Package 'betaselectr'

Title: Betas-Select in Structural Equation Models and Linear Models
Description: It computes betas-select, coefficients after standardization in structural equation models and regression models, standardizing only selected variables. Supports models with moderation, with product terms formed after standardization. It also offers confidence intervals that account for standardization, including bootstrap confidence intervals as proposed by Cheung et al. (2022) <doi:10.1037/hea0001188>.
Authors: Shu Fai Cheung [aut, cre] , Rong Wei Sun [aut] , Florbela Chang [aut] , Wendie Yang [aut] , Sing-Hang Cheung [aut]
Maintainer: Shu Fai Cheung <[email protected]>
License: GPL (>= 3)
Version: 0.1.0
Built: 2024-11-12 05:20:12 UTC
Source: CRAN

Help Index

ANOVA Tables For 'lm_betaselect' and 'glm_betaselect' Objects

Description

Return the analysis of variance tables for the outputs of lm_betaselect() and glm_betaselect().

Usage

## S3 method for class 'lm_betaselect'
anova(object, ..., type = c("beta", "standardized", "raw", "unstandardized"))

## S3 method for class 'glm_betaselect'
anova(
  object,
  ...,
  type = c("beta", "standardized", "raw", "unstandardized"),
  dispersion = NULL,
  test = NULL
)

Arguments

object

The output of lm_betaselect() or glm_betaselect().
...

Additional outputs of lm_betaselect() or glm_betaselect().
type

String. If "unstandardized" or "raw", the output before standardization are used If "beta" or "standardized", then the output after selected variables standardized are returned. Default is "beta".
dispersion

To be passed to stats::anova.glm(). The dispersion parameter. Default ia NULL and it is extracted from the model.
test

String. The test to be conducted. Please refer to stats::anova.glm() for details.

Details

By default, it calls stats::anova() on the results with selected variables standardized. By setting type to "raw" or "unstandardized", it calls stats::anova() on the results before standardization.

Value

It returns an object of class anova, which is identical to the output of stats::anova() in structure.

Author(s)

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

See Also

lm_betaselect()

Examples

data(data_test_mod_cat)

lm_beta_x <- lm_betaselect(dv ~ iv*mod + cov1 + cat1,
                           data = data_test_mod_cat,
                           to_standardize = "iv",
                           do_boot = FALSE)
anova(lm_beta_x)
anova(lm_beta_x, type = "raw")


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)
logistic_beta_x <- glm_betaselect(p ~ iv*mod + cov1 + cat1,
                                  data = data_test_mod_cat,
                                  family = binomial,
                                  to_standardize = "iv")
anova(logistic_beta_x)
anova(logistic_beta_x, type = "raw")

Coefficients of a 'lav_betaselect'-Class Object

Description

Return the betas-select in a 'lav_betaselect'-class object.

Usage

## S3 method for class 'lav_betaselect'
coef(object, drop_na = FALSE, ...)

Arguments

object

The output of lav_betaselect().
drop_na

Logical. Whether betas-select with NA are dropped. Default is FALSE.
...

Optional arguments. Not used.

Details

It just extracts and returns the column est from the object: the betas-select, with selected variables standardized.

Value

A numeric vector: The betas-select in the object. The names of parameters follow the convention in lavaan.

Author(s)

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

See Also

lav_betaselect()

Examples

library(lavaan)
mod <-
"
med ~ iv + mod + iv:mod
dv ~ med + iv
"
fit <- sem(mod,
           data_test_medmod,
           fixed.x = TRUE)
summary(fit)
fit_beta <- lav_betaselect(fit,
                           to_standardize = c("iv", "dv"))
coef(fit_beta)

Coefficients of Beta-Select in Linear Models

Description

Return the estimates of coefficients in an lm_betaselect-class or glm_betaselect-class object.

Usage

## S3 method for class 'lm_betaselect'
coef(
  object,
  complete = FALSE,
  type = c("beta", "standardized", "raw", "unstandardized"),
  ...
)

## S3 method for class 'glm_betaselect'
coef(
  object,
  complete = FALSE,
  type = c("beta", "standardized", "raw", "unstandardized"),
  ...
)

Arguments

object

The output of lm_betaselect() or glm_betaselect(), or an lm_betaselect-class or glm_betaselect-class object.
complete

If TRUE, it returns the full vector of coefficients, including those of terms dropped in an over-determined system. See stats::coef() for further information. Default is FALSE.
type

String. If "unstandardized" or "raw", the coefficients before standardization are returned. If "beta" or "standardized", then the coefficients after selected variables standardized are returned. Default is "beta".
...

Other arguments. Ignored.

Details

By default, it extracts the regression coefficients after the selected variables have been standardized. If requested, it can also return the regression coefficients before standardization.

Value

A numeric vector: The estimate of regression coefficients.

Author(s)

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

See Also

lm_betaselect() and glm_betaselect()

Examples

data(data_test_mod_cat)

lm_beta_x <- lm_betaselect(dv ~ iv*mod + cov1 + cat1,
                           data = data_test_mod_cat,
                           to_standardize = "iv")
coef(lm_beta_x)
coef(lm_beta_x, type = "raw")


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)
logistic_beta_x <- glm_betaselect(p ~ iv*mod + cov1 + cat1,
                                  data = data_test_mod_cat,
                                  family = binomial,
                                  to_standardize = "iv")
coef(logistic_beta_x)
coef(logistic_beta_x, type = "raw")

Confidence Intervals for a 'lav_betaselect'-Class Object

Description

Return the confidence intervals of betas-select in the output of lav_betaselect().

