Conditional Effects by cond_effect()
Shu Fai Cheung
2023-09-09
Source:vignettes/cond_effect.Rmd
cond_effect.RmdIntroduction
This vignette illustrates how to use cond_effect() from
the stdmod package. More about this package can be found in
vignette("stdmod", package = "stdmod") or at https://sfcheung.github.io/stdmod/.
What cond_effect() Can Do
It can compute the conditional effect of a predictor (the focal variable) on an outcome variable (dependent variable) for selected levels of the moderator:
#> Level conscientiousness emotional_stability Effect S.E. t p Sig
#> High 3.950 0.012 0.117 0.107 0.915
#> Medium 3.343 0.214 0.083 2.560 0.011 *
#> Low 2.736 0.415 0.115 3.601 0.000 ***It can also compute standardized conditional moderation effect of this predictor:
#> Level conscientiousness emotional_stability Effect S.E. t p Sig
#> High 1.000 0.007 0.063 0.107 0.915
#> Medium 0.000 0.115 0.045 2.560 0.011 *
#> Low -1.000 0.223 0.062 3.601 0.000 ***Nonparametric bootstrap percentile confidence interval can also be
formed for standardized conditional effect using
cond_effect_boot().
cond_effect() is not designed to be a versatile tool. It
is designed to be a function “good-enough” for common scenarios.
Nevertheless, it can report some useful information along with the
conditional effects, as demonstrated below.
Major Arguments
Regression Output, Predictor (x), and Moderator
(w)
output: The output oflm(),std_selected(), orstd_selected_boot(), with at least one interaction term. Bootstrap estimates instd_selected_boot()will be ignored because bootstrapping will be done for each level again.x: The predictor (focal variable).w: The moderator.
These are the only required arguments. Just setting them can generate the graph:
library(stdmod)
data(sleep_emo_con)
lm_out <- lm(sleep_duration ~ age + gender +
emotional_stability * conscientiousness,
sleep_emo_con)
cond_out <- cond_effect(output = lm_out,
x = "emotional_stability",
w = "conscientiousness")
cond_out
#> The effects of emotional_stability on sleep_duration, conditional on conscientiousness:
#>
#> Level conscientiousness emotional_stability Effect S.E. t p Sig
#> High 3.950 0.012 0.117 0.107 0.915
#> Medium 3.343 0.214 0.083 2.560 0.011 *
#> Low 2.736 0.415 0.115 3.601 0.000 ***
#>
#>
#> The regression model:
#>
#> sleep_duration ~ age + gender + emotional_stability * conscientiousness
#>
#> Interpreting the levels of conscientiousness:
#>
#> Level conscientiousness % Below From Mean (in SD)
#> High 3.950 83.60 1.00
#> Medium 3.343 49.60 0.00
#> Low 2.736 16.60 -1.00
#>
#> - % Below: The percent of cases equal to or less than a level.
#> - From Mean (in SD): Distance of a level from the mean, in standard
#> deviation (+ve above, -ve below).By default, the print method of cond_effect() output
prints the conditional effects, OLS standard errors, t
statistics, p-values, and significant test results, along with
other information such as the value of each level of the moderator, its
distance from the mean, the percentage of cases equal to or less than
this level. The regression model is also printed. If only the table of
effects is needed, call print() and set
table_only to TRUE:
print(cond_out, table_only = TRUE)
#> Level conscientiousness emotional_stability Effect S.E. t p Sig
#> High 3.950 0.012 0.117 0.107 0.915
#> Medium 3.343 0.214 0.083 2.560 0.011 *
#> Low 2.736 0.415 0.115 3.601 0.000 ***More options in printing the output can be found in the help page of
print.cond_effect().
Levels of the Moderator
Numeric Moderators
If the moderator is a numeric variable, then, by default, the conditional effects for three levels of the moderators will be used: one standard deviation (SD) to the mean (“Low”), mean (“Medium”), and one SD above mean (“High”).
