Help for package ieTest

Type:

Package

Title:

Indirect Effects Testing Methods in Mediation Analysis

Version:

2.0

Date:

2025-03-31

Maintainer:

John Kidd <jkidd@uvu.edu>

Description:

Used in testing if the indirect effect from linear regression mediation analysis is equal to 0. Includes established methods such as the Sobel Test, Joint Significant test (maxP), and tests based off the distribution of the Product or Normal Random Variables. Additionally, this package adds more powerful tests based on Intersection-Union theory. These tests are the S-Test, the ps-test, and the ascending squares test. These new methods are uniformly more powerful than maxP, which is more powerful than Sobel and less anti-conservative than the Product of Normal Random Variables. These methods are explored by Kidd and Lin, (2024) <doi:10.1007/s12561-023-09386-6> and Kidd et al., (2025) <doi:10.1007/s10260-024-00777-7>.

License:

GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]

Depends:

R (≥ 3.3.0), grDevices, graphics, methods, stats, utils

Imports:

Rcpp (≥ 1.0.3), RcppArmadillo, RcppDist, twosamples, MASS

LinkingTo:

Rcpp, RcppArmadillo, RcppDist

RoxygenNote:

7.3.2

Encoding:

UTF-8

Suggests:

testthat (≥ 3.0.0)

Config/testthat/edition:

NeedsCompilation:

yes

Packaged:

2025-03-31 21:48:21 UTC; 10975067

Author:

John Kidd [aut, cre]

Repository:

CRAN

Date/Publication:

2025-04-02 09:00:11 UTC

ASQ-Test for the indirect effect - Single mediator path

Description

This function takes a vector of significance levels, as well as estimates and covariances, or 2 U values, for the asq-test for either one mediator of one path of an unordered mediation scenario. If estimates are passed to the function, the user must specify what distribution is to be used to find the cumulative probabilities. The smallest significance level for which the test is significant is returned, or 1 if no provided levels are significant. Additionally, the cutoff, either specified by number of squares or the percentage towards the center of the transformation region, can be specified.

Usage

asq_one(
  alpha,
  u1 = NULL,
  u2 = NULL,
  V1Dist = NULL,
  V1 = NULL,
  V1_VAR = NULL,
  V1_DF = NULL,
  V2Dist = NULL,
  V2 = NULL,
  V2_VAR = NULL,
  V2_DF = NULL,
  V2b = 0,
  V2b_VAR = 0,
  V2bmult = 1L,
  V1_V2_cov = 0,
  V1_V2b_cov = 0,
  V2_V2b_cov = 0,
  V1_0 = 0,
  V2_0 = 0,
  V2b_0 = 0,
  numSquares = 4L,
  upLim = 0.5
)

Arguments

alpha

Significance levels to be tested.

u1, u2

The U values to be used in the test. Given priority over estimates, but both must be supplied.

V1Dist

String value specifying the distribution of the estimate of the independent variable on the mediator. Ignored if u1 and u2 are supplied.

V1

Value of the estimate of the independent variable on the mediator. Ignored if u1 and u2 are supplied.

V1_VAR

Value of the variance of the estimate of the independent variable on the mediator. Ignored if u1 and u2 are supplied.

V1_DF

Degrees of freedom for V1. Only needed if t-distribution is used.

V2Dist

String value specifying the distribution of the estimate of the mediator (and interaction term) on the response.

V2

Value of the estimate of the mediator on the response. Ignored if u1 and u2 are supplied.

V2_VAR

Value of the variance of the estimate of the mediator on the response.. Ignored if u1 and u2 are supplied.

V2_DF

Degrees of freedom for V2. Only needed if t-distribution is used..

V2b

Value of the estimate of the effect of the interaction of the independent and mediator variable on the response. Ignored if u1 and u2 are supplied.

V2b_VAR

Value of the variance of the estimate of the effect of the interaction of the independent and mediator variable on the response. Ignored if u1 and u2 are supplied.

V2bmult

Value indicating the value of the independent variable used for the interaction. Typically 1.

V1_V2_cov

Value of the covariance between V1 and V2. Typically 0 for fully observed data.

V1_V2b_cov

Value of the covariance between V1 and V2b. Typically 0 for fully observed data.

V2_V2b_cov

Value of the covariance between V2 and V2b.

V1_0

Null value for V1.

V2_0

Null value for V2.

V2b_0

Null value for V2b.

numSquares

The number of squares to be used in the asq-test. Always superseded by upLim.

upLim

The allowed extension, between 0 and 1, of the squares towards the center of the region

Value

The smallest significance level that would reject the null hypothesis.

Examples

asq_one(c(.05, .01, .001), u1 = .02, u2= .015, upLim = .55)

ASQ-Test for the indirect effect - Ordered Mediators

Description

This function takes a vector of significance levels, as well as estimates and covariances, or 3 U values, for the asq-test for an ordered mediation scenario. If estimates are passed to the function, the user must specify what distribution is to be used to find the cumulative probabilities. The smallest significance level for which the test is significant is returned, or 1 if no provided levels are significant. Additionally, the cutoff, either specified by number of squares or the percentage towards the center of the transformation region, can be specified.