Usage

## S3 method for class 'lav_betaselect'
confint(object, parm, level = 0.95, ...)

Arguments

object

The output of lav_betaselect().
parm

Ignored due to the complexity in the naming. The confidence intervals of all parameters are always returned.
level

The level of confidence. Ignored because the intervals should be formed when calling lav_betaselect().
...

Optional arguments. Ignored.

Details

The type of confidence intervals depends on the call to lav_betaselect(). This function does not recompute the confidence interval.

Value

A two-column matrix of the confidence intervals.

Author(s)

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

See Also

lav_betaselect()

Examples

library(lavaan)
mod <-
"
med ~ iv + mod + iv:mod
dv ~ med + iv
"
fit <- sem(mod,
           data_test_medmod,
           fixed.x = TRUE)
summary(fit)
fit_beta <- lav_betaselect(fit,
                           to_standardize = c("iv", "dv"))
confint(fit_beta)

Confidence Interval for 'lm_betaselect' or 'glm_betaselect' Objects

Description

Return the confidence interval of the regression coefficients in the output of lm_betaselect() or glm_betaselect().

Usage

## S3 method for class 'lm_betaselect'
confint(
  object,
  parm,
  level = 0.95,
  method = c("boot", "bootstrap", "ls"),
  type = c("beta", "standardized", "raw", "unstandardized"),
  warn = TRUE,
  boot_type = c("perc", "bc"),
  ...
)

## S3 method for class 'glm_betaselect'
confint(
  object,
  parm,
  level = 0.95,
  trace = FALSE,
  test = c("LRT", "Rao"),
  method = c("boot", "bootstrap", "default", "ls"),
  type = c("beta", "standardized", "raw", "unstandardized"),
  warn = TRUE,
  boot_type = c("perc", "bc"),
  transform_b = NULL,
  ...
)

Arguments

object

The output of lm_betaselect() or glm_betaselect().
parm

The terms for which the confidence intervals are returned. If missing, the confidence intervals of all terms will be returned.
level

The level of confidence, default is .95, returning the 95% confidence interval.
method

The method used to compute the confidence intervals/ If bootstrapping was requested when calling lm_betaselect() and this argument is set to "bootstrap" or "boot", the bootstrap confidence intervals are returned. If bootstrapping was not requested or if this argument is set to "ls", then the usual lm confidence intervals are returned, with a warning raised unless type is "raw" or ⁠"unstandardized".⁠ Default is "boot".
type

String. If "unstandardized" or "raw", the confidence intervals of the coefficients before standardization are returned. If "beta" or "standardized", then the confidence intervals of the coefficients after selected variables standardized are returned. Default is "beta".
warn

Logical. Whether a warning will be raised is OLS (or WLS) confidence intervals are requested for the model with some variables standardized (i.e., type is "beta" or "standardized"). Default is TRUE.
boot_type

The type of bootstrap confidence intervals. Currently, it supports "perc", percentile bootstrap confidence intervals, and "bc", bias-corrected bootstrap confidence interval.
...

Optional arguments. Ignored.
trace

Logical. Whether profiling will be traced. See stats::confint.glm() for details. ignored if method is "boot" or "bootstrap".
test

The test used for profiling. See stats::confint.glm for details. ignored if method is "boot" or "bootstrap".
transform_b

The function to be used to transform the confidence limits. For example, if set to exp, the confidence limits will be exponentiated. Users need to decide whether the transformed limits are meaningful. Default is NULL.

Details

The type of confidence intervals depends on the object. If bootstrapping was requested, by default it returns the percentile bootstrap confidence intervals. Otherwise, it returns the default confidence intervals.

Support for other type of confidence intervals may be added in the future.

Value

A p by 2 matrix of the confidence intervals, p being the number of coefficients.

Author(s)

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

See Also

lm_betaselect()

Examples

data(data_test_mod_cat)

# bootstrap should be set to 2000 or 5000 in real studies
lm_beta_x <- lm_betaselect(dv ~ iv*mod + cov1 + cat1,
                           data = data_test_mod_cat,
                           to_standardize = "iv",
                           do_boot = TRUE,
                           bootstrap = 100,
                           iseed = 1234)
confint(lm_beta_x)
confint(lm_beta_x, method = "ls")
confint(lm_beta_x, type = "raw")


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)
# bootstrap should be set to 2000 or 5000 in real studies
logistic_beta_x <- glm_betaselect(p ~ iv*mod + cov1 + cat1,
                                  data = data_test_mod_cat,
                                  family = binomial,
                                  to_standardize = "iv",
                                  do_boot = TRUE,
                                  bootstrap = 100,
                                  iseed = 1234)

confint(logistic_beta_x, method = "default")
confint(logistic_beta_x, type = "raw")

Test Dataset with Moderator and Mediator

Description

This dataset has one mediator, one moderator, one independent variable, one dependent variable, and two control variables.

Usage

data_test_medmod

Format

A data frame with 200 rows and five variables:

dv

Dependent variable, continuous

iv

Independent variable, continuous

mod

Moderator, continuous

med

Mediator, continuous

cov1

Control variable, continuous

cov2

Control variable, continuous

Examples

library(lavaan)
mod <-
"
med ~ iv + mod + iv:mod + cov1 + cov2
dv ~ med + iv + cov1 + cov2
"
fit <- sem(mod,
           data_test_medmod)
summary(fit)

Test Dataset with Moderator and Categorical Variables

Description

This dataset has one predictor, one moderator, one control variable, one dependent variable, and a categorical variable.

