1 Introduction

This article is a brief illustration of how to use mod_levels(), mod_levels_list(), and merge_mod_levels() to generate a table of moderator levels for use by cond_indirect_effects(). No need to use these functions if the default levels generated by cond_indirect_effects() is appropriated, as illustrated in vignette("manymome").

Use these functions only when users want to use levels of the moderators other than those default levels.

2 Numeric Moderators

We first use the sample data set data_med_mod_ab:

library(manymome)
dat <- data_med_mod_ab
print(head(dat), digits = 3)
#>       x   w1   w2    m    y    c1   c2
#> 1  9.27 4.97 2.66 3.46 8.80  9.26 3.14
#> 2 10.79 4.13 3.33 4.05 7.37 10.71 5.80
#> 3 11.10 5.91 3.32 4.04 8.24 10.60 5.45
#> 4  9.53 4.78 2.32 3.54 8.37  9.22 3.83
#> 5 10.00 4.38 2.95 4.65 8.39  9.58 4.26
#> 6 12.25 5.81 4.04 4.73 9.65  9.51 4.01

Suppose this is the model being fitted:

library(lavaan)
dat$w1x <- dat$w1 * dat$x
dat$w2m <- dat$w2 * dat$m
mod <-
"
m ~ x + w1 + w1x
y ~ m + w2 + w2m
m ~~ w2 + w2m
w2  ~~ w2m + x + w1 + w1x
w2m ~~ x + w1 + w1x
x   ~~ w1 + w1x
w1  ~~ w1x
"
fit <- sem(model = mod, data = dat)

2.1 SD and Mean

It has two numeric moderators, w1 and w2. To generate these three levels for w1, one standard deviation (SD) below mean, mean, and one SD above mean, just call mod_levels():

w1levels <- mod_levels(w = "w1", fit = fit)
w1levels
#>               w1
#> M+1.0SD 6.173157
#> Mean    5.105602
#> M-1.0SD 4.038047

This is not necessary in calling cond_indirect_effects() because it will automatically generate these default levels.

Suppose we want to use only two levels, one SD below and one SD above mean, we can set the argument sd_from_mean to a vector of distances from means, which are -1 and 1 in this example:

w1levels <- mod_levels(w = "w1", fit = fit,
                       sd_from_mean = c(-1, 1))
w1levels
#>               w1
#> M+1.0SD 6.173157
#> M-1.0SD 4.038047

2.2 Percentiles

To generate the levels based on percentiles, set the argument w_method to "percentile":

w1levels <- mod_levels(w = "w1", fit = fit,
                       w_method = "percentile")
w1levels
#>           w1
#> 84% 6.207972
#> 50% 5.215974
#> 16% 3.932444

The default percentiles are 16th, 50th, and 84th, corresponding to one SD below mean, mean, and one SD above mean in a normal distribution.

Suppose we want to change the percentiles to be used, for example, 25th and 75th, set the argument percentiles as shown below:

w1levels <- mod_levels(w = "w1", fit = fit,
                       w_method = "percentile",
                       percentiles = c(.25, .75))
w1levels
#>           w1
#> 75% 5.808579
#> 25% 4.196759

2.3 Specific Values

If there are values that are meaningful for a moderator, they can be used by setting values to a vector of values:

w1levels <- mod_levels(w = "w1", fit = fit,
                       values = c(2, 4, 8))
w1levels
#>   w1
#> 8  8
#> 4  4
#> 2  2

The output of mod_levels can be used when calling cond_indirect_effects():

out <- cond_indirect_effects(wlevels = w1levels,
                             x = "x", y = "m",
                             fit = fit)
out
#> 
#> == Conditional effects ==
#> 
#>  Path: x -> m
#>  Conditional on moderator(s): w1
#>  Moderator(s) represented by: w1
#> 
#>   [w1] (w1)    ind    m~x
#> 1    8    8  0.964  0.964
#> 2    4    4  0.165  0.165
#> 3    2    2 -0.235 -0.235
#> 
#>  - The 'ind' column shows the  effects.
#>  - 'm~x' is/are the path coefficient(s) along the path conditional on
#>    the moderators.

cond_indirect_effects() will determine the moderators automatically from the object assigned to wlevels.

2.4 Merging the Levels of Two Or More Moderators

In the previous example, there are two moderators. We can call mod_levels() once for each of them, or call mod_levels_list():

wlevels_list <- mod_levels_list("w1", "w2", fit = fit)
wlevels_list
#> [[1]]
#>               w1
#> M+1.0SD 6.173157
#> M-1.0SD 4.038047
#> 
#> [[2]]
#>               w2
#> M+1.0SD 4.040487
#> M-1.0SD 2.055091

The output is a list of the output of mod_levels(). With two or more moderators, the default levels are two: one SD below mean and one SD above mean.