Users can also use percentiles to define “Low”, “Medium”, and “High”
by setting w_method to "percentile". The
default are 16th percentile, 50th percentile, and 84th percentile, which
corresponds approximately to one SD below mean, mean, and one SD above
mean, respectively, for a normal distribution.
data(sleep_emo_con)
lm_out <- lm(sleep_duration ~ age + gender +
emotional_stability * conscientiousness,
sleep_emo_con)
cond_out <- cond_effect(output = lm_out,
x = "emotional_stability",
w = "conscientiousness",
w_method = "percentile")
print(cond_out, title = FALSE, model = FALSE)
#> Level conscientiousness emotional_stability Effect S.E. t p Sig
#> High 4.000 -0.004 0.122 -0.034 0.973
#> Medium 3.400 0.195 0.084 2.322 0.021 *
#> Low 2.700 0.427 0.119 3.600 0.000 ***
#>
#> Interpreting the levels of conscientiousness:
#>
#> Level conscientiousness % Below From Mean (in SD)
#> High 4.000 87.20 1.08
#> Medium 3.400 57.00 0.09
#> Low 2.700 16.60 -1.06
#>
#> - % Below: The percent of cases equal to or less than a level.
#> - From Mean (in SD): Distance of a level from the mean, in standard
#> deviation (+ve above, -ve below).Note that the empirical percentage of cases equal to or less than a level may not be exactly equal to that for the requested percentile if the number of cases is small and/or the number of unique values of the moderator is small.
Categorical Moderators
If the moderator is a categorical variable (a string variable or a factor), then the conditional effect of the moderator for each value of this categorical moderator will be printed:
set.seed(61452)
sleep_emo_con$city <- sample(c("Alpha", "Beta", "Gamma"),
nrow(sleep_emo_con), replace = TRUE)
lm_cat <- lm(sleep_duration ~ age + gender + emotional_stability*city,
sleep_emo_con)
cond_out <- cond_effect(lm_cat,
x = "emotional_stability",
w = "city")
print(cond_out, title = FALSE, model = FALSE)
#> Level city emotional_stability Effect S.E. t p Sig
#> Alpha Alpha 0.408 0.135 3.027 0.003 **
#> Beta Beta 0.351 0.147 2.388 0.017 *
#> Gamma Gamma 0.020 0.149 0.131 0.896Nonparametric Bootstrap Confidence Intervals
If one or more variables are standardized, the OLS confidence
intervals are not appropriate (Cheung, Cheung, Lau, Hui,
& Vong, 2022; Yuan & Chan,
2011). Users can call cond_effect_boot() to use
nonparametric bootstrapping to form the percentile confidence interval
for each conditional effect.
-
conf: The level of confidence, expressed as a proportion. Default is .95, requesting a 95% confidence interval. -
nbootThe number of bootstrap samples to drawn. Should be at least 2000 but 5000 is preferable.
To make the results reproducible, call set.seed() before
calling cond_effect_boot(), as illustrated below.
lm_out <- lm(sleep_duration ~ age + gender +
emotional_stability * conscientiousness,
sleep_emo_con)
# Standardize all variables and do the moderated regression again
# Use to_standardize as a shortcut to to_center and to_scale
lm_std <- std_selected(lm_out,
to_standardize = ~ .)
set.seed(897043)
cond_std <- cond_effect_boot(output = lm_std,
x = "emotional_stability",
w = "conscientiousness",
nboot = 2000)
print(cond_std, model = FALSE, title = FALSE, level_info = FALSE)
#> Level conscientiousness emotional_stability Effect CI Lower CI Upper S.E.
#> High 1.000 0.007 -0.107 0.117 0.063
#> Medium 0.000 0.115 0.029 0.202 0.045
#> Low -1.000 0.223 0.071 0.364 0.062
#> t p Sig
#> 0.107 0.915
#> 2.560 0.011 *
#> 3.601 0.000 ***
#>
#> [CI Lower, CI Upper] shows the 95% nonparametric bootstrap confidence
#> interval(s) (based on 2000 bootstrap samples).
#>
#> Note:
#>
#> - The variable(s) sleep_duration, emotional_stability,
#> conscientiousness is/are standardized.
#> - The conditional effects are the standardized effects of
#> emotional_stability on sleep_duration.Further Information
Please refer to the help page of cond_effect() and
cond_effect_boot() for other options available, such as
defining the number of SDs from mean to define “Low” and “High”, the
percentiles to be used, or using parallel processing to speed up
bootstrapping.
Reference
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. https://doi.org/10.1037/hea0001188.
Yuan, K.-H., & Chan, W. (2011). Biases and standard errors of standardized regression coefficients. Psychometrika, 76(4), 670-690. https://doi.org/10.1007/s11336-011-9224-6