Usage

data_test_mod_cat

Format

A data frame with 500 rows and five variables:

dv

Dependent variable, continuous

iv

Independent variable, continuous

mod

Moderator, continuous

cov1

Control variable, continuous

cat1

String variable with these values: "gp1", "gp2", and "gp3"

Examples

lm_out <- lm(dv ~ iv * mod + cov1 + cat1, data_test_mod_cat)
summary(lm_out)

Test Dataset with a Binary Outcome Variable

Description

This dataset has one predictor, one moderator, one control variable, one binary dependent variable, and a categorical variable.

Usage

data_test_mod_cat_binary

Format

A data frame with 300 rows and five variables:

dv

Dependent variable, binary: 0, 1

iv

Independent variable, continuous

mod

Moderator, continuous

cov1

Control variable, continuous

cat1

String variable with these values: "gp1", "gp2", and "gp3"

Examples

glm_out <- glm(dv ~ iv * mod + cov1 + cat1, data_test_mod_cat_binary, family = binomial())
summary(glm_out)

Test Dataset with Moderator and Categorical Variables (Version 2)

Description

This dataset has one predictor, one moderator, one control variable, one dependent variable, and a categorical variable.

Similar to data_test_mod_cat but generated from another population.

Usage

data_test_mod_cat2

Format

A data frame with 300 rows and five variables:

dv

Dependent variable, continuous

iv

Independent variable, continuous

mod

Moderator, continuous

cov1

Control variable, continuous

cat1

String variable with these values: "gp1", "gp2", and "gp3"

Examples

lm_out <- lm(dv ~ iv * mod + cov1 + cat1, data_test_mod_cat)
summary(lm_out)

Call in an 'lm_betaselect' or 'glm_betaselect' Object

Description

The getCall-method for an lm_betaselect-class or glm_betaselectd-class objects.

Usage

## S3 method for class 'lm_betaselect'
getCall(
  x,
  what = c("lm_betaselect", "beta", "standardized", "raw", "unstandardized"),
  ...
)

## S3 method for class 'glm_betaselect'
getCall(
  x,
  what = c("glm_betaselect", "beta", "standardized", "raw", "unstandardized"),
  ...
)

Arguments

x

An lm_betaselect-class or glm_betaselect-class object from which the call is to be extracted.
what

Which call to extract. For "lm_betaselect" or "glm_betaselect" the call to lm_betaselect() or glm_betaselect() is extracted. For "beta" or "standardized", the call used to fit the model after selected variables standardized is extracted. For "raw" or "unstandardized", the call used to fit hte model before standardization is extracted.
...

Additional arguments. Ignored.

Details

This works in the same way the default getCall-method does for the outputs of stats::lm() and stats::glm().

Value

It returns the call requested.

Author(s)

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

See Also

lm_betaselect(), glm_betaselect(), and stats::getCall()

Examples

data(data_test_mod_cat)

lm_beta_x <- lm_betaselect(dv ~ iv*mod + cov1,
                           data = data_test_mod_cat,
                           to_standardize = "iv")
getCall(lm_beta_x)
getCall(lm_beta_x, what = "beta")
getCall(lm_beta_x, what = "raw")

Betas-Select in a 'lavaan'-Model

Description

Can standardize selected variables in a lavaan model without refitting the models, can handle product term correctly and skip categorical predictors in standardization.

Usage

lav_betaselect(
  object,
  to_standardize = ".all.",
  not_to_standardize = NULL,
  skip_categorical_x = TRUE,
  output = c("data.frame", "text"),
  std_se = c("none", "delta", "bootstrap"),
  std_z = TRUE,
  std_pvalue = TRUE,
  std_ci = TRUE,
  level = 0.95,
  progress = TRUE,
  boot_out = NULL,
  bootstrap = 100L,
  store_boot_est = TRUE,
  parallel = c("no", "snow", "multicore"),
  ncpus = parallel::detectCores(logical = FALSE) - 1,
  cl = NULL,
  iseed = NULL,
  find_product_terms = TRUE,
  ...,
  delta_method = c("lavaan", "numDeriv"),
  vector_form = TRUE
)

Arguments

object

The output of lavaan model fit functions, such as lavaan::sem() and lavaan::cfa().
to_standardize

A string vector, which should be the names of the variables to be standardized. Default is ".all.", indicating all variables are to be standardized (but see skip_categorical_x).
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_standardize at the same time. Default is NULL, and only to_standardize is used.
skip_categorical_x

Logical. If TRUE, the default, all categorical predictors, defined as variables with only two possible values in the data analyzed, will be skipped in standardization. This overrides the argument to_standardize. That is, a categorical predictor will not be standardized even if listed in to_standardize, unless users set this argument to FALSE.
output

The format of the output. Not used because the format of the printout is now controlled by the print-method of the output of this function. Kept for backward compatibility.
std_se

String. If set to "none", the default, standard errors will not be computed for the standardized solution. If set to "delta", delta method will be used to compute the standard errors. If set to "bootstrap", then what it does depends whether boot_out is set. If boot_out is to an output of manymome::do_boot(), its content will be used. If boot_out is NULL and bootstrap estimates are available in object (e.g., bootstrapping is requested when fitting the model in lavaan), then the stored bootstrap estimates will be sued. If not available, the bootstrapping will be conducted using lavaan::bootstrapLavaan(), using arguments bootstrap, parallel, ncpus, cl, and iseed.'
std_z

Logical. If TRUE and std_se is not set to "none", standard error will be computed using the method specified in std_se. Default is TRUE.
std_pvalue

Logical. If TRUE, std_se is not set to "none", and std_z is TRUE, p-values will be computed using the method specified in std_se. For bootstrapping, the method proposed by Asparouhov and Muthén (2021) is used. Default is TRUE.
std_ci

Logical. If TRUE and std_se is not set to "none", confidence intervals will be computed using the method specified in std_se. Default is FALSE.
level