The function mod_levels_list() can merge the output into one table by setting merge to TRUE:

wlevels_list <- mod_levels_list("w1", "w2", fit = fit,
                                merge = TRUE)
wlevels_list
#>                                w1       w2
#> w1: M+1.0SD; w2: M+1.0SD 6.173157 4.040487
#> w1: M+1.0SD; w2: M-1.0SD 6.173157 2.055091
#> w1: M-1.0SD; w2: M+1.0SD 4.038047 4.040487
#> w1: M-1.0SD; w2: M-1.0SD 4.038047 2.055091

Calling mod_levels_list() is useful when the same settings will be used for all moderators. Most arguments of mod_levels() can be used in mod_levels_list(). For example, if we want to use 25th and 75th percentiles for both w1 and w2, use w_method and percentiles as before:

wlevels_list <- mod_levels_list("w1", "w2", fit = fit,
                                w_method = "percentile",
                                percentiles = c(.25, .75),
                                merge = TRUE)
wlevels_list
#>                        w1       w2
#> w1: 75%; w2: 75% 5.808579 3.692675
#> w1: 75%; w2: 25% 5.808579 2.430643
#> w1: 25%; w2: 75% 4.196759 3.692675
#> w1: 25%; w2: 25% 4.196759 2.430643

2.5 Different Settings For Moderators

If we need to use different settings for the two moderators, then we need to call mod_levels() once for each of them, and merge the results by merge_mod_levels():

w1levels <- mod_levels(w = "w1", fit = fit)
w1levels
#>               w1
#> M+1.0SD 6.173157
#> Mean    5.105602
#> M-1.0SD 4.038047
w2levels <- mod_levels(w = "w2", fit = fit, values = c(2, 5))
w2levels
#>   w2
#> 5  5
#> 2  2
wlevels_all <- merge_mod_levels(w1levels, w2levels)
wlevels_all
#>                          w1 w2
#> w1: M+1.0SD; w2: 5 6.173157  5
#> w1: M+1.0SD; w2: 2 6.173157  2
#> w1: Mean; w2: 5    5.105602  5
#> w1: Mean; w2: 2    5.105602  2
#> w1: M-1.0SD; w2: 5 4.038047  5
#> w1: M-1.0SD; w2: 2 4.038047  2

3 Categorical Moderators

We use the dataset data_med_mod_serial_cat for illustration:

dat <- data_med_mod_serial_cat
print(head(dat), digits = 3)
#>      x     w1    w2   m1   m2    y   c1   c2
#> 1 8.09 group2 team1 7.70 5.26 3.17 4.31 5.03
#> 2 6.16 group2 team2 5.71 4.36 3.12 4.69 3.19
#> 3 6.03 group2 team2 5.40 5.22 4.23 4.07 4.25
#> 4 6.92 group1 team1 7.26 5.98 3.65 5.87 5.35
#> 5 7.76 group3 team1 4.49 4.83 4.01 4.35 4.16
#> 6 6.84 group2 team2 5.72 6.31 3.38 4.32 4.48

It has two categorical moderators, w1 with three categories and w2 with two categories. We use only w1 here for illustration.

3.1 Create Dummy Variables and Fit the Model

To fit a model using path analysis, two dummy variables need to be created for w1. This can be done by factor2var() or similar functions from other packages.

w1dummies <- factor2var(dat$w1, prefix = "w1")
head(w1dummies)
#>        w1group2 w1group3
#> group2        1        0
#> group2        1        0
#> group2        1        0
#> group1        0        0
#> group3        0        1
#> group2        1        0
# Add them to the dataset
dat[, c("w1group2", "w1group3")] <- w1dummies
print(head(dat), digits = 3)
#>      x     w1    w2   m1   m2    y   c1   c2 w1group2 w1group3
#> 1 8.09 group2 team1 7.70 5.26 3.17 4.31 5.03        1        0
#> 2 6.16 group2 team2 5.71 4.36 3.12 4.69 3.19        1        0
#> 3 6.03 group2 team2 5.40 5.22 4.23 4.07 4.25        1        0
#> 4 6.92 group1 team1 7.26 5.98 3.65 5.87 5.35        0        0
#> 5 7.76 group3 team1 4.49 4.83 4.01 4.35 4.16        0        1
#> 6 6.84 group2 team2 5.72 6.31 3.38 4.32 4.48        1        0

