Can fit a linear regression models with selected variables standardized; handle product terms correctly and skip categorical predictors in standardization.
Usage
lm_betaselect(
...,
to_standardize = NULL,
not_to_standardize = NULL,
skip_response = FALSE,
do_boot = TRUE,
bootstrap = 100L,
iseed = NULL,
parallel = FALSE,
ncpus = parallel::detectCores(logical = FALSE) - 1,
progress = TRUE,
load_balancing = FALSE,
model_call = c("lm", "glm")
)
glm_betaselect(
...,
to_standardize = NULL,
not_to_standardize = NULL,
skip_response = FALSE,
do_boot = TRUE,
bootstrap = 100L,
iseed = NULL,
parallel = FALSE,
ncpus = parallel::detectCores(logical = FALSE) - 1,
progress = TRUE,
load_balancing = FALSE
)
# S3 method for class 'lm_betaselect'
print(
x,
digits = max(3L, getOption("digits") - 3L),
type = c("beta", "standardized", "raw", "unstandardized"),
...
)
# S3 method for class 'glm_betaselect'
print(
x,
digits = max(3L, getOption("digits") - 3L),
type = c("beta", "standardized", "raw", "unstandardized"),
...
)
raw_output(x)Arguments
- ...
For
lm_betaselect(). these arguments will be passed directly tolm(). Forglm_betaselect(), these arguments will be passed toglm(). For theprint-method oflm_betaselectorglm_betaselectobjects, this will be passed to other methods.- to_standardize
A string vector, which should be the names of the variables to be standardized. Default is
NULL, indicating all variables are to be standardized.- not_to_standardize
A string vector, which should be the names of the variables that should not be standardized. This argument is useful when most variables, except for a few, are to be standardized. This argument cannot be ued with
to_standardizeat the same time. Default isNULL, and onlyto_standardizeis used.- skip_response
Logical. If
TRUE, will not standardize the response (outcome) variable even if it appears into_standardizeorto_standardizeis not specified. Used for models such as logistic regression models in which there are some restrictions on the response variables (e.g., only 0 or 1 for logistic regression).- do_boot
Whether bootstrapping will be conducted. Default is
TRUE.- bootstrap
If
do_bootisTRUE, this argument is the number of bootstrap samples to draw. Default is 100. Should be set to 5000 or even 10000 for stable results.- iseed
If
do_bootisTRUEand this argument is notNULL, it will be used byset.seed()to set the seed for the random number generator. Default isNULL.- parallel
If
do_bootisTRUEand this argument isTRUE, parallel processing will be used to do bootstrapping. Default isFALSEbecause bootstrapping for models fitted bystats::lm()orstats::glm()is rarely slow. Actually, if bothparallelandprogressare set toTRUE, the speed may even be slower than serial processing.- ncpus
If
do_bootisTRUEandparallelis alsoTRUE, this argument is the number of processes to be used in parallel processing. Default isparallel::detectCores(logical = FALSE) - 1- progress
Logical. If
TRUE, progress bars will be displayed for long process. Default isTRUE.- load_balancing
Logical. If
parallelisTRUE, this determines whether load balancing will be used. Default isFALSEbecause the gain in speed is usually minor.- model_call
The model function to be called. If
"lm", the default, the model will be fitted bystats::lm(). If"glm", the model will be fitted bystats::glm(). Users should call the corresponding function directly rather than setting this argument manually.- x
An
lm_betaselectorglm_betaselectobject.- digits
The number of significant digits to be printed for the coefficients.
- type
The coefficients to be printed. For
"beta"or"standardized", the coefficients after selected variables standardized will be printed. For"raw"or"unstandardized", the coefficients before standardization was done will be printed.
Value
The function lm_betaselect()
returns an object of the class lm_betaselect,
The function glm_betaselect()
returns an object of the class
glm_betaselect. They are similar
in structure to the output of
stats::lm() and stats::glm(),
with additional information stored.
The function raw_output() returns
an object of the class lm or
glm, which are
the results of fitting the model
to the data by stats::lm()
or stats::glm() without
standardization.
Details
The functions lm_betaselect()
and glm_betaselect()
let users
select which variables to be
standardized when computing the
standardized solution. They have the
following features:
They automatically skip categorical predictors (i.e., factor or string variables).