The level of confidence of the confidence intervals. Default is .95. It will be used in the confidence intervals of both the unstandardized and standardized solution.
progress

Logical. If TRUE, progress bars will be displayed for long process.
boot_out

If std_se is "bootstrap" and this argument is set to an output of manymome::do_boot(), its output will be used in computing statistics such as standard errors and confidence intervals. This allows users to use methods other than bootstrapping when fitting the model, while they can still request bootstrapping for the standardized solution.
bootstrap

If std_se is "bootstrap" but bootstrapping is not requested when fitting the model and boot_out is not set, lavaan::bootstrapLavaan() will be called to do bootstrapping. This argument is the number of bootstrap samples to draw. Default is 100. Should be set to 5000 or even 10000 for stable results.
store_boot_est

Logical. If std_se is "bootstrap" and this argument is TRUE, the default, the bootstrap estimates of the standardized solution will be stored in the attribute "boot_est". These estimates can be used for diagnosis of the bootstrapping. If FALSE, then the bootstrap estimates will not be stored.
parallel

If std_se is "bootstrap" but bootstrapping is not requested when fitting the model and boot_out is not set, lavaan::bootstrapLavaan() will be called to do bootstrapping. This argument is to be passed to lavaan::bootstrapLavaan(). Default is "no".
ncpus

If std_se is "bootstrap" but bootstrapping is not requested when fitting the model and boot_out is not set, lavaan::bootstrapLavaan() will be called to do bootstrapping. This argument is to be passed to lavaan::bootstrapLavaan(). Default is parallel::detectCores(logical = FALSE) - 1. Ignored if parallel is "no".
cl

If std_se is "bootstrap" but bootstrapping is not requested when fitting the model and boot_out is not set, lavaan::bootstrapLavaan() will be called to do bootstrapping. This argument is to be passed to lavaan::bootstrapLavaan(). Default is NULL. Ignored if parallel is "no".
iseed

If std_se is "bootstrap" but bootstrapping is not requested when fitting the model and boot_out is not set, lavaan::bootstrapLavaan() will be called to do bootstrapping. This argument is to be passed to lavaan::bootstrapLavaan() to set the seed for the random resampling. Default is NULL. Should be set to an integer for reproducible results. Ignored if parallel is "no".
find_product_terms

String. If it is certain that a model does not have product terms, setting this to FALSE will skip the search, which is time consuming for a models with many paths and/or many variables. Default is TRUE, and the function will automatically identify product terms, if any.
...

Optional arguments to be passed to the lavaan::parameterEstimates(), which will be use to generate the output.
delta_method

The method used to compute delta-method standard errors. For internal use and should not be changed.
vector_form

The internal method used to compute standardized solution. For internal use and should not be changed.

Details

This function lets users select which variables to be standardized when computing the standardized solution. It has the following features:

  • It automatically skips predictors which has only two unique values, assuming that they are dummy variables.

  • It does not standardize product term, which is incorrect. Instead, it computes the product term with its component variables standardized first.

  • It can be used to generate bootstrap confidence intervals for the standardized solution (Falk, 2018). Bootstrap confidence interval is better than doing standardization before fitting a model because it correctly takes into account the sampling variance of the standard deviations. It is also better than delta-method confidence interval because it takes into account the usually asymmetric distribution of parameters after standardization, such as standardized loadings and correlations.

  • For comparison, it can also report delta-method standard errors and confidence intervals if requested.

Problems With Common Approaches

In most SEM programs, users have limited control on which variables to standardize when requesting the standardized solution. 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).

Moreover, the delta method is usually used in standardization, which is suboptimal for standardization unless the sample size is large (Falk, 2018). For example, the covariance with variables standardized is a correlation, and its sampling distribution is skewed unless its population value is zero. However, delta-method confidence interval for the correlation is necessarily symmetric around the point estimate.

Limitations

  • It only supports observed variable interaction terms, and only support two-way interactions.

  • It does not support multilevel models.

  • It only supports models fitted to raw data.

  • Intercepts not supported.

Value

A lav_betaselect-class object, which is a data frame storing the parameter estimates, similar in form to the output of lavaan::parameterEstimates().

Author(s)

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

References

Asparouhov, A., & Muthén, B. (2021). Bootstrap p-value computation. Retrieved from https://www.statmodel.com/download/FAQ-Bootstrap%20-%20Pvalue.pdf

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

Falk, C. F. (2018). Are robust standard errors the best approach for interval estimation with nonnormal data in structural equation modeling? Structural Equation Modeling: A Multidisciplinary Journal, 25(2) 244-266. doi:10.1080/10705511.2017.1367254

See Also

print.lav_betaselect() for its print method.

Examples

library(lavaan)
mod <-
"
med ~ iv + mod + iv:mod
dv ~ med + iv
"
fit <- sem(mod,
           data_test_medmod,
           fixed.x = TRUE)
summary(fit)
fit_beta <- lav_betaselect(fit,
                           to_standardize = c("iv", "dv"))
fit_beta
print(fit_beta, standardized_only = FALSE)

# In real studies:
# - should set bootstrap to at least 5000
# - should set parallel to "snow" or "multicore"
fit_beta_boot <- lav_betaselect(fit,
                                to_standardize = c("iv", "dv"),
                                std_se = "bootstrap",
                                std_ci = TRUE,
                                bootstrap = 100,
                                iseed = 1234)
fit_beta_boot
print(fit_beta_boot, standardized_only = FALSE)

# Print full results
print(fit_beta_boot,
      standardized_only = FALSE)

Betas-Select in a Regression Model

Description

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 to lm(). For glm_betaselect(), these arguments will be passed to glm(). For the print-method of lm_betaselect or glm_betaselect objects, 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_standardize at the same time. Default is NULL, and only to_standardize is used.
skip_response