Usage

asq_ord(
  alpha,
  u1 = NULL,
  u2 = NULL,
  u3 = NULL,
  V1Dist = NULL,
  V1 = NULL,
  V1_VAR = NULL,
  V1_DF = NULL,
  V2Dist = NULL,
  V2 = NULL,
  V2_VAR = NULL,
  V2_DF = NULL,
  V2b = 0,
  V2b_VAR = 0,
  V2bmult = 1L,
  V3Dist = NULL,
  V3 = NULL,
  V3_VAR = NULL,
  V3_DF = NULL,
  V3b = 0,
  V3b_VAR = 0,
  V1_V2_cov = 0,
  V1_V2b_cov = 0,
  V1_V3_cov = 0,
  V1_V3b_cov = 0,
  V2_V2b_cov = 0,
  V2_V3_cov = 0,
  V2_V3b_cov = 0,
  V2b_V3_cov = 0,
  V2b_V3b_cov = 0,
  V3_V3b_cov = 0,
  V1_0 = 0,
  V2_0 = 0,
  V2b_0 = 0,
  V3_0 = 0,
  V3b_0 = 0,
  numSquares = 4L,
  upLim = 0.5
)

Arguments

alpha

Significance levels to be tested.

u1, u2, u3

The U values to be used in the test. Given priority over estimates, but all must be supplied.

V1Dist

String value specifying the distribution of the estimate of the independent variable on the first mediator. Ignored if u1, u2, and u3 are supplied.

V1

Value of the estimate of the independent variable on the first mediator. Ignored if u1, u2, and u3 are supplied.

V1_VAR

Value of the variance of the estimate of the independent variable on the first mediator. Ignored if u1, u2, and u3 are supplied.

V1_DF

Degrees of freedom for V1. Only needed if t-distribution is used.

V2Dist

String value specifying the distribution of the estimate of the first mediator (and interaction term) on the second mediator.

V2

Value of the estimate of the first mediator on the second mediator. Ignored if u1, u2, and u3 are supplied.

V2_VAR

Value of the variance of the estimate of the first mediator on the second mediator. Ignored if u1, u2, and u3 are supplied.

V2_DF

Degrees of freedom for V2.

V2b

Value of the estimate of the effect of the interaction of the independent and first mediator variable on the second mediator. Ignored if u1, u2, and u3 are supplied.

V2b_VAR

Value of the variance of the estimate of the effect of the interaction of the independent and first mediator variable on the second mediator. Ignored if u1, u2, and u3 are supplied.

V2bmult

Value indicating the value of the independent variable used for the interactions. Typically 1.

V3Dist

String value specifying the distribution of the estimate of the second mediator (and interaction term) on the response.

V3

Value of the estimate of the second mediator on the response. Ignored if u1, u2, and u3 are supplied.

V3_VAR

Value of the variance of the estimate of the second mediator on the response. Ignored if u1, u2, and u3 are supplied.

V3_DF

Degrees of freedom for V3.

V3b

Value of the estimate of the effect of the interaction of the independent and second mediator variable on the response. Ignored if u1, u2, and u3 are supplied.

V3b_VAR

Value of the variance of the estimate of the effect of the interaction of the independent and second mediator variable on the response. Ignored if u1, u2, and u3 are supplied.

V1_V2_cov

Value of the covariance between V1 and V2. Typically 0 for fully observed data.

V1_V2b_cov

Value of the covariance between V1 and V2b. Typically 0 for fully observed data.

V1_V3_cov

Value of the covariance between V1 and V3. Typically 0 for fully observed data.

V1_V3b_cov

Value of the covariance between V1 and V3b. Typically 0 for fully observed data.

V2_V2b_cov

Value of the covariance between V2 and V2b.

V2_V3_cov

Value of the covariance between V2 and V3. Typically 0 for fully observed data.

V2_V3b_cov

Value of the covariance between V2 and V3b. Typically 0 for fully observed data.

V2b_V3_cov

Value of the covariance between V2b and V3. Typically 0 for fully observed data.

V2b_V3b_cov

Value of the covariance between V2b and V3b. Typically 0 for fully observed data.

V3_V3b_cov

Value of the covariance between V3 and V3b.

V1_0

Null value for V1.

V2_0

Null value for V2.

V2b_0

Null value for V2b.

V3_0

Null value for V3.

V3b_0

Null value for V3b.

numSquares

The number of squares to be used in the asq-test. Always superseded by upLim.

upLim

The allowed extension, between 0 and 1, of the squares towards the center of the region

Value

The smallest significance level that would reject the null hypothesis.

Examples

asq_ord(c(.05, .01, .001), u1 = .02, u2= .015, u3 = .995, upLim = .55)

Is the mediation effect significant?

