Package 'betaDelta' reference manual

Title:	Confidence Intervals for Standardized Regression Coefficients
Description:	Generates confidence intervals for standardized regression coefficients using delta method standard errors for models fitted by lm() as described in Yuan and Chan (2011) <doi:10.1007/s11336-011-9224-6> and Jones and Waller (2015) <doi:10.1007/s11336-013-9380-y>. The package can also be used to generate confidence intervals for differences of standardized regression coefficients and as a general approach to performing the delta method. A description of the package and code examples are presented in Pesigan, Sun, and Cheung (2023) <doi:10.1080/00273171.2023.2201277>.
Authors:	Ivan Jacob Agaloos Pesigan [aut, cre, cph]
Maintainer:	Ivan Jacob Agaloos Pesigan <[email protected]>
License:	MIT + file LICENSE
Version:	1.0.5.9000
Built:	2024-10-22 17:20:18 UTC
Source:	https://github.com/jeksterslab/betaDelta

Estimate Standardized Regression Coefficients and the Corresponding Sampling Covariance Matrix

Description

Estimate Standardized Regression Coefficients and the Corresponding Sampling Covariance Matrix

Usage

BetaDelta(object, type = "mvn", alpha = c(0.05, 0.01, 0.001))
BetaDelta(object, type = "mvn", alpha = c(0.05, 0.01, 0.001))

Arguments

`object`	Object of class `lm`.
`type`	Character string. If `type = "mvn"`, use the multivariate normal-theory approach. If `type = "adf"`, use the asymptotic distribution-free approach.
`alpha`	Numeric vector. Significance level $\alpha$ .

Value

Returns an object of class betadelta which is a list with the following elements:

call: Function call.
args: Function arguments.
lm_process: Processed lm object.
gamma: Asymptotic covariance matrix of the sample covariance matrix.
acov: Asymptotic covariance matrix of the standardized slopes.
vcov: Sampling covariance matrix of the standardized slopes.
est: Vector of standardized slopes.

Author(s)

Ivan Jacob Agaloos Pesigan

References

Jones, J. A., & Waller, N. G. (2015). The normal-theory and asymptotic distribution-free (ADF) covariance matrix of standardized regression coefficients: Theoretical extensions and finite sample behavior. Psychometrika, 80(2), 365–378. doi:10.1007/s11336-013-9380-y

Pesigan, I. J. A., Sun, R. W., & Cheung, S. F. (2023). betaDelta and betaSandwich: Confidence intervals for standardized regression coefficients in R. Multivariate Behavioral Research. doi:10.1080/00273171.2023.2201277

Yuan, K.-H., & Chan, W. (2011). Biases and standard errors of standardized regression coefficients. Psychometrika, 76(4), 670–690. doi:10.1007/s11336-011-9224-6

Examples

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = nas1982)
std <- BetaDelta(object)
# Methods -------------------------------------------------------
print(std)
summary(std)
coef(std)
vcov(std)
confint(std, level = 0.95)

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = nas1982)
std <- BetaDelta(object)
# Methods -------------------------------------------------------
print(std)
summary(std)
coef(std)
vcov(std)
confint(std, level = 0.95)

Standardized Regression Slopes

Description

Standardized Regression Slopes

Usage

## S3 method for class 'betadelta'
coef(object, ...)
## S3 method for class 'betadelta'
coef(object, ...)

Arguments

`object`	Object of class `betadelta`.
`...`	additional arguments.

Value

Returns a vector of standardized regression slopes.

Author(s)

Ivan Jacob Agaloos Pesigan

Examples

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = nas1982)
std <- BetaDelta(object)
coef(std)

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = nas1982)
std <- BetaDelta(object)
coef(std)

Estimates

Description

Estimates

Usage

## S3 method for class 'deltamethod'
coef(object, ...)
## S3 method for class 'deltamethod'
coef(object, ...)

Arguments

`object`	Object of class `deltamethod`.
`...`	additional arguments.

Value

Returns a vector of estimates.