Logical. If TRUE, will not standardize the response (outcome) variable even if it appears in to_standardize or to_standardize is 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_boot is TRUE, 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_boot is TRUE and this argument is not NULL, it will be used by set.seed() to set the seed for the random number generator. Default is NULL.
parallel

If do_boot is TRUE and this argument is TRUE, parallel processing will be used to do bootstrapping. Default is FALSE because bootstrapping for models fitted by stats::lm() or stats::glm() is rarely slow. Actually, if both parallel and progress are set to TRUE, the speed may even be slower than serial processing.
ncpus

If do_boot is TRUE and parallel is also TRUE, this argument is the number of processes to be used in parallel processing. Default is parallel::detectCores(logical = FALSE) - 1
progress

Logical. If TRUE, progress bars will be displayed for long process. Default is TRUE.
load_balancing

Logical. If parallel is TRUE, this determines whether load balancing will be used. Default is FALSE because the gain in speed is usually minor.
model_call

The model function to be called. If "lm", the default, the model will be fitted by stats::lm(). If "glm", the model will be fitted by stats::glm(). Users should call the corresponding function directly rather than setting this argument manually.
x

An lm_betaselect or glm_betaselect object.
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.

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) and x is one of the selected variables, the model used the logarithm of the standardized x in the model, instead of standardized log(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:

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.

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.

Author(s)

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

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

See Also

print.lm_betaselect() and print.glm_betaselect() for the print-methods.

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
summary(lm_beta_x)

# 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)
coef(lm_beta_x_manual)

# 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)


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)

logistic_beta_x
summary(logistic_beta_x)

# 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)
coef(logistic_beta_x_manual)

# 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)


summary(raw_output(lm_beta_x))

Predict Method for a 'glm_betaselect' Object

Description

Compute the predicted values in a model fitted by glm_betaselect().

Usage

## S3 method for class 'glm_betaselect'
predict(
  object,
  model_type = c("beta", "standardized", "raw", "unstandardized"),
  newdata,
  ...
)

Arguments

object

A glm_betaselect-class object.
model_type

The model from which the the predicted values are computed. For "beta" or "standardized", the model is the one after selected variables standardized. For "raw" or "unstandardized", the model is the one before standardization was done.
newdata

If set to a data frame, the predicted values are computed using this data frame. The data must be unstandardized. That is, the variables are of the same units as in the data frame used in glm_betaselect(). If model_type is "beta" or "standardized", it will be standardized using the setting of to_standardize when object is created in glm_betaselect().
...

Arguments to be passed to stats::predict.glm(). Please refer to the help page of stats::predict.glm().

Details

It simply passes the model before or after selected variables are standardized to the predict-method of a glm object.

IMPORTANT

Some statistics, such as prediction or confidence interval, which make use of the sampling variances and covariances of coefficient estimates may not be applicable to the models with one or more variables standardized. Therefore, they should only be used for exploratory purpose.

Value

It returns the output of stats::predict.glm().

Author(s)

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

See Also

glm_betaselect() and stats::predict.glm()

Examples

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)
logistic_beta_x <- glm_betaselect(p ~ iv*mod + cov1 + cat1,
                                  data = data_test_mod_cat,
                                  family = binomial,
                                  to_standardize = "iv")

predict(logistic_beta_x)
predict(logistic_beta_x, model_type = "raw")

Predict Method for an 'lm_betaselect' Object

Description

Compute the predicted values in a model fitted by lm_betaselect().

Usage

## S3 method for class 'lm_betaselect'
predict(
  object,
  model_type = c("beta", "standardized", "raw", "unstandardized"),
  newdata,
  ...
)

Arguments

object

An lm_betaselect-class object.
model_type

The model from which the the predicted values are computed. For "beta" or "standardized", the model is the one after selected variables standardized. For "raw" or "unstandardized", the model is the one before standardization was done.
newdata

If set to a data frame, the predicted values are computed using this data frame. The data must be unstandardized. That is, the variables are of the same units as in the data frame used in lm_betaselect(). If model_type is "beta" or "standardized", it will be standardized using the setting of to_standardize when object is created in lm_betaselect().
...

Arguments to be passed to stats::predict.lm(). Please refer to the help page of stats::predict.lm().

Details

It simply passes the model before or after selected variables are standardized to the predict-method of an lm object.

IMPORTANT

Some statistics, such as prediction or confidence interval, which make use of the sampling variances and covariances of coefficient estimates may not be applicable to the models with one or more variables standardized. Therefore, they should only be used for exploratory purpose.

Value

It returns the output of stats::predict.lm().

Author(s)

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

See Also

lm_betaselect() and stats::predict.lm()

Examples

data(data_test_mod_cat)

lm_beta_x <- lm_betaselect(dv ~ iv*mod + cov1 + cat1,
                           data = data_test_mod_cat,
                           to_standardize = "iv")
predict(lm_beta_x)
predict(lm_beta_x, model_type = "raw")

Print a 'lav_betaselect' Object

Description

Print method for a 'lav_betaselect' object, which is the output of lav_betaselect().

Usage

## S3 method for class 'lav_betaselect'
print(
  x,
  ...,
  nd = 3,
  output = c("lavaan.printer", "table"),
  standardized_only = TRUE,
  show_Bs.by = FALSE,
  by_group = TRUE,
  na_str = " ",
  sig_stars = TRUE,
  ci_sig = TRUE
)

Arguments

x

A lav_betaselect-class object, such as the output of lav_betaselect().
...