Description

This function takes 3 U values for the asq-test for 2 ordered mediators, as well as an alpha level. It returns whether the test would reject at the given alpha level. Additionally, the cutoff, either specified by number of squares or the percentage towards the center of the transformation region, can be specified. This function is primarily called by the asq_ord function to determine if the test is significant at one of a chosen set of alpha values.

Usage

asq_ord_bool(alpha, u1, u2, u3, numSquares = 4L, upLim = 0.5)

Arguments

alpha

Significance level for the test.

u1, u2, u3

The U values to be used in the test

numSquares

The number of squares to be used in the asq-test. Always superceded by upLim

upLim

The allowed extension, between 0 and 1, of the squares towards the center of the region

Value

A boolean variable indicating if the indirect effect null hypothesis is rejected.

Examples

asq_ord_bool(.05, .02, .015, .995, upLim = .75)

Testing the indirect effect.

Description

This function takes a vector estimates and a matrix of covariances or a vector of U values to be used in various indirect effect tests. Estimate vectors with three parameters will default to single mediator analysis (or one path of unordered mediation), and five parameters will default to the ordered scenario. Values for the interaction term must be provided for this wrapper. The user can then specify the distribution(s) to be used as well as the test to be performed.

Usage

ieTest(
  test,
  u = NULL,
  V = NULL,
  cov = NULL,
  df = NULL,
  V_0 = 0,
  V1Dist = NULL,
  V2Dist = NULL,
  V3Dist = NULL,
  numSquares = 10,
  upLim = 0.5,
  alpha = 0.05,
  interMult = 1
)

Arguments

test

Denotes the test to be performed. ("maxP", "ps-test", "asq-test", "sobel", "sobel unordered")

u

A vector with the U values to be used in the test. Given priority over estimates, but all must be supplied. Order defined in note.

V

A vector containing the estimates to be used in the test. Must follow same order as u.

cov

A matrix of the covariance matrix of the estimates in V. Must be square with dimensions compatible with V. Must follow same order as u.

df

A vector of the degrees of freedom for the effect estimates. Length of 2 for single mediator, 3 for ordered.

V_0

A vector containing the null values of the estimates to be used in the test. Defaults to zero.

V1Dist

String value specifying the distribution of the estimate of the independent variable on the mediator.

V2Dist

String value specifying the distribution of the second estimate.

V3Dist

String value specifying the distribution of the third estimate (only needed for ordered scenario).

numSquares

The number of squares to be used in the asq-test. Always superseded by upLim.

upLim

The allowed extension, between 0 and 1, for the asq and ps-tests.

alpha

A vector for the asq-test of significance levels to test. A value in the ps-test to control type I error.

interMult

Integer indicating the level of the independent variable to use for the interaction terms.

Value

A p-value or p-value cutoff for the specified test for the indirect effect.

Note

Order of parameters Values must be in the correct order within u, V, and the cov matrix.

Single mediator (or single path in unordered scenarios):
Independent variable to mediator, mediator to response, interaction of independent and mediator.

Ordered mediators:
Independent variable to first mediator, first mediator to second mediator, interaction of independent and first mediator on second mediator, second mediator to response, interaction of independent and second mediator on response.

Combined Unordered Mediator:
Independent variable to first mediator, first mediator to response, interaction of independent and first mediator on response, Independent variable to second mediator, second mediator to response, interaction of independent and second mediator on response.

Examples

ieTest( test = "ps-test", u = c(.015, .02, .998), alpha = 0.05, upLim = 0.5)

Indirect Effects Testing methods in Mediation Analysis

Description

A package to provide a multitude of methods used in testing if the indirect effect from linear regression mediation analysis is equal to 0. Includes established methods such as the Sobel test, joint-significanct test (maxP), and test based off the distribution of the product or normal random variables. A modification of the Sobel test by Aroian is also provided. Additionally, this packed addes more powerful tests based on intersection-union theory. These tests are the S-test, the modified S-test, and the ascending squares test. These new methods are uniformly more powerful than maxP, which is more powerful than Sobel and less anti-conservative than the product of normal random variables.

Details

Functions should be used to test a hypothesis that the indirect effect is equal to zero. Alternate hypothesis values for individual effects can be specified. Functions are provided for one and two mediator scenarios.

Test methods for one mediator and two ordered (sequential) mediators are provided for all above mentioned methods except the S-test. The S-test has logically falacies defined in (cited paper), and thus extensions to two mediators have not been conducted. In unordered (simultaneous) mediator scenarios, two mediation affects (one through each mediator) can be determined. Single mediator approaches should be used in these circumstances. For the methods defined by Sobel and Aroian, an overall test for a mediation affect exists using a sumation.

Single mediator function names are in the format of "test_one". For ordered/sequential approaches, functions are named "test_two_seq". The two unordered approaches are called by "sobelTest_two_sim" and "aroian_two_sim".