Author(s)

Ivan Jacob Agaloos Pesigan

Examples

object <- glm(
  formula = vs ~ wt + disp,
  family = "binomial",
  data = mtcars
)
def <- list("exp(wt)", "exp(disp)")
out <- DeltaGeneric(
  object = object,
  def = def,
  alpha = 0.05
)
coef(out)

object <- glm(
  formula = vs ~ wt + disp,
  family = "binomial",
  data = mtcars
)
def <- list("exp(wt)", "exp(disp)")
out <- DeltaGeneric(
  object = object,
  def = def,
  alpha = 0.05
)
coef(out)

Differences of Standardized Regression Slopes

Description

Differences of Standardized Regression Slopes

Usage

## S3 method for class 'diffbetadelta'
coef(object, ...)
## S3 method for class 'diffbetadelta'
coef(object, ...)

Arguments

`object`	Object of class `diffbetadelta`.
`...`	additional arguments.

Value

Returns a vector of differences of standardized regression slopes.

Author(s)

Ivan Jacob Agaloos Pesigan

Examples

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = nas1982)
std <- BetaDelta(object)
diff <- DiffBetaDelta(std)
coef(diff)

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = nas1982)
std <- BetaDelta(object)
diff <- DiffBetaDelta(std)
coef(diff)

Confidence Intervals for Standardized Regression Slopes

Description

Confidence Intervals for Standardized Regression Slopes

Usage

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

Arguments

`object`	Object of class `betadelta`.
`parm`	a specification of which parameters are to be given confidence intervals, either a vector of numbers or a vector of names. If missing, all parameters are considered.
`level`	the confidence level required.
`...`	additional arguments.

Value

Returns a matrix of confidence intervals.

Author(s)

Ivan Jacob Agaloos Pesigan

Examples

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = nas1982)
std <- BetaDelta(object)
confint(std, level = 0.95)

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = nas1982)
std <- BetaDelta(object)
confint(std, level = 0.95)

Confidence Intervals

Description

Confidence Intervals

Usage

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

Arguments

`object`	Object of class `deltamethod`.
`parm`	a specification of which parameters are to be given confidence intervals, either a vector of numbers or a vector of names. If missing, all parameters are considered.
`level`	the confidence level required.
`...`	additional arguments.

Value

Returns a matrix of confidence intervals.

Author(s)

Ivan Jacob Agaloos Pesigan

Examples

object <- glm(
  formula = vs ~ wt + disp,
  family = "binomial",
  data = mtcars
)
def <- list("exp(wt)", "exp(disp)")
out <- DeltaGeneric(
  object = object,
  def = def,
  alpha = 0.05
)
confint(out, level = 0.95)

object <- glm(
  formula = vs ~ wt + disp,
  family = "binomial",
  data = mtcars
)
def <- list("exp(wt)", "exp(disp)")
out <- DeltaGeneric(
  object = object,
  def = def,
  alpha = 0.05
)
confint(out, level = 0.95)

Confidence Intervals for Differences of Standardized Regression Slopes

Description

Confidence Intervals for Differences of Standardized Regression Slopes

Usage

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

Arguments

`object`	Object of class `diffbetadelta`.
`parm`	a specification of which parameters are to be given confidence intervals, either a vector of numbers or a vector of names. If missing, all parameters are considered.
`level`	the confidence level required.
`...`	additional arguments.

Value

Returns a matrix of confidence intervals.

Author(s)

Ivan Jacob Agaloos Pesigan

Examples

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = nas1982)
std <- BetaDelta(object)
diff <- DiffBetaDelta(std)
confint(diff)

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = nas1982)
std <- BetaDelta(object)
diff <- DiffBetaDelta(std)
confint(diff)

Delta Method

Description

Calculates delta method sampling variance-covariance matrix for a function of parameters using a numerical Jacobian.