Optional arguments to be passed to print() methods.
nd

The number of digits after the decimal place. Default is 3.
output

String. How the results are printed. Default is "lavaan.printer", and the results will be printed in a format similar to the printout of the output of the summary-method of a 'lavaan'-class object. If set to "table", the results are printed in a table format similar to that of lavaan::parameterEstimates() with output set to "data.frame".
standardized_only

Logical. If TRUE, the default, only the results for the standardized solution will be printed. If FALSE, then the standardized solution is printed alongside the unstandardized solution, as in the printout of the output of summary() of a 'lavaan'-class object.
show_Bs.by

Logical. If TRUE and output is "lavaan.printer", then the column "Bs.by" is shown, indicating, for each parameter, the variables standardized. This column is not shown if output is not "lavaan.printer".
by_group

If TRUE, the default, and the model has more than one group, sections will be grouped by groups first, as in the print out of summary() in lavaan. If FALSE, then the sections will be grouped by sections first.
na_str

The string to be used for cells with NA. Default is " ", a whitespace.
sig_stars

If TRUE, the default, symbols such as asterisks (*, ⁠**⁠, ⁠***⁠) will be used to denote whether a beta-select is significant.
ci_sig

If TRUE, the default, a beta-select will be denoted as significant or not significant based on its confidence interval.

Details

The default format of the printout, "lavaan.printer", is similar to that of the summary() of a lavaan object. Users can also select whether only the standardized solution is printed or whether the standardized solution is appended to the right of the printout.

If output is set to ⁠"table"' the format is that of [lavaan::parameterEstimates()] with ⁠output = "data.frame"', which is compact but not easy to read.

Value

x is returned invisibly. Called for its side effect.

Author(s)

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

See Also

lav_betaselect(). This function is adapted from semhelpinghands::print.std_solution_boot().

Examples

library(lavaan)
mod <-
"
med ~ iv + mod + iv:mod
dv ~ med + iv
"
fit <- sem(mod,
           data_test_medmod,
           fixed.x = TRUE)
summary(fit)
fit_beta <- lav_betaselect(fit,
                           to_standardize = c("iv", "dv"))
fit_beta
print(fit_beta)
print(fit_beta, show_Bs.by = TRUE)
print(fit_beta, output = "table")

Standardize Selected Variables

Description

Standardize selected variables in a data frame or similar object.

Usage

std_data(data, to_standardize)

Arguments

data

A data frame or similar object.
to_standardize

A character vector of the column names of variables to be standardized.

Details

This is a helper functions to be used by lm_betaselect() and glm_betaselect(). It assumes that the variables selected has been checked whether they are numeric.

Value

A data frame similar to data, with selected variables standardized.

Author(s)

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

Examples

data(data_test_mod_cat)
dat <- data_test_mod_cat
dat <- std_data(dat, to_standardize = c("iv", "dv"))
colMeans(dat[, c("dv", "iv")])
apply(dat[, c("dv", "iv")], 2, sd)

Summary of an 'glm_betaselect'-Class Object

Description

The summary method for glm_betaselect-class objects.

Usage

## S3 method for class 'glm_betaselect'
summary(
  object,
  dispersion = NULL,
  correlation = FALSE,
  symbolic.cor = FALSE,
  trace = FALSE,
  test = c("LRT", "Rao"),
  se_method = c("boot", "bootstrap", "z", "glm", "default"),
  ci = TRUE,
  level = 0.95,
  boot_type = c("perc", "bc"),
  boot_pvalue_type = c("asymmetric", "norm"),
  type = c("beta", "standardized", "raw", "unstandardized"),
  print_raw = c("none", "before_ci", "after_ci"),
  transform_b = NULL,
  transform_b_name = NULL,
  ...
)

## S3 method for class 'summary.glm_betaselect'
print(
  x,
  est_digits = 3,
  symbolic.cor = x$symbolic.cor,
  signif.stars = getOption("show.signif.stars"),
  show.residuals = FALSE,
  z_digits = 3,
  pvalue_less_than = 0.001,
  ...
)

Arguments

object

The output of glm_betaselect().
dispersion

The dispersion parameter. If NULL, then it is extracted from the object. If a scalar, it will be used as the dispersion parameter. See stats::summary.glm() for details.
correlation

If TRUE, the correlation matrix of the estimates will be returned. The same argument in stats::summary.glm(). Default is FALSE.
symbolic.cor

If TRUE, correlations are printed in symbolic form as in stats::summary.glm(). Default is FALSE.
trace

Logical. Whether profiling will be traced when forming the confidence interval if se_method is "default", "z", or "glm". Ignored if ci is FALSE. See stats::confint.glm() for details.
test

The test used for se_method is "default", "z", or "glm". Ignored if ci is FALSE. See stats::confint.glm() for details.
se_method

The method used to compute the standard errors and confidence intervals (if requested). If bootstrapping was requested when calling glm_betaselect() and this argument is set to "bootstrap" or "boot", the bootstrap standard errors are returned. If bootstrapping was not requested or if this argument is set to "z", "glm", or "default", then the usual glm standard errors are returned. Default is "boot".
ci

Logical. Whether confidence intervals are computed. Default is FALSE.
level

The level of confidence, default is .95, returning the 95% confidence interval.
boot_type

The type of bootstrap confidence intervals, if requested. Currently, it supports "perc", percentile bootstrap confidence intervals, and "bc", bias-corrected bootstrap confidence interval.
boot_pvalue_type

The type of p-values if se_method is "boot" or "bootstrap". If "norm", then the z score is used to compute the p-value using a standard normal distribution. If "asymmetric", the default, then the method presented in Asparouhov and Muthén (2021) is used to compute the p-value based on the bootstrap distribution.
type

String. If "unstandardized" or "raw", the output before standardization are used If "beta" or "standardized", then the output after selected variables standardized are returned. Default is "beta".
print_raw

Control whether the estimates before selected standardization are printed when type is "beta" or "standardized". If "none", the default, then it will not be printed. If set to "before_ci" and ci is TRUE, then will be inserted to the left of the confidence intervals. If set to "after_ci"andciisTRUE⁠, then will be printed to the right of the confidence intervals. If ⁠ciisFALSE', then will be printed to the right of the standardized estimates.
transform_b

The function to be used to transform the confidence limits. For example, if set to exp, the confidence limits will be exponentiated. Users need to decide whether the transformed limits are meaningful. Default is NULL.
transform_b_name

If transform_b is a function, then this is the name of the transformed coefficients. Default is "Estimate(Transformed)"
...

