Compute the standardized moderation effect in a moderated regression model.

stdmod(
lm_out,
x = NULL,
w = NULL,
y = NULL,
x_rescale = TRUE,
w_rescale = TRUE,
y_rescale = TRUE
)

stdmod_boot(
lm_out,
...,
nboot = 100,
conf = 0.95,
boot_args = NULL,
full_output = FALSE
)

## Arguments

lm_out

The output from lm().

x

The focal variable, that is, the variable with its effect being moderated. If supplied, its standard deviation will be used for rescaling. Also called the independent variable in some models. Default is NULL.

w

The moderator. If supplied, its standard deviation will be used for rescaling. Default is NULL.

y

The outcome variable (dependent variable) . If supplied, its standard deviation will be used for rescaling. Default is NULL.

x_rescale

If TRUE, will rescale x by its standard deviation. Default is TRUE.

w_rescale

If TRUE, will rescale w by its standard deviation. Default is TRUE.

y_rescale

If TRUE, will rescale y by its standard deviation. Default is TRUE.

...

Parameters to be passed to stdmod().

nboot

The number of bootstrap samples. Default is 100.

conf

The level of confidence for the confidence interval. Default is .95.

boot_args

A named list of arguments to be passed to boot::boot(). Default is NULL.

full_output

Whether the full output from boot::boot() is returned. Default is FALSE.

## Value

stdmod() returns a scalar: The standardized moderation effect.

stdmod_boot() returns a list with two elements. The element ci is a numeric vector of the bootstrap confidence interval. The element boot_out, if not NA, is the output of boot::boot(), which is used to do the bootstrapping.

## Details

Two more general functions, std_selected() and std_selected_boot(), have been developed and can do what these functions do and more. Users are recommended to use them instead of stdmod() and stdmod_boot(). These two functions will not be updated in the near future.

Nevertheless, if computing the standardized moderation effect and forming its nonparametric bootstrap interval are all required, then these functions can still be used.

stdmod() computes the standardized moderation effect given an lm() output using the formula from Cheung, Cheung, Lau, Hui, and Vong (2022). Users specify the moderator, the focal variable (the variable with its effect on the outcome variable moderated), the outcome variable (dependent variable) , and the corresponding standardized moderation effect. Users can also select which variable(s) will be standardized.

stdmod_boot() is a wrapper of stdmod(). It computes the nonparametric bootstrap confidence interval of the standardized moderation effect, as suggested by Cheung, Cheung, Lau, Hui, and Vong (2022), given the output of lm()

Percentile interval from boot::boot.ci() is returned by this function. If other types of confidence intervals are desired, set full_output = TRUE and use boot::boot.ci() on the element boot_out in the output of this function.

## Functions

• stdmod(): The base function for computing standardized moderation effect

• stdmod_boot(): A wrapper of stdmod() that computes the nonparametric bootstrap confidence interval of the standardized moderation effect.

## References

Cheung, S. F., Cheung, S.-H., Lau, E. Y. Y., Hui, C. H., & Vong, W. N. (2022) Improving an old way to measure moderation effect in standardized units. Health Psychology, 41(7), 502-505. doi:10.1037/hea0001188

## Author

Shu Fai Cheung https://orcid.org/0000-0002-9871-9448

## Examples


# Load a test data of 500 cases

dat <- test_x_1_w_1_v_2_n_500

# Do regression as usual:
lm_raw <- lm(dv ~ iv*mod + v1 + v2, dat)
summary(lm_raw)
#>
#> Call:
#> lm(formula = dv ~ iv * mod + v1 + v2, data = dat)
#>
#> Residuals:
#>      Min       1Q   Median       3Q      Max
#> -1650.87  -513.21     6.61   460.18  2189.74
#>
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 2814.565   4684.595   0.601   0.5482
#> iv          -164.942    304.407  -0.542   0.5882
#> mod          -17.223     46.420  -0.371   0.7108
#> v1           -12.157     10.684  -1.138   0.2557
#> v2            -4.284      6.290  -0.681   0.4962
#> iv:mod         5.515      3.038   1.815   0.0701 .
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 708.1 on 494 degrees of freedom
#> Multiple R-squared:  0.5862,	Adjusted R-squared:  0.582
#> F-statistic:   140 on 5 and 494 DF,  p-value: < 2.2e-16
#>

# The standard deviations of iv, dv, and mod:
sds <- apply(dat, 2, sd)
sds
#>          dv          iv         mod          v1          v2
#> 1095.222413    1.991458    5.004342    2.970378    5.064710

# Compute the standardized moderation effect:
stdmod_xyw <- stdmod(lm_raw, x = iv, y = dv, w = mod)
stdmod_xyw
#>     iv:mod
#> 0.05018003
# By default, all three variables will be standardized.

# Check against self-computed standardized moderation effect:
coef(lm_raw)["iv:mod"] * sds["iv"] * sds["mod"] / sds["dv"]
#>     iv:mod
#> 0.05018003

# Standardize only the iv, i.e., do not standardized dv and the moderator:
stdmod_x <- stdmod(lm_raw, x = iv, y = dv, w = mod,
x_rescale = TRUE,  y_rescale = FALSE, w_rescale = FALSE)
stdmod_x
#>   iv:mod
#> 10.98212
# Check against self-computed moderation effect with only iv standardized:
coef(lm_raw)["iv:mod"] * sds["iv"]
#>   iv:mod
#> 10.98212

dat <- test_x_1_w_1_v_2_n_500
# Do regression as usual:
lm_raw <- lm(dv ~ iv*mod + v1 + v2, dat)

# Compute the standardized moderation effect.
# Form its confidence interval by nonparametric bootstrapping.
set.seed(85740917)
stdmod_xyw_boot <- stdmod_boot(lm_raw, x = iv, w = mod, y = dv, nboot = 100)
# In real analysis, nboot should be at least 2000.

# Print the ci
stdmod_xyw_boot$ci #> [1] 0.01014322 0.10050906 # Repeat the analysis but keep the results from boot: set.seed(85740917) stdmod_xyw_boot <- stdmod_boot(lm_raw, x = iv, w = mod, y = dv, nboot = 200, full_output = TRUE) # In real analysis, nboot should be at least 2000. # Print the 95% percentile confidence interval stdmod_xyw_boot$ci
#> [1] 0.005379417 0.103307077