They do not standardize a product term, which is incorrect. Instead, they compute the product term with its component variables standardized, if requested.
They standardize the selected variables before fitting a model. Therefore, If a model has the term
log(x)andxis one of the selected variables, the model used the logarithm of the standardizedxin the model, instead of standardizedlog(x)which is difficult to interpret.They can be used to generate nonparametric bootstrap confidence intervals for the standardized solution. Bootstrap confidence interval is better than the default confidence interval ignoring the standardization because it takes into account the sampling variance of the standard deviations. Preliminary support for bootstrap confidence has been found for forming confidence intervals for coefficients involving standardized variables in linear regression (Jones & Waller, 2013).
Problems With Common Approaches
In some regression programs, users have limited control on which variables to standardize when requesting the so-called "betas". The solution may be uninterpretable or misleading in these conditions:
Dummy variables are standardized and their coefficients cannot be interpreted as the difference between two groups on the outcome variables.
Product terms (interaction terms) are standardized and they cannot be interpreted as the changes in the effects of focal variables when the moderators change (Cheung, Cheung, Lau, Hui, & Vong, 2022).
Variables with meaningful units can be more difficult to interpret when they are standardized (e.g., age).
How The Function Work
They standardize the original variables before they are used in the model. Therefore, strictly speaking, they do not standardize the predictors in model, but standardize the input variable (Gelman et al., 2021).
The requested model is then fitted to
the dataset with selected variables
standardized. For the ease of
follow-up analysis, both the results
with selected variables standardized
and the results without
standardization are stored. If
required, the results without
standardization can be retrieved
by raw_output().
Methods
The output of lm_betaselect() is
an lm_betaselect-class object,
and the output of glm_betaselect()
is a glm_betaselect-class object.
They have the following methods:
A
coef-method for extracting the coefficients of the model. (Seecoef.lm_betaselect()andcoef.glm_betaselect()for details.)A
vcov-method for extracting the variance-covariance matrix of the estimates of the coefficients. If bootstrapping is requested, it can return the matrix based on the bootstrapping estimates. (Seevcov.lm_betaselect()andvcov.glm_betaselect()for details.)A
confint-method for forming the confidence intervals of the estimates of the coefficients. If bootstrapping is requested, it can return the bootstrap confidence intervals. (Seeconfint.lm_betaselect()andconfint.glm_betaselect()for details.)A
summary-method for printing the summary of the results, with additional information such as the number of bootstrap samples and which variables have been standardized. (Seesummary.lm_betaselect()andsummary.glm_betaselect()for details.)An
anova-method for printing the ANOVA table. Can also be used to compare two or more outputs oflm_betaselect()orglm_betaselect()(Seeanova.glm_betaselect()andanova.glm_betaselect()for details.)A
predict-method for computing predicted values. It can be used to compute the predicted values given a set of new unstandardized data. The data will be standardized before computing the predicted values in the models with standardization. (Seepredict.lm_betaselect()andpredict.glm_betaselect()for details.)The default
update-method for updating a call also works for anlm_betaselectobject or aglm_betaselect()object. It can update the model in the same way it updates a model fitted bystats::lm()orstats::glm(), and also update the arguments oflm_betaselect()orglm_betaselect()such as the variables to be standardized. (Seestats::update()for details.)
Most other methods for the output
of stats::lm() and stats::glm()
should also work
on an lm_betaselect-class object
or a glm_betaselect-class object,
respectively.
Some of them will give the same
results regardless of the variables
standardized. Examples are
rstandard() and cooks.distance().
For some others, they should be used
with cautions if they make use of
the variance-covariance matrix
of the estimates.
To use the methods for lm objects
or glm objects
on the results without standardization,
simply use raw_output(). For example,
to get the fitted values without
standardization, call
fitted(raw_output(x)), where x
is the output of lm_betaselect()
or glm_betaselect().
The function raw_output() simply extracts
the regression output by stats::lm()
or stats::glm()
on the variables without standardization.
