simple slopes analysis

library(modsem)

Simple slope effects can be plotted using the included plot_interaction() function. This function takes a fitted model object and the names of the two variables that are interacting. The function will plot the interaction effect of the two variables, where:

The x-variable is plotted on the x-axis.
The y-variable is plotted on the y-axis.
The z-variable determines at which points the effect of x on y is plotted.

The function will also plot the 95% confidence interval for the interaction effect. Note that the vals_z argument (as well as the values of x) are scaled by the mean and standard deviation of the variables. Unless the rescale argument is set to FALSE.

Here is a simple example using the double-centering approach:

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

# Inner Model
  Y ~ X + Z + X:Z
"
est1 <- modsem(m1, data = oneInt)
plot_interaction(x = "X", z = "Z", y = "Y", vals_z = c(0, 1), model = est1)

If you want to see the numerical values of the simple slopes, you can use the simple_slopes() function:

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

# Inner Model
  Y ~ X + Z + X:Z
"

est1 <- modsem(m1, data = oneInt)
simple_slopes(x = "X", z = "Z", y = "Y", vals_z = c(0, 1), model = est1)
#> 
#> Predicted Y, given Z = 0:
#> --------------------------------------------------------------------
#>     X | Predicted Y | Std.Error | z.value | p.value |  Conf.Interval 
#> --------------------------------------------------------------------
#> -2.97 |       -2.00 |     0.079 |     -25 |   0.000 | [-2.16, -1.85] 
#> -1.98 |       -1.34 |     0.053 |     -25 |   0.000 | [-1.44, -1.23] 
#> -0.99 |       -0.67 |     0.026 |     -25 |   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 |   0.000 | [ 0.62,  0.72] 
#>  1.98 |        1.34 |     0.053 |      25 |   0.000 | [ 1.23,  1.44] 
#>  2.97 |        2.00 |     0.079 |      25 |   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 |   0.000 | [-3.78, -3.31] 
#> -1.98 |       -2.17 |     0.084 |     -26 |   0.000 | [-2.34, -2.01] 
#> -0.99 |       -0.80 |     0.049 |     -16 |   0.000 | [-0.90, -0.71] 
#>  0.00 |        0.57 |     0.026 |      22 |   0.000 | [ 0.51,  0.62] 
#>  0.99 |        1.93 |     0.042 |      46 |   0.000 | [ 1.85,  2.02] 
#>  1.98 |        3.30 |     0.076 |      44 |   0.000 | [ 3.16,  3.45] 
#>  2.97 |        4.67 |     0.112 |      42 |   0.000 | [ 4.45,  4.89]

The simple_slopes() function returns a simple_slopes object, which is a data.frame with some additional attributes. It only has a single method (or technically, a generic function), print.simple_slopes(), which prints the simple slopes in a easy-to-read format. If you want to extract the simple slopes as a data.frame, you can use the as.data.frame() function:

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

# Inner Model
  Y ~ X + Z + X:Z
"

est1 <- modsem(m1, data = oneInt)
slopes <- simple_slopes(x = "X", z = "Z", y = "Y", 
                        vals_z = c(0, 1), model = est1)
as.data.frame(slopes)
#>        vals_x   vals_z  predicted  std.error   z.value       p.value   ci.upper
#> 1  -2.9713704 0.000000 -2.0043501 0.07897710 -25.37887 4.315370e-142 -1.8495578
#> 2  -1.9809136 0.000000 -1.3362334 0.05265140 -25.37887 4.315370e-142 -1.2330385
#> 3  -0.9904568 0.000000 -0.6681167 0.02632570 -25.37887 4.315370e-142 -0.6165193
#> 4   0.0000000 0.000000  0.0000000 0.00000000       NaN           NaN  0.0000000
#> 5   0.9904568 0.000000  0.6681167 0.02632570  25.37887 4.315370e-142  0.7197141
#> 6   1.9809136 0.000000  1.3362334 0.05265140  25.37887 4.315370e-142  1.4394282
#> 7   2.9713704 0.000000  2.0043501 0.07897710  25.37887 4.315370e-142  2.1591423
#> 8  -2.9713704 1.008084 -3.5419750 0.12016032 -29.47708 5.664083e-191 -3.3064651
#> 9  -1.9809136 1.008084 -2.1729185 0.08376085 -25.94194 2.242150e-148 -2.0087503
#> 10 -0.9904568 1.008084 -0.8038620 0.04930659 -16.30334  9.344238e-60 -0.7072229
#> 11  0.0000000 1.008084  0.5651944 0.02615878  21.60630 1.567068e-103  0.6164647
#> 12  0.9904568 1.008084  1.9342509 0.04213438  45.90671  0.000000e+00  2.0168328
#> 13  1.9809136 1.008084  3.3033074 0.07552624  43.73721  0.000000e+00  3.4513362
#> 14  2.9713704 1.008084  4.6723639 0.11167365  41.83945  0.000000e+00  4.8912403
#>      ci.lower
#> 1  -2.1591423
#> 2  -1.4394282
#> 3  -0.7197141
#> 4   0.0000000
#> 5   0.6165193
#> 6   1.2330385
#> 7   1.8495578
#> 8  -3.7774849
#> 9  -2.3370868
#> 10 -0.9005012
#> 11  0.5139242
#> 12  1.8516691
#> 13  3.1552787
#> 14  4.4534876