Author(s)

John Kidd

Maintainer: John Kidd <jkidd@uvu.edu>

References

Kidd, J., Howard, A.G., Highland, H.M. et al. Hypothesis tests of indirect effects for multiple mediators. Stat Methods Appl, 2025.

Kidd, J., Lin, DY. Improving the Power to Detect Indirect Effects in Mediation Analysis. Stat Biosci, 2025.

MaxP test for the indirect effect - Single mediator path

Description

This function takes estimates and covariances, or 2 U values, for the maxP test for either one mediator of one path of an unordered mediation scenario. If estimates are passed to the function, the user must specify what distribution is to be used to find the cumulative probabilities. The maximum p-value is returned.

Usage

maxp_one(
  u1 = NULL,
  u2 = NULL,
  V1Dist = NULL,
  V1 = NULL,
  V1_VAR = NULL,
  V1_DF = NULL,
  V2Dist = NULL,
  V2 = NULL,
  V2_VAR = NULL,
  V2_DF = NULL,
  V2b = 0,
  V2b_VAR = 0,
  V2bmult = 1L,
  V1_V2_cov = 0,
  V1_V2b_cov = 0,
  V2_V2b_cov = 0,
  V1_0 = 0,
  V2_0 = 0,
  V2b_0 = 0
)

Arguments

u1, u2

The U values to be used in the test. Given priority over estimates, but both must be supplied.

V1Dist

String value specifying the distribution of the estimate of the independent variable on the mediator. Ignored if u1 and u2 are supplied.

V1

Value of the estimate of the independent variable on the mediator. Ignored if u1 and u2 are supplied.

V1_VAR

Value of the variance of the estimate of the independent variable on the mediator. Ignored if u1 and u2 are supplied.

V1_DF

Degrees of freedom for V1. Only needed if t-distribution is used.

V2Dist

String value specifying the distribution of the estimate of the mediator (and interaction term) on the response.

V2

Value of the estimate of the mediator on the response. Ignored if u1 and u2 are supplied.

V2_VAR

Value of the variance of the estimate of the mediator on the response.. Ignored if u1 and u2 are supplied.

V2_DF

Degrees of freedom for V2. Only needed if t-distribution is used..

V2b

Value of the estimate of the effect of the interaction of the independent and mediator variable on the response. Ignored if u1 and u2 are supplied.

V2b_VAR

Value of the variance of the estimate of the effect of the interaction of the independent and mediator variable on the response. Ignored if u1 and u2 are supplied.

V2bmult

Value indicating the value of the independent variable used for the interaction. Typically 1.

V1_V2_cov

Value of the covariance between V1 and V2. Typically 0 for fully observed data.

V1_V2b_cov

Value of the covariance between V1 and V2b. Typically 0 for fully observed data.

V2_V2b_cov

Value of the covariance between V2 and V2b.

V1_0

Null value for V1.

V2_0

Null value for V2.

V2b_0

Null value for V2b.

Value

The p-value of the test in the form of the larger of the p-values for the individual parameters.

Examples

maxp_one(u1 = .02, u2= .015)

MaxP-Test for the indirect effect - Ordered Mediators

Description

This function takes estimates and covariances, or 3 U values, for the maxp-test for an ordered mediation scenario. If estimates are passed to the function, the user must specify what distribution is to be used to find the cumulative probabilities. The p-value of the maxp-test is returned.

Usage

maxp_ord(
  u1 = NULL,
  u2 = NULL,
  u3 = NULL,
  V1Dist = NULL,
  V1 = NULL,
  V1_VAR = NULL,
  V1_DF = NULL,
  V2Dist = NULL,
  V2 = NULL,
  V2_VAR = NULL,
  V2_DF = NULL,
  V2b = 0,
  V2b_VAR = 0,
  V2bmult = 1L,
  V3Dist = NULL,
  V3 = NULL,
  V3_VAR = NULL,
  V3_DF = NULL,
  V3b = 0,
  V3b_VAR = 0,
  V1_V2_cov = 0,
  V1_V2b_cov = 0,
  V1_V3_cov = 0,
  V1_V3b_cov = 0,
  V2_V2b_cov = 0,
  V2_V3_cov = 0,
  V2_V3b_cov = 0,
  V2b_V3_cov = 0,
  V2b_V3b_cov = 0,
  V3_V3b_cov = 0,
  V1_0 = 0,
  V2_0 = 0,
  V2b_0 = 0,
  V3_0 = 0,
  V3b_0 = 0
)

Arguments

u1, u2, u3

The U values to be used in the test. Given priority over estimates, but all must be supplied.

V1Dist

String value specifying the distribution of the estimate of the independent variable on the first mediator. Ignored if u1, u2, and u3 are supplied.

V1

Value of the estimate of the independent variable on the first mediator. Ignored if u1, u2, and u3 are supplied.

V1_VAR

Value of the variance of the estimate of the independent variable on the first mediator. Ignored if u1, u2, and u3 are supplied.