Additional arguments passed to other methods.
x

The output of summary.glm_betaselect().
est_digits

The number of digits after the decimal to be displayed for the coefficient estimates, their standard errors, and confidence intervals (if present). Note that the values will be rounded to this number of digits before printing. If all digits at this position are zero for all values, the values may be displayed with fewer digits. Note that the coefficient table is printed by stats::printCoefmat(). If some numbers are vary large, the number of digits after the decimal may be smaller than est_digits due to a limit on the column width.
signif.stars

Whether "stars" (asterisks) are printed to denote the level of significance achieved for each coefficient. Default is TRUE.
show.residuals

If TRUE, a summary of the deviance residuals will be printed. Default is FALSE.
z_digits

The number of digits after the decimal to be displayed for the z or similar statistic (in the column "z value").
pvalue_less_than

If a p-value is less than this value, it will be displayed with ⁠"<(this value)".⁠ For example, if pvalue_less_than is .001, the default, p-values less than .001 will be displayed as ⁠<.001⁠. This value also determines the printout of the p-value of the F statistic. (This argument does what eps.Pvalue does in stats::printCoefmat().)

Details

By default, it returns a summary.glm_betaselect-class object for the results with selected variables standardized. By setting type to "raw" or "unstandardized", it returns the summary for the results before standardization.

The print method of summary.glm_betaselect-class objects is adapted from stdmod::print.summary.std_selected().

Value

It returns an object of class summary.glm_betaselect, which is similar to the output of stats::summary.glm(), with additional information on the standardization and bootstrapping, if requested.

The print-method of summary.glm_betaselect is called for its side effect. The object x is returned invisibly.

Author(s)

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

References

Asparouhov, A., & Muthén, B. (2021). Bootstrap p-value computation. Retrieved from https://www.statmodel.com/download/FAQ-Bootstrap%20-%20Pvalue.pdf

See Also

glm_betaselect()

Examples

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)
# bootstrap should be set to 2000 or 5000 in real studies
logistic_beta_x <- glm_betaselect(p ~ iv*mod + cov1 + cat1,
                                  data = data_test_mod_cat,
                                  family = binomial,
                                  to_standardize = "iv",
                                  do_boot = TRUE,
                                  bootstrap = 100,
                                  iseed = 1234)
summary(logistic_beta_x)

Summary of an 'lm_betaselect'-Class Object

Description

The summary method for lm_betaselect-class objects.

Usage

## S3 method for class 'lm_betaselect'
summary(
  object,
  correlation = FALSE,
  symbolic.cor = FALSE,
  se_method = c("boot", "bootstrap", "t", "lm", "ls"),
  ci = TRUE,
  level = 0.95,
  boot_type = c("perc", "bc"),
  boot_pvalue_type = c("asymmetric", "norm"),
  type = c("beta", "standardized", "raw", "unstandardized"),
  print_raw = c("none", "before_ci", "after_ci"),
  ...
)

## S3 method for class 'summary.lm_betaselect'
print(
  x,
  est_digits = 3,
  symbolic.cor = x$symbolic.cor,
  signif.stars = getOption("show.signif.stars"),
  tz_digits = 3,
  pvalue_less_than = 0.001,
  ...
)

Arguments

object

The output of lm_betaselect().
correlation

If TRUE, the correlation matrix of the estimates will be returned. The same argument in stats::summary.lm(). Default is FALSE.
symbolic.cor

If TRUE, correlations are printed in symbolic form as in stats::summary.lm(). Default is FALSE.
se_method

The method used to compute the standard errors and confidence intervals (if requested). If bootstrapping was requested when calling lm_betaselect() and this argument is set to "bootstrap" or "boot", the bootstrap standard errors are returned. If bootstrapping was not requested or if this argument is set to "t", "lm", or "ls", then the usual lm standard errors are returned. Default is "boot".
ci

Logical. Whether confidence intervals are computed. Default is TRUE.
level

The level of confidence, default is .95, returning the 95% confidence interval.
boot_type

The type of bootstrap confidence intervals, if requested. Currently, it supports "perc", percentile bootstrap confidence intervals, and "bc", bias-corrected bootstrap confidence interval.
boot_pvalue_type

The type of p-values if se_method is "boot" or "bootstrap". If "norm", then the z score is used to compute the p-value using a standard normal distribution. If "asymmetric", the default, then the method presented in Asparouhov and Muthén (2021) is used to compute the p-value based on the bootstrap distribution.
type

String. If "unstandardized" or "raw", the output before standardization are used If "beta" or "standardized", then the output after selected variables standardized are returned. Default is "beta".
print_raw

Control whether the estimates before selected standardization are printed when type is "beta" or "standardized". If "none", the default, then it will not be printed. If set to "before_ci" and ci is TRUE, then will be inserted to the left of the confidence intervals. If set to "after_ci"andciisTRUE⁠, then will be printed to the right of the confidence intervals. If ⁠ciisFALSE', then will be printed to the right of the standardized estimates.
...