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
Craig, C. C. (1936). On the frequency function of xy. The Annals of Mathematical Statistics, 7(1), 1–15. doi:10.1214/aoms/1177732541
Gelman, A., Hill, J., & Vehtari, A. (2021). Regression and other stories. Cambridge University Press. doi:10.1017/9781139161879
Jones, J. A., & Waller, N. G. (2013). Computing confidence intervals for standardized regression coefficients. Psychological Methods, 18(4), 435–453. doi:10.1037/a0033269
Author
Shu Fai Cheung https://orcid.org/0000-0002-9871-9448
Examples
data(data_test_mod_cat)
# Standardize only iv
lm_beta_x <- lm_betaselect(dv ~ iv*mod + cov1 + cat1,
data = data_test_mod_cat,
to_standardize = "iv")
lm_beta_x
#>
#> Call to lm_betaselect():
#> betaselectr::lm_betaselect(formula = dv ~ iv * mod + cov1 + cat1,
#> data = data_test_mod_cat, to_standardize = "iv")
#>
#> Variable(s) standardized: iv
#>
#> Model *after* standardization:
#>
#> Call:
#> stats::lm(formula = dv ~ iv * mod + cov1 + cat1, data = betaselectr::std_data(data = data_test_mod_cat,
#> to_standardize = "iv"))
#>
#> Coefficients:
#> (Intercept) iv mod cov1 cat1gp2 cat1gp3
#> 790.550 -94.302 57.578 10.024 -112.588 -53.106
#> iv:mod
#> 8.661
#>
summary(lm_beta_x)
#> Call to lm_betaselect():
#> betaselectr::lm_betaselect(formula = dv ~ iv * mod + cov1 + cat1,
#> data = data_test_mod_cat, to_standardize = "iv")
#>
#> Variable(s) standardized: iv
#>
#> Call:
#> stats::lm(formula = dv ~ iv * mod + cov1 + cat1, data = betaselectr::std_data(data = data_test_mod_cat,
#> to_standardize = "iv"))
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -1987.03 -463.99 0.25 455.14 2152.48
#>
#> Coefficients:
#> Estimate CI.Lower CI.Upper Std. Error z value Pr(Boot)
#> (Intercept) 790.550 -616.077 2200.706 628.105 1.259 0.16
#> iv -94.302 -1608.007 1514.014 721.336 -0.131 0.82
#> mod 57.578 43.098 70.722 6.133 9.388 <0.001 ***
#> cov1 10.024 -10.567 33.103 10.126 0.990 0.34
#> cat1gp2 -112.588 -276.419 57.141 76.889 -1.464 0.22
#> cat1gp3 -53.106 -217.405 90.518 77.879 -0.682 0.54
#> iv:mod 8.661 -7.435 24.082 7.200 1.203 0.26
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 681.1 on 493 degrees of freedom
#>
#> R-squared : 0.602
#> Adjusted R-squared : 0.597
#> ANOVA test of R-squared : F(6, 493) = 124.344, p < 0.001
#>
#> Note:
#> - Results *after* standardization are reported.
#> - Nonparametric bootstrapping conducted.
#> - The number of bootstrap samples is 100.
#> - Standard errors are bootstrap standard errors.
#> - Z values are computed by 'Estimate / Std. Error'.
#> - The bootstrap p-values are asymmetric p-values by Asparouhov and
#> Muthén (2021).
#> - Percentile bootstrap 95.0% confidence interval reported.