V1_DF

Degrees of freedom for V1. Only needed if t-distribution is used.

V2Dist

String value specifying the distribution of the estimate of the first mediator (and interaction term) on the second mediator.

V2

Value of the estimate of the first mediator on the second mediator. Ignored if u1, u2, and u3 are supplied.

V2_VAR

Value of the variance of the estimate of the first mediator on the second mediator. Ignored if u1, u2, and u3 are supplied.

V2_DF

Degrees of freedom for V2.

V2b

Value of the estimate of the effect of the interaction of the independent and first mediator variable on the second mediator. Ignored if u1, u2, and u3 are supplied.

V2b_VAR

Value of the variance of the estimate of the effect of the interaction of the independent and first mediator variable on the second mediator. Ignored if u1, u2, and u3 are supplied.

V2bmult

Value indicating the value of the independent variable used for the interactions. Typically 1.

V3Dist

String value specifying the distribution of the estimate of the second mediator (and interaction term) on the response.

V3

Value of the estimate of the second mediator on the response. Ignored if u1, u2, and u3 are supplied.

V3_VAR

Value of the variance of the estimate of the second mediator on the response. Ignored if u1, u2, and u3 are supplied.

V3_DF

Degrees of freedom for V3.

V3b

Value of the estimate of the effect of the interaction of the independent and second mediator variable on the response. Ignored if u1, u2, and u3 are supplied.

V3b_VAR

Value of the variance of the estimate of the effect of the interaction of the independent and second mediator variable on the response. Ignored if u1, u2, and u3 are supplied.

V1_V2_cov

Value of the covariance between V1 and V2. Typically 0 for fully observed data.

V1_V2b_cov

Value of the covariance between V1 and V2b. Typically 0 for fully observed data.

V1_V3_cov

Value of the covariance between V1 and V3. Typically 0 for fully observed data.

V1_V3b_cov

Value of the covariance between V1 and V3b. Typically 0 for fully observed data.

V2_V2b_cov

Value of the covariance between V2 and V2b

V2_V3_cov

Value of the covariance between V2 and V3 Typically 0 for fully observed data.

V2_V3b_cov

Value of the covariance between V2 and V3b Typically 0 for fully observed data.

V2b_V3_cov

Value of the covariance between V2b and V3. Typically 0 for fully observed data.

V2b_V3b_cov

Value of the covariance between V2b and V3b Typically 0 for fully observed data.

V3_V3b_cov

Value of the covariance between V3 and V3b.

V1_0

Null value for V1.

V2_0

Null value for V2.

V2b_0

Null value for V2b.

V3_0

Null value for V3.

V3b_0

Null value for V3b.

Value

The p-value of the test in the form of the larger of the p-values for the individual parameters.

Examples

maxp_ord( u1 = .02, u2= .015, u3 = .995)

PS-Test for the indirect effect - Single mediator path

Description

This function takes estimates and covariances, or 2 U values, for the ps-test for either one mediator of one path of an unordered mediation scenario. If estimates are passed to the function, the user must specify what distribution is to be used to find the cumulative probabilities. The p-value of the ps-test is returned. Additionally, the cutoff, specified by the percentage towards the center of the transformation region, can be specified.

Usage

ps_one(
  u1 = NULL,
  u2 = NULL,
  V1Dist = NULL,
  V1 = NULL,
  V1_VAR = NULL,
  V1_DF = NULL,
  V2Dist = NULL,
  V2 = NULL,
  V2_VAR = NULL,
  V2_DF = NULL,
  V2b = 0,
  V2b_VAR = 0,
  V2bmult = 1L,
  V1_V2_cov = 0,
  V1_V2b_cov = 0,
  V2_V2b_cov = 0,
  V1_0 = 0,
  V2_0 = 0,
  V2b_0 = 0,
  upLim = 0.5,
  alpha = NULL
)

Arguments

u1, u2

The U values to be used in the test. Given priority over estimates, but both must be supplied.

V1Dist

String value specifying the distribution of the estimate of the independent variable on the mediator. Ignored if u1 and u2 are supplied.

V1

Value of the estimate of the independent variable on the mediator. Ignored if u1 and u2 are supplied.

V1_VAR

Value of the variance of the estimate of the independent variable on the mediator. Ignored if u1 and u2 are supplied.

V1_DF

Degrees of freedom for V1. Only needed if t-distribution is used.

V2Dist

String value specifying the distribution of the estimate of the mediator (and interaction term) on the response.

V2

Value of the estimate of the mediator on the response. Ignored if u1 and u2 are supplied.

V2_VAR

Value of the variance of the estimate of the mediator on the response.. Ignored if u1 and u2 are supplied.

V2_DF

Degrees of freedom for V2. Only needed if t-distribution is used..

V2b

Value of the estimate of the effect of the interaction of the independent and mediator variable on the response. Ignored if u1 and u2 are supplied.