Usage

Delta(
  coef,
  vcov,
  func,
  ...,
  theta = 0,
  alpha = c(0.05, 0.01, 0.001),
  z = TRUE,
  df = NULL
)
Delta(
  coef,
  vcov,
  func,
  ...,
  theta = 0,
  alpha = c(0.05, 0.01, 0.001),
  z = TRUE,
  df = NULL
)

Arguments

`coef`	Numeric vector. Vector of parameters.
`vcov`	Numeric matrix. Matrix of sampling variance-covariance matrix of parameters.
`func`	R function. The first argument `x` is the argument `coef`. The function algebraically manipulates `coef` to return a new numeric vector. It is best to have a named vector as an output. The function can take additional named arguments passed using `...`.
`...`	Additional arguments to pass to `func`.
`theta`	Numeric vector. Parameter values when the null hypothesis is true.
`alpha`	Numeric vector. Significance level/s.
`z`	Logical. If `z = TRUE`, use the standard normal distribution. If `z = FALSE`, use the t distribution.
`df`	Numeric. Degrees of freedom if `z = FALSE`.

Value

Returns an object of class deltamethod which is a list with the following elements:

call: Function call.
args: Function arguments.
coef: Estimates.
vcov: Sampling variance-covariance matrix.
jacobian: Jacobian matrix.
fun: Function used ("Delta").

Author(s)

Ivan Jacob Agaloos Pesigan

Examples

object <- glm(
  formula = vs ~ wt + disp,
  family = "binomial",
  data = mtcars
)
func <- function(x) {
  y <- exp(x)
  names(y) <- paste0("exp", "(", names(x), ")")
  return(y[-1])
}
Delta(
  coef = coef(object),
  vcov = vcov(object),
  func = func,
  alpha = 0.05
)
object <- glm(
  formula = vs ~ wt + disp,
  family = "binomial",
  data = mtcars
)
func <- function(x) {
  y <- exp(x)
  names(y) <- paste0("exp", "(", names(x), ")")
  return(y[-1])
}
Delta(
  coef = coef(object),
  vcov = vcov(object),
  func = func,
  alpha = 0.05
)

Delta Method (Generic Object Input)

Description

Calculates delta method sampling variance-covariance matrix for a function of parameters using a numerical Jacobian.

Usage

DeltaGeneric(
  object,
  def,
  theta = 0,
  alpha = c(0.05, 0.01, 0.001),
  z = TRUE,
  df = NULL
)
DeltaGeneric(
  object,
  def,
  theta = 0,
  alpha = c(0.05, 0.01, 0.001),
  z = TRUE,
  df = NULL
)

Arguments

`object`	R object. Fitted model object with `coef` and `vcov` methods that return a named vector of estimated parameters and sampling variance-covariance matrix, respectively.
`def`	List of character strings. A list of defined functions of parameters. The string should be a valid R expression when parsed and should result a single value when evaluated.
`theta`	Numeric vector. Parameter values when the null hypothesis is true.
`alpha`	Numeric vector. Significance level/s.
`z`	Logical. If `z = TRUE`, use the standard normal distribution. If `z = FALSE`, use the t distribution.
`df`	Numeric. Degrees of freedom if `z = FALSE`.

Value

Returns an object of class deltamethod which is a list with the following elements:

call: Function call.
args: Function arguments.
coef: Estimates.
vcov: Sampling variance-covariance matrix.
jacobian: Jacobian matrix.
fun: Function used ("DeltaGeneric").

Author(s)

Ivan Jacob Agaloos Pesigan

Examples

object <- glm(
  formula = vs ~ wt + disp,
  family = "binomial",
  data = mtcars
)
def <- list("exp(wt)", "exp(disp)")
DeltaGeneric(
  object = object,
  def = def,
  alpha = 0.05
)
object <- glm(
  formula = vs ~ wt + disp,
  family = "binomial",
  data = mtcars
)
def <- list("exp(wt)", "exp(disp)")
DeltaGeneric(
  object = object,
  def = def,
  alpha = 0.05
)

Estimate Differences of Standardized Slopes and the Corresponding Sampling Covariance Matrix

Description

Estimate Differences of Standardized Slopes and the Corresponding Sampling Covariance Matrix

Usage

DiffBetaDelta(object, alpha = c(0.05, 0.01, 0.001))
DiffBetaDelta(object, alpha = c(0.05, 0.01, 0.001))

Arguments

`object`	Object of class `betadelta`, that is, the output of the `BetaDelta()` function.
`alpha`	Numeric vector. Significance level $\alpha$ .