This is the model:

dat$w1group2x <- dat$w1group2 * dat$x
dat$w1group3x <- dat$w1group3 * dat$x
mod <-
"
m1 ~ x + w1group2 + w1group3 + w1group2x + w1group3x
y ~ m1 + x
"
fit <- sem(model = mod, data = dat)

3.2 Default Levels

The levels of a categorical moderator are just the categories (unique combinations of the coding). This can be generated by mod_levels(). w should be a vector of the dummy variables:

w1levels <- mod_levels(w = c("w1group2", "w1group3"), fit = fit)
w1levels
#>           w1group2 w1group3
#> Reference        0        0
#> 2                1        0
#> 3                0        1

The names of group2 and group3 are 2 and 3 because they are inferred from the names of the dummy variables. The common part, "w1group", is removed.

To tell mod_levels which part to be removed, set prefix to the part to be removed:

w1levels <- mod_levels(w = c("w1group2", "w1group3"), fit = fit,
                       prefix = "w1")
w1levels
#>           w1group2 w1group3
#> Reference        0        0
#> group2           1        0
#> group3           0        1

By default, the group with 0s on all dummy variables is labelled Reference because its name cannot be determined from the names of the dummy variables. The label can be changed by setting reference_group_label:

w1levels <- mod_levels(w = c("w1group2", "w1group3"), fit = fit,
                       prefix = "w1",
                       reference_group_label = "group1")
w1levels
#>        w1group2 w1group3
#> group1        0        0
#> group2        1        0
#> group3        0        1

The output can then be used in cond_indirect_effects():

out <- cond_indirect_effects(wlevels = w1levels,
                             x = "x", y = "y", m = "m1",
                             fit = fit)
out
#> 
#> == Conditional indirect effects ==
#> 
#>  Path: x -> m1 -> y
#>  Conditional on moderator(s): w1
#>  Moderator(s) represented by: w1group2, w1group3
#> 
#>     [w1] (w1group2) (w1group3)   ind  m1~x  y~m1
#> 1 group1          0          0 0.263 1.002 0.262
#> 2 group2          1          0 0.249 0.950 0.262
#> 3 group3          0          1 0.122 0.467 0.262
#> 
#>  - The 'ind' column shows the indirect effects.
#>  - 'm1~x','y~m1' is/are the path coefficient(s) along the path
#>    conditional on the moderators.

3.3 User-Supplied Levels

To have full control on the labels and coding, use values and supply a named list of numeric vectors: the name is the group label and the vector is the coding:

w1levels <- mod_levels(w = c("w1group2", "w1group3"), fit = fit,
                       values = list(group1 = c(0, 0),
                                     group2 = c(1, 0),
                                     group3 = c(0, 1)))
w1levels
#>        w1group2 w1group3
#> group1        0        0
#> group2        1        0
#> group3        0        1

4 Mixing Numeric and Categorical Moderators

Numeric and categorical moderators can be mixed but they need to be generated separately and then merged by merge_mod_levels().

Using the example in the previous section, pretending that x is a numeric moderator:

xlevels <- mod_levels(w = "x", fit = fit,
                      sd_from_mean = c(-1, 1))
xlevels
#>                x
#> M+1.0SD 7.149362
#> M-1.0SD 5.087437
w1levels <- mod_levels(w = c("w1group2", "w1group3"), fit = fit,
                       prefix = "w1",
                       reference_group_label = "group1")
w1levels
#>        w1group2 w1group3
#> group1        0        0
#> group2        1        0
#> group3        0        1
wlevels_all <- merge_mod_levels(xlevels, w1levels)
wlevels_all
#>                               x w1group2 w1group3
#> x: M+1.0SD; w1: group1 7.149362        0        0
#> x: M+1.0SD; w1: group2 7.149362        1        0
#> x: M+1.0SD; w1: group3 7.149362        0        1
#> x: M-1.0SD; w1: group1 5.087437        0        0
#> x: M-1.0SD; w1: group2 5.087437        1        0
#> x: M-1.0SD; w1: group3 5.087437        0        1

5 Determining The Type of a Moderator

The function mod_levels() and mod_levels_list() usually can determine the type correctly. However, if the detected type is wrong or users want to specify explicitly the type, set the argument w_type to either "numeric" or "categorical".

6 Further Information

For further information on mod_levels(), mod_levels_list(), and merge_mod_levels(), please refer to their help pages.

Setting Moderator Levels

Shu Fai Cheung & Sing-Hang Cheung

2022-09-08