It computes the Delta_Med proposed by Liu, Yuan, and Li (2023), an \(R^2\)-like measure of indirect effect.

## Usage

```
delta_med(
x,
y,
m,
fit,
paths_to_remove = NULL,
boot_out = NULL,
level = 0.95,
progress = TRUE,
skip_check_single_x = FALSE,
skip_check_m_between_x_y = FALSE,
skip_check_x_to_y = FALSE,
skip_check_latent_variables = FALSE,
boot_type = c("perc", "bc")
)
```

## Arguments

- x
The name of the

`x`

variable. Must be supplied as a quoted string.- y
The name of the

`y`

variable. Must be supplied as a quoted string.- m
A vector of the variable names of the mediator(s). If more than one mediators, they do not have to be on the same path from

`x`

to`y`

. Cannot be`NULL`

for this function.- fit
The fit object. Must be a lavaan::lavaan object.

- paths_to_remove
A character vector of paths users want to manually remove, specified in

`lavaan`

model syntax. For example,`c("m2~x", "m3~m2")`

removes the path from`x`

to`m2`

and the path from`m2`

to`m3`

. The default is`NULL`

, and the paths to remove will be determined using the method by Liu et al. (2023). If supplied, then only paths specified explicitly will be removed.- boot_out
The output of

`do_boot()`

. If supplied, the stored bootstrap estimates will be used to form the nonparametric percentile bootstrap confidence interval of Delta_Med.- level
The level of confidence of the bootstrap confidence interval. Default is .95.

- progress
Logical. Display bootstrapping progress or not. Default is

`TRUE`

.- skip_check_single_x
Logical Check whether the model has one and only one x-variable. Default is

`TRUE`

.- skip_check_m_between_x_y
Logical. Check whether all

`m`

variables are along a path from`x`

to`y`

. Default is`TRUE`

.- skip_check_x_to_y
Logical. Check whether there is a direct path from

`x`

to`y`

. Default is`TRUE`

.- skip_check_latent_variables
Logical. Check whether the model has any latent variables. Default is

`TRUE`

.- boot_type
If bootstrap confidence interval is to be formed, the type of bootstrap confidence interval. The supported types are

`"perc"`

(percentile bootstrap confidence interval, the default and recommended type) and`"bc"`

(bias-corrected, or BC, bootstrap confidence interval).

## Value

A `delta_med`

class object.
It is a list-like object with these
major elements:

`delta_med`

: The Delta_Med.`x`

: The name of the`x`

-variable.`y`

: The name of the`y`

-variable.`m`

: A character vector of the mediator(s) along a path. The path runs from the first element to the last element.

This class has a `print`

method,
a `coef`

method, and a `confint`

method. See `print.delta_med()`

,
`coef.delta_med()`

, and
`confint.delta_med()`

.

## Details

It computes Delta_Med, an
\(R^2\)-like effect
size measure for the indirect effect
from one variable (the `y`

-variable)
to another variable (the `x`

-variable)
through one or more mediators
(`m`

, or `m1`

, `m2`

, etc. when
there are more than one mediator).

The Delta_Med of one or more mediators was computed as the difference between two \(R^2\)s:

\(R^2_1\), the \(R^2\) when

`y`

is predicted by`x`

and all mediators.\(R^2_2\), the \(R^2\) when the mediator(s) of interest is/are removed from the models, while the error term(s) of the mediator(s) is/are kept.

Delta_Med is given by \(R^2_1 - R^2_2\).

Please refer to Liu et al. (2023) for the technical details.

The function can also form a nonparametric percentile bootstrap confidence of Delta_Med.

## Implementation

The function identifies all the
path(s) pointing to the mediator(s)
of concern and fixes the path(s) to
zero, effectively removing the
mediator(s). However, the model is
not refitted, hence keeping the
estimates of all other parameters
unchanged.
It then uses `lavaan::lav_model_set_parameters()`

to update the parameters,
`lavaan::lav_model_implied()`

to
update the implied statistics, and
then calls `lavaan::lavInspect()`

to
retrieve the implied variance of the
predicted values of `y`

for computing
the \(R^2_2\). Subtracting this
\(R^2_2\) from \(R^2_1\) of
`y`

can then yield Delta_Med.

## Model Requirements

For now, by default, it only computes Delta_Med for the types of models discussed in Liu et al. (2023):

Having one predictor (the

`x`

-variable).Having one or more mediators, the

`m`

-variables, with arbitrary way to mediate the effect of`x`

on the outcome variable (`y`

-variable).Having one or more outcome variables. Although their models only have outcome variables, the computation of the Delta_Med is not affected by the presence of other outcome variables.

Having no control variables.

The mediator(s),

`m`

, and the`y`

-variable are continuous.`x`

can be continuous or categorical. If categorical, it needs to be handle appropriately when fitting the model.`x`

has a direct path to`y`

.All the mediators listed in the argument

`m`

is present in at least one path from`x`

to`y.`

None of the paths from

`x`

to`y`

are moderated.

It can be used for other kinds
of models but support for them is
disabled by default. To use
this function for
cases not discussed in
Liu et al. (2023), please disable
relevant requirements stated above
using the relevant
`skip_check_*`

arguments. An error
will be raised if the models failed
any of the checks not skipped by
users.

## References

Liu, H., Yuan, K.-H., & Li, H. (2023).
A systematic framework for defining
R-squared measures in mediation
analysis. *Psychological Methods*.
Advance online publication.
https://doi.org/10.1037/met0000571

## Examples

```
library(lavaan)
dat <- data_med
mod <-
"
m ~ x
y ~ m + x
"
fit <- sem(mod, dat)
dm <- delta_med(x = "x",
y = "y",
m = "m",
fit = fit)
dm
#> Call:
#> delta_med(x = "x", y = "y", m = "m", fit = fit)
#>
#> Predictor (x) : x
#> Mediator(s) (m) : m
#> Outcome variable (y): y
#>
#> Delta_med: 0.230
#>
#> Paths removed:
#> m~x
print(dm, full = TRUE)
#> Call:
#> delta_med(x = "x", y = "y", m = "m", fit = fit)
#>
#> Predictor (x) : x
#> Mediator(s) (m) : m
#> Outcome variable (y): y
#>
#> Delta_med: 0.230
#>
#> Paths removed:
#> m~x
#>
#> Additional information:
#> R-sq: Original : 0.351
#> R-sq: Mediator(s) removed : 0.121
#> Variance of y : 6.273
#> Variance of predicted y : 2.203
#> Variance of predicted: mediator(s) removed: 0.759
# Call do_boot() to generate
# bootstrap estimates
# Use 2000 or even 5000 for R in real studies
# Set parallel to TRUE in real studies for faster bootstrapping
boot_out <- do_boot(fit,
R = 45,
seed = 879,
parallel = FALSE,
progress = FALSE)
# Remove 'progress = FALSE' in practice
dm_boot <- delta_med(x = "x",
y = "y",
m = "m",
fit = fit,
boot_out = boot_out,
progress = FALSE)
dm_boot
#> Call:
#> delta_med(x = "x", y = "y", m = "m", fit = fit, boot_out = boot_out,
#> progress = FALSE)
#>
#> Predictor (x) : x
#> Mediator(s) (m) : m
#> Outcome variable (y): y
#>
#> Delta_med : 0.230
#> 95.0% Bootstrap percentile confidence interval: [0.097, 0.318]
#> Number of bootstrap samples : 45
#>
#> Paths removed:
#> m~x
confint(dm_boot)
#> Percentile 2.5 % Percentile 97.5 %
#> Delta_Med 0.09725932 0.3175632
```