Value

Returns an object of class diffbetadelta which is a list with the following elements:

call: Function call.
fit: The argument object.
args: Function arguments.
vcov: Sampling covariance matrix of differences of standardized slopes.
est: Vector of differences of standardized slopes.

Author(s)

Ivan Jacob Agaloos Pesigan

Examples

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = nas1982)
std <- BetaDelta(object)
diff <- DiffBetaDelta(std)
# Methods -------------------------------------------------------
print(diff)
summary(diff)
coef(diff)
vcov(diff)
confint(diff, level = 0.95)

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = nas1982)
std <- BetaDelta(object)
diff <- DiffBetaDelta(std)
# Methods -------------------------------------------------------
print(diff)
summary(diff)
coef(diff)
vcov(diff)
confint(diff, level = 0.95)

1982 National Academy of Sciences Doctoral Programs Data

Description

1982 National Academy of Sciences Doctoral Programs Data

Usage

nas1982
nas1982

Format

Ratings of 46 doctoral programs in psychology in the USA with the following variables:

QUALITY: Program quality ratings.
NFACUL: Number of faculty members in the program.
NGRADS: Number of program graduates.
PCTSUPP: Percentage of program graduates who received support.
PCTGRT: Percent of faculty members holding research grants.
NARTIC: Number of published articles attributed to program faculty member.
PCTPUB: Percent of faculty with one or more published article.

References

National Research Council. (1982). An assessment of research-doctorate programs in the United States: Social and behavioral sciences. doi:10.17226/9781. Reproduced with permission from the National Academy of Sciences, Courtesy of the National Academies Press, Washington, D.C.

Print Method for an Object of Class `betadelta`

Description

Print Method for an Object of Class betadelta

Usage

## S3 method for class 'betadelta'
print(x, alpha = NULL, digits = 4, ...)
## S3 method for class 'betadelta'
print(x, alpha = NULL, digits = 4, ...)

Arguments

`x`	Object of class `betadelta`.
`alpha`	Numeric vector. Significance level $\alpha$ . If `alpha = NULL`, use the argument `alpha` used in `x`.
`digits`	Digits to print.
`...`	additional arguments.

Value

Prints a matrix of standardized regression slopes, standard errors, test statistics, degrees of freedom, p-values, and confidence intervals.

Author(s)

Ivan Jacob Agaloos Pesigan

Examples

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = nas1982)
std <- BetaDelta(object)
print(std)

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = nas1982)
std <- BetaDelta(object)
print(std)

Print Method for an Object of Class `deltamethod`

Description

Print Method for an Object of Class deltamethod

Usage

## S3 method for class 'deltamethod'
print(x, alpha = NULL, digits = 4, ...)
## S3 method for class 'deltamethod'
print(x, alpha = NULL, digits = 4, ...)

Arguments

`x`	Object of class `deltamethod`.
`alpha`	Numeric vector. Significance level $\alpha$ . If `alpha = NULL`, use the argument `alpha` used in `x`.
`digits`	Digits to print.
`...`	additional arguments.

Value

Returns a matrix of coefficients, standard errors, test statistics, degrees of freedom (if z = FALSE), p-values, and confidence intervals.