# Manually standardize iv and call lm()
data_test_mod_cat$iv_z <- scale(data_test_mod_cat[, "iv"])[, 1]
lm_beta_x_manual <- lm(dv ~ iv_z*mod + cov1 + cat1,
data = data_test_mod_cat)
coef(lm_beta_x)
#> (Intercept) iv mod cov1 cat1gp2 cat1gp3
#> 790.549933 -94.301982 57.578053 10.024281 -112.587966 -53.106405
#> iv:mod
#> 8.661027
coef(lm_beta_x_manual)
#> (Intercept) iv_z mod cov1 cat1gp2 cat1gp3
#> 790.549933 -94.301982 57.578053 10.024281 -112.587966 -53.106405
#> iv_z:mod
#> 8.661027
# Standardize all numeric variables
lm_beta_all <- lm_betaselect(dv ~ iv*mod + cov1 + cat1,
data = data_test_mod_cat)
# Note that cat1 is not standardized
summary(lm_beta_all)
#> Call to lm_betaselect():
#> betaselectr::lm_betaselect(formula = dv ~ iv * mod + cov1 + cat1,
#> data = data_test_mod_cat)
#>
#> Variable(s) standardized: dv, iv, mod, cov1, iv_z
#>
#> Call:
#> stats::lm(formula = dv ~ iv * mod + cov1 + cat1, data = betaselectr::std_data(data = data_test_mod_cat,
#> to_standardize = c("dv", "iv", "mod", "cov1", "iv_z")))
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -1.85143 -0.43232 0.00024 0.42408 2.00559
#>
#> Coefficients:
#> Estimate CI.Lower CI.Upper Std. Error z value Pr(Boot)
#> (Intercept) 0.051 -0.047 0.146 0.042 1.217 0.22
#> iv 0.720 0.671 0.758 0.022 32.675 <0.001 ***
#> mod 0.269 0.228 0.325 0.025 10.584 <0.001 ***
#> cov1 0.028 -0.016 0.082 0.025 1.105 0.28
#> cat1gp2 -0.105 -0.259 0.056 0.075 -1.393 0.12
#> cat1gp3 -0.049 -0.191 0.088 0.065 -0.759 0.38
#> iv:mod 0.040 -0.022 0.099 0.030 1.366 0.16
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 0.6346 on 493 degrees of freedom
#>
#> R-squared : 0.602
#> Adjusted R-squared : 0.597
#> ANOVA test of R-squared : F(6, 493) = 124.344, p < 0.001
#>
#> Note:
#> - Results *after* standardization are reported.
#> - Nonparametric bootstrapping conducted.
#> - The number of bootstrap samples is 100.
#> - Standard errors are bootstrap standard errors.
#> - Z values are computed by 'Estimate / Std. Error'.
#> - The bootstrap p-values are asymmetric p-values by Asparouhov and
#> Muthén (2021).
#> - Percentile bootstrap 95.0% confidence interval reported.
data(data_test_mod_cat)
data_test_mod_cat$p <- scale(data_test_mod_cat$dv)[, 1]
data_test_mod_cat$p <- ifelse(data_test_mod_cat$p > 0,
yes = 1,
no = 0)
# Standardize only iv
logistic_beta_x <- glm_betaselect(p ~ iv*mod + cov1 + cat1,
family = binomial,
data = data_test_mod_cat,
to_standardize = "iv")
summary(logistic_beta_x)
#> Call to glm_betaselect():
#> betaselectr::lm_betaselect(formula = p ~ iv * mod + cov1 + cat1,
#> family = binomial, data = data_test_mod_cat, to_standardize = "iv",
#> model_call = "glm")
#>
#> Variable(s) standardized: iv
#>
#> Call:
#> stats::glm(formula = p ~ iv * mod + cov1 + cat1, family = binomial,
#> data = betaselectr::std_data(data = data_test_mod_cat, to_standardize = "iv"))
#>
#> Coefficients:
#> Estimate CI.Lower CI.Upper Std. Error z value Pr(Boot)
#> (Intercept) -16.205 -25.558 -10.935 3.337 -4.856 <0.001 ***
#> iv -1.148 -9.603 7.538 4.062 -0.283 0.80
#> mod 0.165 0.115 0.264 0.034 4.918 <0.001 ***
#> cov1 -0.004 -0.079 0.105 0.048 -0.091 0.92
#> cat1gp2 -0.211 -0.870 0.502 0.344 -0.611 0.48
#> cat1gp3 -0.189 -0.829 0.420 0.307 -0.616 0.60
#> iv:mod 0.031 -0.056 0.116 0.041 0.757 0.42
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> (Dispersion parameter for binomial family taken to be 1)
#>
#> Null deviance: 692.86 on 499 degrees of freedom
#> Residual deviance: 440.10 on 493 degrees of freedom
#> AIC: 454.1
#>
#> Number of Fisher Scoring iterations: 5
#>
#> Transformed Parameter Estimates:
#> Exp(B) CI.Lower CI.Upper
#> (Intercept) 0.000 0.000 0.000
#> iv 0.317 0.000 1946.771
#> mod 1.180 1.122 1.302
#> cov1 0.996 0.924 1.111
#> cat1gp2 0.810 0.419 1.653
#> cat1gp3 0.828 0.437 1.521
#> iv:mod 1.031 0.945 1.123
#>
#> Note:
#> - Results *after* standardization are reported.