V2b_VAR

Value of the variance of the estimate of the effect of the interaction of the independent and mediator variable on the response. Ignored if u1 and u2 are supplied.

V2bmult

Value indicating the value of the independent variable used for the interaction. Typically 1.

V1_V2_cov

Value of the covariance between V1 and V2. Typically 0 for fully observed data.

V1_V2b_cov

Value of the covariance between V1 and V2b. Typically 0 for fully observed data.

V2_V2b_cov

Value of the covariance between V2 and V2b.

V1_0

Null value for V1.

V2_0

Null value for V2.

V2b_0

Null value for V2b.

upLim

The allowed extension, between 0 and 1, of the band towards the center of the region

alpha

Used to ensure correctly controlled type I error for large values of upLim.

Value

The smallest alpha value for which the generated rejection region leads to rejection of the hypothesis test. Can be used as a p-value.

Examples

ps_one(u1 = .02, u2= .015, upLim = .55)

PS-Test for the indirect effect - Ordered Mediators

Description

This function takes estimates and covariances, or 3 U values, for the ps-test for an ordered mediation scenario. If estimates are passed to the function, the user must specify what distribution is to be used to find the cumulative probabilities. The p-value of the ps-test is returned. Additionally, the cutoff, specified by the percentage towards the center of the transformation region, can be specified.

Usage

ps_ord(
  u1 = NULL,
  u2 = NULL,
  u3 = NULL,
  V1Dist = NULL,
  V1 = NULL,
  V1_VAR = NULL,
  V1_DF = NULL,
  V2Dist = NULL,
  V2 = NULL,
  V2_VAR = NULL,
  V2_DF = NULL,
  V2b = 0,
  V2b_VAR = 0,
  V2bmult = 1L,
  V3Dist = NULL,
  V3 = NULL,
  V3_VAR = NULL,
  V3_DF = NULL,
  V3b = 0,
  V3b_VAR = 0,
  V1_V2_cov = 0,
  V1_V2b_cov = 0,
  V1_V3_cov = 0,
  V1_V3b_cov = 0,
  V2_V2b_cov = 0,
  V2_V3_cov = 0,
  V2_V3b_cov = 0,
  V2b_V3_cov = 0,
  V2b_V3b_cov = 0,
  V3_V3b_cov = 0,
  V1_0 = 0,
  V2_0 = 0,
  V2b_0 = 0,
  V3_0 = 0,
  V3b_0 = 0,
  upLim = 0.5,
  alpha = NULL
)

Arguments

u1, u2, u3

The U values to be used in the test. Given priority over estimates, but all must be supplied.

V1Dist

String value specifying the distribution of the estimate of the independent variable on the first mediator. Ignored if u1, u2, and u3 are supplied.

V1

Value of the estimate of the independent variable on the first mediator. Ignored if u1, u2, and u3 are supplied.

V1_VAR

Value of the variance of the estimate of the independent variable on the first mediator. Ignored if u1, u2, and u3 are supplied.

V1_DF

Degrees of freedom for V1. Only needed if t-distribution is used.

V2Dist

String value specifying the distribution of the estimate of the first mediator (and interaction term) on the second mediator.

V2

Value of the estimate of the first mediator on the second mediator. Ignored if u1, u2, and u3 are supplied.

V2_VAR

Value of the variance of the estimate of the first mediator on the second mediator. Ignored if u1, u2, and u3 are supplied.

V2_DF

Degrees of freedom for V2.

V2b

Value of the estimate of the effect of the interaction of the independent and first mediator variable on the second mediator. Ignored if u1, u2, and u3 are supplied.

V2b_VAR

Value of the variance of the estimate of the effect of the interaction of the independent and first mediator variable on the second mediator. Ignored if u1, u2, and u3 are supplied.

V2bmult

Value indicating the value of the independent variable used for the interaction. Typically 1.

V3Dist

String value specifying the distribution of the estimate of the second mediator (and interaction term) on the response.

V3

Value of the estimate of the second mediator on the response. Ignored if u1, u2, and u3 are supplied.

V3_VAR

Value of the variance of the estimate of the second mediator on the response. Ignored if u1, u2, and u3 are supplied.

V3_DF

Degrees of freedom for V3.

V3b

Value of the estimate of the effect of the interaction of the independent and second mediator variable on the response. Ignored if u1, u2, and u3 are supplied.

V3b_VAR

Value of the variance of the estimate of the effect of the interaction of the independent and second mediator variable on the response. Ignored if u1, u2, and u3 are supplied.

V1_V2_cov

Value of the covariance between V1 and V2. Typically 0 for fully observed data.

V1_V2b_cov

Value of the covariance between V1 and V2b. Typically 0 for fully observed data.

V1_V3_cov

Value of the covariance between V1 and V3. Typically 0 for fully observed data.

V1_V3b_cov

Value of the covariance between V1 and V3b. Typically 0 for fully observed data.

V2_V2b_cov

Value of the covariance between V2 and V2b

V2_V3_cov

Value of the covariance between V2 and V3 Typically 0 for fully observed data.