Additional arguments passed to other methods.
x

The output of summary.lm_betaselect().
est_digits

The number of digits after the decimal to be displayed for the coefficient estimates, their standard errors, and confidence intervals (if present). Note that the values will be rounded to this number of digits before printing. If all digits at this position are zero for all values, the values may be displayed with fewer digits. Note that the coefficient table is printed by stats::printCoefmat(). If some numbers are vary large, the number of digits after the decimal may be smaller than est_digits due to a limit on the column width. This value also determines the number of digits for displayed R-squared.
signif.stars

Whether "stars" (asterisks) are printed to denote the level of significance achieved for each coefficient. Default is TRUE.
tz_digits

The number of digits after the decimal to be displayed for the t or similar statistic (in the column "t value" or "z value"). This value also determines the number of digits for the F statistic for the R-squared.
pvalue_less_than

If a p-value is less than this value, it will be displayed with ⁠"<(this value)".⁠ For example, if pvalue_less_than is .001, the default, p-values less than .001 will be displayed as ⁠<.001⁠. This value also determines the printout of the p-value of the F statistic. (This argument does what eps.Pvalue does in stats::printCoefmat().)

Details

By default, it returns a summary.lm_betaselect-class object for the results with selected variables standardized. By setting type to "raw" or "unstandardized", it return the summary for the results before standardization.

The print method of summary.lm_betaselect-class objects is adapted from stdmod::print.summary.std_selected().

Value

It returns an object of class summary.lm_betaselect, which is similar to the output of stats::summary.lm(), with additional information on the standardization and bootstrapping, if requested.

The print-method of summary.lm_betaselect is called for its side effect. The object x is returned invisibly.

Author(s)

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

References

Asparouhov, A., & Muthén, B. (2021). Bootstrap p-value computation. Retrieved from https://www.statmodel.com/download/FAQ-Bootstrap%20-%20Pvalue.pdf

See Also

lm_betaselect()

Examples

data(data_test_mod_cat)

# bootstrap should be set to 2000 or 5000 in real studies
lm_beta_x <- lm_betaselect(dv ~ iv*mod + cov1 + cat1,
                           data = data_test_mod_cat,
                           to_standardize = "iv",
                           do_boot = TRUE,
                           bootstrap = 100,
                           iseed = 1234)

summary(lm_beta_x)
summary(lm_beta_x, ci = TRUE)
summary(lm_beta_x, boot_pvalue_type = "norm")
summary(lm_beta_x, type = "raw")

The 'vcov' Method for 'lm_betaselect' and glm_betaselect Objects

Description

Compute the variance-covariance matrix of estimates in the output of lm_betaselect() or glm_betaselect().

Usage

## S3 method for class 'lm_betaselect'
vcov(
  object,
  method = c("boot", "bootstrap", "ls", "default"),
  type = c("beta", "standardized", "raw", "unstandardized"),
  warn = TRUE,
  ...
)

## S3 method for class 'glm_betaselect'
vcov(
  object,
  method = c("boot", "bootstrap", "ls", "default"),
  type = c("beta", "standardized", "raw", "unstandardized"),
  warn = TRUE,
  ...
)

Arguments

object

The output of lm_betaselect() or an lm_betaselect-class object, or the output of glm_betaselect() or a glm_betaselect-class object.
method

The method used to compute the variance-covariance matrix. If bootstrapping was requested when calling lm_betaselect() or glm_betaselect() and this argument is set to "bootstrap" or "boot", the bootstrap variance-covariance matrix is returned. If bootstrapping was not requested or if this argument is set to "ls" or "default", then the usual lm or glm variance-covariance matrix is returned, with a warning raised unless type is "raw" or ⁠"unstandardized".⁠ Default is "boot".
type

String. If "unstandardized" or "raw", the variance-covariance matrix of the coefficients before standardization are returned. If "beta" or "standardized", then the variance-covariance matrix of the coefficients after selected variables standardized are returned. Default is "beta".
warn

Logical. WHether a warning will be raised is OLS (or WLS) variance-covariance matrix is requested for the model with some variables standardized (i.e., type is "beta" or "standardized"). Default is TRUE.
...

Other arguments to be passed to stats::vcov().

Details

The type of variance-covariance matrix depends on the object. If bootstrapping was requested, by default it returns the bootstrap variance-covariance matrix. Otherwise, it returns the default variance-covariance matrix and raises a warning.

Support for other type of variance-covariance matrix will be added.

Value

A matrix of the variances and covariances of the parameter estimates.

Author(s)

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

See Also

lm_betaselect() and glm_betaselect()

Examples

data(data_test_mod_cat)

# bootstrap should be set to 2000 or 5000 in real studies
lm_beta_x <- lm_betaselect(dv ~ iv*mod + cov1 + cat1,
                           data = data_test_mod_cat,
                           to_standardize = "iv",
                           do_boot = TRUE,
                           bootstrap = 100,
                           iseed = 1234)
vcov(lm_beta_x)
# A warning is expected for the following call
vcov(lm_beta_x, method = "ls")
vcov(lm_beta_x, type = "raw")



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)
# bootstrap should be set to 2000 or 5000 in real studies
logistic_beta_x <- glm_betaselect(p ~ iv*mod + cov1 + cat1,
                                  data = data_test_mod_cat,
                                  family = binomial,
                                  to_standardize = "iv",
                                  do_boot = TRUE,
                                  bootstrap = 100,
                                  iseed = 1234)
vcov(logistic_beta_x)
# A warning is expected for the following call
vcov(logistic_beta_x, method = "default")
vcov(logistic_beta_x, type = "raw")