#> - Nonparametric bootstrapping conducted.
#> - The number of bootstrap samples is 100.
#> - Standard errors are bootstrap standard errors.
#> - Z values are computed by 'Estimate / Std. Error'.
#> - The bootstrap p-values are asymmetric p-values by Asparouhov and
#> Muthén (2021).
#> - Percentile bootstrap 95.0% confidence interval reported.
logistic_beta_x
#>
#> Call to lm_betaselect():
#> betaselectr::lm_betaselect(formula = p ~ iv * mod + cov1 + cat1,
#> family = binomial, data = data_test_mod_cat, to_standardize = "iv",
#> model_call = "glm")
#>
#> Variable(s) standardized: iv
#>
#> Model *after* standardization:
#>
#> Call: stats::glm(formula = p ~ iv * mod + cov1 + cat1, family = binomial,
#> data = betaselectr::std_data(data = data_test_mod_cat, to_standardize = "iv"))
#>
#> Coefficients:
#> (Intercept) iv mod cov1 cat1gp2 cat1gp3
#> -16.205362 -1.148483 0.165202 -0.004369 -0.210518 -0.189053
#> iv:mod
#> 0.030878
#>
#> Degrees of Freedom: 499 Total (i.e. Null); 493 Residual
#> Null Deviance: 692.9
#> Residual Deviance: 440.1 AIC: 454.1
summary(logistic_beta_x)
#> Call to glm_betaselect():
#> betaselectr::lm_betaselect(formula = p ~ iv * mod + cov1 + cat1,
#> family = binomial, data = data_test_mod_cat, to_standardize = "iv",
#> model_call = "glm")
#>
#> Variable(s) standardized: iv
#>
#> Call:
#> stats::glm(formula = p ~ iv * mod + cov1 + cat1, family = binomial,
#> data = betaselectr::std_data(data = data_test_mod_cat, to_standardize = "iv"))
#>
#> Coefficients:
#> Estimate CI.Lower CI.Upper Std. Error z value Pr(Boot)
#> (Intercept) -16.205 -25.558 -10.935 3.337 -4.856 <0.001 ***
#> iv -1.148 -9.603 7.538 4.062 -0.283 0.80
#> mod 0.165 0.115 0.264 0.034 4.918 <0.001 ***
#> cov1 -0.004 -0.079 0.105 0.048 -0.091 0.92
#> cat1gp2 -0.211 -0.870 0.502 0.344 -0.611 0.48
#> cat1gp3 -0.189 -0.829 0.420 0.307 -0.616 0.60
#> iv:mod 0.031 -0.056 0.116 0.041 0.757 0.42
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> (Dispersion parameter for binomial family taken to be 1)
#>
#> Null deviance: 692.86 on 499 degrees of freedom
#> Residual deviance: 440.10 on 493 degrees of freedom
#> AIC: 454.1
#>
#> Number of Fisher Scoring iterations: 5
#>
#> Transformed Parameter Estimates:
#> Exp(B) CI.Lower CI.Upper
#> (Intercept) 0.000 0.000 0.000
#> iv 0.317 0.000 1946.771
#> mod 1.180 1.122 1.302
#> cov1 0.996 0.924 1.111
#> cat1gp2 0.810 0.419 1.653
#> cat1gp3 0.828 0.437 1.521
#> iv:mod 1.031 0.945 1.123
#>
#> Note:
#> - Results *after* standardization are reported.
#> - Nonparametric bootstrapping conducted.
#> - The number of bootstrap samples is 100.
#> - Standard errors are bootstrap standard errors.
#> - Z values are computed by 'Estimate / Std. Error'.
#> - The bootstrap p-values are asymmetric p-values by Asparouhov and
#> Muthén (2021).
#> - Percentile bootstrap 95.0% confidence interval reported.