Author(s)

Ivan Jacob Agaloos Pesigan

Examples

object <- glm(
  formula = vs ~ wt + disp,
  family = "binomial",
  data = mtcars
)
def <- list("exp(wt)", "exp(disp)")
out <- DeltaGeneric(
  object = object,
  def = def,
  alpha = 0.05
)
print(out)

object <- glm(
  formula = vs ~ wt + disp,
  family = "binomial",
  data = mtcars
)
def <- list("exp(wt)", "exp(disp)")
out <- DeltaGeneric(
  object = object,
  def = def,
  alpha = 0.05
)
print(out)

Print Method for an Object of Class `diffbetadelta`

Description

Print Method for an Object of Class diffbetadelta

Usage

## S3 method for class 'diffbetadelta'
print(x, alpha = NULL, digits = 4, ...)
## S3 method for class 'diffbetadelta'
print(x, alpha = NULL, digits = 4, ...)

Arguments

`x`	Object of class `diffbetadelta`.
`alpha`	Numeric vector. Significance level $\alpha$ . If `alpha = NULL`, use the argument `alpha` used in `x`.
`digits`	Digits to print.
`...`	additional arguments.

Value

Prints a matrix of standardized regression slopes, standard errors, test statistics, degrees of freedom, p-values, and confidence intervals.

Author(s)

Ivan Jacob Agaloos Pesigan

Examples

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = nas1982)
std <- BetaDelta(object)
diff <- DiffBetaDelta(std)
print(diff)

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = nas1982)
std <- BetaDelta(object)
diff <- DiffBetaDelta(std)
print(diff)

Summary Method for an Object of Class `betadelta`

Description

Summary Method for an Object of Class betadelta

Usage

## S3 method for class 'betadelta'
summary(object, alpha = NULL, digits = 4, ...)
## S3 method for class 'betadelta'
summary(object, alpha = NULL, digits = 4, ...)

Arguments

`object`	Object of class `betadelta`.
`alpha`	Numeric vector. Significance level $\alpha$ . If `alpha = NULL`, use the argument `alpha` used in `object`.
`digits`	Digits to print.
`...`	additional arguments.

Value

Returns a matrix of standardized regression slopes, standard errors, test statistics, degrees of freedom, p-values, and confidence intervals.

Author(s)

Ivan Jacob Agaloos Pesigan

Examples

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = nas1982)
std <- BetaDelta(object)
summary(std)

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = nas1982)
std <- BetaDelta(object)
summary(std)

Summary Method for an Object of Class `deltamethod`

Description

Summary Method for an Object of Class deltamethod

Usage

## S3 method for class 'deltamethod'
summary(object, alpha = NULL, digits = 4, ...)
## S3 method for class 'deltamethod'
summary(object, alpha = NULL, digits = 4, ...)

Arguments

`object`	Object of class `deltamethod`.
`alpha`	Numeric vector. Significance level $\alpha$ . If `alpha = NULL`, use the argument `alpha` used in `object`.
`digits`	Digits to print.
`...`	additional arguments.

Value

Returns a matrix of standardized regression slopes, standard errors, test statistics, degrees of freedom, p-values, and confidence intervals.

Author(s)

Ivan Jacob Agaloos Pesigan

Examples

object <- glm(
  formula = vs ~ wt + disp,
  family = "binomial",
  data = mtcars
)
def <- list("exp(wt)", "exp(disp)")
out <- DeltaGeneric(
  object = object,
  def = def,
  alpha = 0.05
)
summary(out)

object <- glm(
  formula = vs ~ wt + disp,
  family = "binomial",
  data = mtcars
)
def <- list("exp(wt)", "exp(disp)")
out <- DeltaGeneric(
  object = object,
  def = def,
  alpha = 0.05
)
summary(out)

Summary Method for an Object of Class `diffbetadelta`

Description

Summary Method for an Object of Class diffbetadelta

Usage

## S3 method for class 'diffbetadelta'
summary(object, alpha = NULL, digits = 4, ...)
## S3 method for class 'diffbetadelta'
summary(object, alpha = NULL, digits = 4, ...)

Arguments

`object`	Object of class `diffbetadelta`.
`alpha`	Numeric vector. Significance level $\alpha$ . If `alpha = NULL`, use the argument `alpha` used in `object`.
`digits`	Digits to print.
`...`	additional arguments.

Value

Returns a matrix of standardized regression slopes, standard errors, test statistics, degrees of freedom, p-values, and confidence intervals.

