Compute the standardized moderation effect in a moderated regression model.
Usage
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 isTRUE.- w_rescale
If
TRUE, will rescale w by its standard deviation. Default isTRUE.- y_rescale
If
TRUE, will rescale y by its standard deviation. Default isTRUE.- ...
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 isNULL.- full_output
Whether the full output from
boot::boot()is returned. Default isFALSE.
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 effectstdmod_boot(): A wrapper ofstdmod()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