡
#> │      1.40 │     0.053 │   26.36 │   0.000 │  [1.30, 1.51] │
#> └───────────┴───────────┴─────────┴─────────┴───────────────┘
#> 
#> Effect of Y~X|Z given values of Z:
#> ┌────────┬─────┬───────────┬─────────┬─────────┬─────────────────┐
#> │    Y~X │   Z │ Std.Error │ z.value │ p.value │   Conf.Interval │
#> ╞════════╪═════╪═══════════╪═════════╪═════════╪═════════════════╡
#> │ -0.027 │  -1 │     0.037 │   -0.73 │   0.462 │  [-0.10, 0.046] │
#> │  0.675 │   0 │     0.027 │   25.38 │   0.000 │  [ 0.62, 0.727] │
#> │  1.377 │   1 │     0.038 │   36.34 │   0.000 │  [ 1.30, 1.451] │
#> └────────┴─────┴───────────┴─────────┴─────────┴─────────────────┘
#> 
#> 
#> Predicted Y, given Z = -1:
#> ┌────┬─────────────┬───────────┬─────────┬─────────┬─────────────────┐
#> │  X │ Predicted Y │ Std.Error │ z.value │ p.value │   Conf.Interval │
#> ╞════╪═════════════╪═══════════╪═════════╪═════════╪═════════════════╡
#> │ -3 │       -0.48 │     0.112 │   -4.25 │   0.000 │  [-0.70, -0.26] │
#> │ -2 │       -0.51 │     0.077 │   -6.61 │   0.000 │  [-0.66, -0.36] │
#> │ -1 │       -0.53 │     0.043 │  -12.33 │   0.000 │  [-0.62, -0.45] │
#> │  0 │       -0.56 │     0.026 │  -21.61 │   0.000 │  [-0.61, -0.51] │
#> │  1 │       -0.59 │     0.048 │  -12.34 │   0.000 │  [-0.68, -0.49] │
#> │  2 │       -0.62 │     0.082 │   -7.54 │   0.000 │  [-0.78, -0.46] │
#> │  3 │       -0.64 │     0.118 │   -5.46 │   0.000 │  [-0.87, -0.41] │
#> └────┴─────────────┴───────────┴─────────┴─────────┴─────────────────┘
#> 
#> 
#> Predicted Y, given Z = 0:
#> ┌────┬─────────────┬───────────┬─────────┬─────────┬─────────────────┐
#> │  X │ Predicted Y │ Std.Error │ z.value │ p.value │   Conf.Interval │
#> ╞════╪═════════════╪═══════════╪═════════╪═════════╪═════════════════╡
#> │ -3 │       -2.02 │     0.080 │  -25.38 │   0.000 │  [-2.18, -1.87] │
#> │ -2 │       -1.35 │     0.053 │  -25.38 │   0.000 │  [-1.45, -1.24] │
#> │ -1 │       -0.67 │     0.027 │  -25.38 │   0.000 │  [-0.73, -0.62] │
#> │  0 │        0.00 │     0.000 │     NaN │     NaN │  [ 0.00,  0.00] │
#> │  1 │        0.67 │     0.027 │   25.38 │   0.000 │  [ 0.62,  0.73] │
#> │  2 │        1.35 │     0.053 │   25.38 │   0.000 │  [ 1.24,  1.45] │
#> │  3 │        2.02 │     0.080 │   25.38 │   0.000 │  [ 1.87,  2.18] │
#> └────┴─────────────┴───────────┴─────────┴─────────┴─────────────────┘
#> 
#> 
#> Predicted Y, given Z = 1:
#> ┌────┬─────────────┬───────────┬─────────┬─────────┬─────────────────┐
#> │  X │ Predicted Y │ Std.Error │ z.value │ p.value │   Conf.Interval │
#> ╞════╪═════════════╪═══════════╪═════════╪═════════╪═════════════════╡
#> │ -3 │       -3.57 │     0.121 │  -29.57 │   0.000 │  [-3.81, -3.33] │
#> │ -2 │       -2.19 │     0.084 │  -26.08 │   0.000 │  [-2.36, -2.03] │
#> │ -1 │       -0.82 │     0.049 │  -16.53 │   0.000 │  [-0.91, -0.72] │
#> │  0 │        0.56 │     0.026 │   21.61 │   0.000 │  [ 0.51,  0.61] │
#> │  1 │        1.94 │     0.042 │   45.91 │   0.000 │  [ 1.85,  2.02] │
#> │  2 │        3.31 │     0.076 │   43.68 │   0.000 │  [ 3.17,  3.46] │
#> │  3 │        4.69 │     0.112 │   41.78 │   0.000 │  [ 4.47,  4.91] │
#> └────┴─────────────┴───────────┴─────────┴─────────┴─────────────────┘
#> 
# }