Author(s)

Ivan Jacob Agaloos Pesigan

Examples

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = nas1982)
std <- BetaDelta(object)
diff <- DiffBetaDelta(std)
summary(diff)

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = nas1982)
std <- BetaDelta(object)
diff <- DiffBetaDelta(std)
summary(diff)

Sampling Covariance Matrix of the Standardized Regression Slopes

Description

Sampling Covariance Matrix of the Standardized Regression Slopes

Usage

## S3 method for class 'betadelta'
vcov(object, ...)
## S3 method for class 'betadelta'
vcov(object, ...)

Arguments

`object`	Object of class `betadelta`.
`...`	additional arguments.

Value

Returns a matrix of the variance-covariance matrix of standardized slopes.

Author(s)

Ivan Jacob Agaloos Pesigan

Examples

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = nas1982)
std <- BetaDelta(object)
vcov(std)

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = nas1982)
std <- BetaDelta(object)
vcov(std)

Sampling Covariance Matrix

Description

Sampling Covariance Matrix

Usage

## S3 method for class 'deltamethod'
vcov(object, ...)
## S3 method for class 'deltamethod'
vcov(object, ...)

Arguments

`object`	Object of class `deltamethod`.
`...`	additional arguments.

Value

Returns a matrix of the variance-covariance matrix.

Author(s)

Ivan Jacob Agaloos Pesigan

Examples

object <- glm(
  formula = vs ~ wt + disp,
  family = "binomial",
  data = mtcars
)
def <- list("exp(wt)", "exp(disp)")
out <- DeltaGeneric(
  object = object,
  def = def,
  alpha = 0.05
)
vcov(out)

object <- glm(
  formula = vs ~ wt + disp,
  family = "binomial",
  data = mtcars
)
def <- list("exp(wt)", "exp(disp)")
out <- DeltaGeneric(
  object = object,
  def = def,
  alpha = 0.05
)
vcov(out)

Sampling Covariance Matrix of Differences of Standardized Regression Slopes

Description

Sampling Covariance Matrix of Differences of Standardized Regression Slopes

Usage

## S3 method for class 'diffbetadelta'
vcov(object, ...)
## S3 method for class 'diffbetadelta'
vcov(object, ...)

Arguments

`object`	Object of class `diffbetadelta`.
`...`	additional arguments.

Value

Returns a matrix of the variance-covariance matrix of differences of standardized regression slopes.

Author(s)

Ivan Jacob Agaloos Pesigan

Examples

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = nas1982)
std <- BetaDelta(object)
diff <- DiffBetaDelta(std)
vcov(diff)

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = nas1982)
std <- BetaDelta(object)
diff <- DiffBetaDelta(std)
vcov(diff)

Package 'betaDelta'

Help Index

Estimate Standardized Regression Coefficients and the Corresponding Sampling Covariance Matrix

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Standardized Regression Slopes

Description

Usage

Arguments

Value

Author(s)

Examples

Estimates

Description

Usage

Arguments

Value

Author(s)

Examples

Differences of Standardized Regression Slopes

Description

Usage

Arguments

Value

Author(s)

Examples

Confidence Intervals for Standardized Regression Slopes

Description

Usage

Arguments

Value

Author(s)

Examples

Confidence Intervals

Description

Usage

Arguments

Value

Author(s)

Examples

Confidence Intervals for Differences of Standardized Regression Slopes

Description

Usage

Arguments

Value

Author(s)

Examples

Delta Method

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Delta Method (Generic Object Input)

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Estimate Differences of Standardized Slopes and the Corresponding Sampling Covariance Matrix

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

1982 National Academy of Sciences Doctoral Programs Data

Description

Usage

Print Method for an Object of Class `betadelta`

Print Method for an Object of Class `deltamethod`

Print Method for an Object of Class `diffbetadelta`

Summary Method for an Object of Class `betadelta`

Summary Method for an Object of Class `deltamethod`

Summary Method for an Object of Class `diffbetadelta`