V2_V3b_cov

Value of the covariance between V2 and V3b Typically 0 for fully observed data.

V2b_V3_cov

Value of the covariance between V2b and V3. Typically 0 for fully observed data.

V2b_V3b_cov

Value of the covariance between V2b and V3b Typically 0 for fully observed data.

V3_V3b_cov

Value of the covariance between V3 and V3b.

V1_0

Null value for V1.

V2_0

Null value for V2.

V2b_0

Null value for V2b.

V3_0

Null value for V3.

V3b_0

Null value for V3b.

upLim

The allowed extension, between 0 and 1, of the band towards the center of the region.

alpha

Used to ensure correctly controlled type I error for large values of upLim.

Value

The smallest alpha value for which the generated rejection region leads to rejection of the hypothesis test. Can be used as a p-value.

Examples

ps_ord( u1 = .02, u2= .015, u3 = .995, upLim = .55)

S test for Indirect Effect for a single mediator

Description

This function takes the estimate of the effect of the independent variable on the mediator and the effect of the mediator on the effect as well as their variances and performs the S test. Alternative null hypothesis can be specified as well. Additionally, covariances of the parameters can be specified for cases involving missing data where the estimates may be correlated.

Usage

sTest_one(alpha, x1, s11, df1, x2, s22, df2, x10 = 0, x20 = 0, s12 = 0)

Arguments

alpha

Significance level for the test of significance

x1

Numeric value of the estimated first effect of interest

s11

Numeric value of the estimated first effect variance

df1

Degrees of freedom for estimate x1

x2

Numeric value of estimated second effect of interest

s22

Numeric value of the estimated second effect variance

df2

Degrees of freedom for estimate x2. Often the same as x1

x10

Optional numeric value of alternative null hypothesis value for the first effect

x20

Optional numeric value of alternative null hypothesis value for the second effect

s12

Specification of covariance between x1 and x2. Typically 0, but may be non-zero in the prescence of missing data

Value

Boolean True/False value of whether the test rejects the Null hypothesis

Note

The function for the S-test does not incorporate interactions between the independent and mediating variables. The user must first calculate the mean and variance of the second product term to be used in the function call.

References

Berger, Roger L. Likelihood Ratio Tests and Intersection-Union Tests. Advances in Statistical Decision Theory and Applications, 2011.

Examples

sTest_one(0.05, .5, 1, 100, -.25, .1, 100)

Sobel test for the indirect effect - Single mediator path

Description

This function takes the parameter estimates and covariances and performs the Sobel test for one mediator, or a single mediator path for multiple unordered mediators.

Usage

sobelTest_one(
  mu1,
  sig1,
  mu2,
  sig2,
  sig12,
  indL = 1,
  mu3 = 0L,
  sig3 = 0L,
  sig13 = 0L,
  sig23 = 0L,
  mu1_0 = 0,
  mu2_0 = 0,
  mu3_0 = 0
)

Arguments

mu1

Value of the estimate of the independent variable on the mediator.

sig1

Value of the variance of the estimate of the independent variable on the mediator.

mu2

Value of the estimate of the mediator on the response.

sig2

Value of the variance of the estimate of the mediator on the response.

sig12

Value of the covariance between mu1 and mu2.

indL

Value indicating the value of the independent variable used for the interaction. Typically 1.

mu3

Value of the estimate of the effect of the interaction of the independent and mediator variable on the response.

sig3

Value of the variance of the estimate of the effect of the interaction of the independent and mediator variable on the response.

sig13

Value of the covariance between mu1 and mu3.

sig23

Value of the covariance between mu2 and mu3.

mu1_0

Null value for mu1.

mu2_0

Null value for mu2.

mu3_0

Null value for mu3.

Value

A p-value for the test for the indirect effect.

Examples

sobelTest_one(1, .1, .25, .01, .05)

Sobel test for the indirect effect - Two ordered mediator path

Description

This function takes the parameter estimates and covariances and performs the Sobel test for two ordered mediators.

Usage

sobelTest_ord(
  mu1,
  sig1,
  mu2,
  sig2,
  mu3,
  sig3,
  mu2b = 0L,
  sig2b = 0L,
  mu3b = 0L,
  sig3b = 0L,
  sig12 = 0L,
  sig12b = 0L,
  sig13 = 0L,
  sig13b = 0L,
  sig22b = 0L,
  sig23 = 0L,
  sig23b = 0L,
  sig2b3 = 0L,
  sig2b3b = 0L,
  sig33b = 0L,
  indL = 1L,
  mu1_0 = 0,
  mu2_0 = 0,
  mu3_0 = 0,
  mu2b_0 = 0,
  mu3b_0 = 0
)

Arguments

mu1

Value of the estimate of the independent variable on the first mediator.

sig1

Value of the variance of the estimate of the independent variable on the first mediator.

mu2

Value of the estimate of the first mediator on the second mediator.