# Manually standardize iv and call glm()
data_test_mod_cat$iv_z <- scale(data_test_mod_cat[, "iv"])[, 1]
logistic_beta_x_manual <- glm(p ~ iv_z*mod + cov1 + cat1,
family = binomial,
data = data_test_mod_cat)
coef(logistic_beta_x)
#> (Intercept) iv mod cov1 cat1gp2
#> -16.205361985 -1.148482578 0.165201690 -0.004369295 -0.210517691
#> cat1gp3 iv:mod
#> -0.189052500 0.030878129
coef(logistic_beta_x_manual)
#> (Intercept) iv_z mod cov1 cat1gp2
#> -16.205361985 -1.148482578 0.165201690 -0.004369295 -0.210517691
#> cat1gp3 iv_z:mod
#> -0.189052500 0.030878129
# Standardize all numeric predictors
logistic_beta_allx <- glm_betaselect(p ~ iv*mod + cov1 + cat1,
family = binomial,
data = data_test_mod_cat,
to_standardize = c("iv", "mod", "cov1"))
# Note that cat1 is not standardized
summary(logistic_beta_allx)
#> Call to glm_betaselect():
#> betaselectr::lm_betaselect(formula = p ~ iv * mod + cov1 + cat1,
#> family = binomial, data = data_test_mod_cat, to_standardize = c("iv",
#> "mod", "cov1"), model_call = "glm")
#>
#> Variable(s) standardized: iv, mod, cov1
#>
#> Call:
#> stats::glm(formula = p ~ iv * mod + cov1 + cat1, family = binomial,
#> data = betaselectr::std_data(data = data_test_mod_cat, to_standardize = c("iv",
#> "mod", "cov1")))
#>
#> Coefficients:
#> Estimate CI.Lower CI.Upper Std. Error z value Pr(Boot)
#> (Intercept) 0.280 -0.290 0.862 0.256 1.093 0.18
#> iv 1.941 1.626 2.430 0.202 9.603 <0.001 ***
#> mod 0.827 0.499 1.223 0.158 5.229 <0.001 ***
#> cov1 -0.013 -0.232 0.229 0.116 -0.113 0.98
#> cat1gp2 -0.211 -0.963 0.454 0.311 -0.677 0.32
#> cat1gp3 -0.189 -0.866 0.496 0.329 -0.575 0.40
#> iv:mod 0.155 -0.224 0.701 0.210 0.736 0.32
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> (Dispersion parameter for binomial family taken to be 1)
#>
#> Null deviance: 692.86 on 499 degrees of freedom
#> Residual deviance: 440.10 on 493 degrees of freedom
#> AIC: 454.1
#>
#> Number of Fisher Scoring iterations: 5
#>
#> Transformed Parameter Estimates:
#> Exp(B) CI.Lower CI.Upper
#> (Intercept) 1.323 0.748 2.373
#> iv 6.965 5.083 11.364
#> mod 2.287 1.648 3.399
#> cov1 0.987 0.793 1.257
#> cat1gp2 0.810 0.382 1.576
#> cat1gp3 0.828 0.421 1.643
#> iv:mod 1.167 0.800 2.019
#>
#> Note:
#> - Results *after* standardization are reported.
#> - Nonparametric bootstrapping conducted.
#> - The number of bootstrap samples is 100.
#> - Standard errors are bootstrap standard errors.
#> - Z values are computed by 'Estimate / Std. Error'.
#> - The bootstrap p-values are asymmetric p-values by Asparouhov and
#> Muthén (2021).
#> - Percentile bootstrap 95.0% confidence interval reported.
summary(raw_output(lm_beta_x))
#>
#> Call:
#> stats::lm(formula = dv ~ iv * mod + cov1 + cat1, data = data_test_mod_cat)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -1987.03 -463.99 0.25 455.14 2152.48
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 1488.568 4540.789 0.328 0.743
#> iv -46.545 300.046 -0.155 0.877
#> mod -6.530 45.372 -0.144 0.886
#> cov1 10.024 10.173 0.985 0.325
#> cat1gp2 -112.588 76.046 -1.481 0.139
#> cat1gp3 -53.106 75.126 -0.707 0.480
#> iv:mod 4.275 2.993 1.428 0.154
#>
#> Residual standard error: 681.1 on 493 degrees of freedom
#> Multiple R-squared: 0.6021, Adjusted R-squared: 0.5973
#> F-statistic: 124.3 on 6 and 493 DF, p-value: < 2.2e-16
#>