sig2

Value of the variance of the estimate of the first mediator on the second mediator.

mu3

Value of the estimate of the second mediator on the response.

sig3

Value of the variance of the estimate of the second mediator on the response.

mu2b

Value of the estimate of the effect of the interaction of the independent and first mediator variable on the second mediator.

sig2b

Value of the variance of the estimate of the effect of the interaction of the independent and first mediator variable on the second mediator.

mu3b

Value of the estimate of the effect of the interaction of the independent and second mediator variable on the response.

sig3b

Value of the variance of the estimate of the effect of the interaction of the independent and second mediator variable on the response.

sig12

Value of the covariance between mu1 and mu2.

sig12b

Value of the covariance between mu1 and mu2b.

sig13

Value of the covariance between mu1 and mu3.

sig13b

Value of the covariance between mu1 and mu3b.

sig22b

Value of the covariance between mu2 and mu2b.

sig23

Value of the covariance between mu2 and mu3.

sig23b

Value of the covariance between mu2 and mu2b.

sig2b3

Value of the covariance between mu2b and mu3.

sig2b3b

Value of the covariance between mu2b and mu3b.

sig33b

Value of the covariance between mu3 and mu3b.

indL

Value indicating the value of the independent variable used for the interaction. Typically 1.

mu1_0

Null value for mu1.

mu2_0

Null value for mu2.

mu3_0

Null value for mu3.

mu2b_0

Null value for mu2b.

mu3b_0

Null value for mu3b.

Value

A p-value for the test for the indirect effect.

Examples

sobelTest_ord(1, .1, .25, .01, 0, 0, .15, .01, 0, 0)

Sobel test for the indirect effect - Two ordered mediator path

Description

This function takes the parameter estimates and covariances and performs the Sobel test for two ordered mediators.

Usage

sobelTest_unord(
  mu1,
  sig1,
  mu2,
  sig2,
  mu3,
  sig3,
  mu4,
  sig4,
  mu2b,
  sig2b,
  mu4b,
  sig4b,
  sig12 = 0L,
  sig12b = 0L,
  sig13 = 0L,
  sig14 = 0L,
  sig14b = 0L,
  sig22b = 0L,
  sig23 = 0L,
  sig24 = 0L,
  sig24b = 0L,
  sig2b3 = 0L,
  sig2b4 = 0L,
  sig2b4b = 0L,
  sig34 = 0L,
  sig34b = 0L,
  sig44b = 0L,
  indL = 1L,
  mu1_0 = 0,
  mu2_0 = 0,
  mu3_0 = 0,
  mu4_0 = 0,
  mu2b_0 = 0,
  mu4b_0 = 0
)

Arguments

mu1

Value of the estimate of the independent variable on the first mediator.

sig1

Value of the variance of the estimate of the independent variable on the first mediator.

mu2

Value of the estimate of the first mediator on the response.

sig2

Value of the variance of the estimate of the first mediator on the response.

mu3

Value of the estimate of the independent variable on the second mediator.

sig3

Value of the variance of the estimate of the independent variable on the second mediator.

mu4

Value of the estimate of the second mediator on the response.

sig4

Value of the variance of the estimate of the second mediator on the response.

mu2b

Value of the estimate of the effect of the interaction of the independent and first mediator variable on the response.

sig2b

Value of the variance of the estimate of the effect of the interaction of the independent and first mediator variable on the response.

mu4b

Value of the estimate of the effect of the interaction of the independent and second mediator variable on the response.

sig4b

Value of the variance of the estimate of the effect of the interaction of the independent and second mediator variable on the response.

sig12

Value of the covariance between mu1 and mu2.

sig12b

Value of the covariance between mu1 and mu2b.

sig13

Value of the covariance between mu1 and mu3.

sig14

Value of the covariance between mu1 and mu4.

sig14b

Value of the covariance between mu1 and mu4b.

sig22b

Value of the covariance between mu1 and mu2b.

sig23

Value of the covariance between mu2 and mu3.

sig24

Value of the covariance between mu2 and mu4.

sig24b

Value of the covariance between mu2 and mu4b.

sig2b3

Value of the covariance between mu2b and mu3.

sig2b4

Value of the covariance between mu2b and mu4.

sig2b4b

Value of the covariance between mu2b and mu4b.

sig34

Value of the covariance between mu3 and mu4.

sig34b

Value of the covariance between mu3 and mu4b.

sig44b

Value of the covariance between mu4 and mu4b.

indL

Value indicating the value of the independent variable used for the interaction. Typically 1.

mu1_0

Null value for mu1.

mu2_0

Null value for mu2.

mu3_0

Null value for mu3.

mu4_0

Null value for mu4.

mu2b_0

Null value for mu2b.

mu4b_0

Null value for mu4b.

Value

A p-value for the test for the indirect effect.

Examples

sobelTest_unord(1, .1, .25, .01, 0, 0, .15, .01, 0, 0, 0, 0)