Package {RMediation}

Type:	Package
Title:	Mediation Analysis Confidence Intervals
Version:	1.5.0
Date:	2026-06-18
Author:	Davood Tofighi [aut, cre]
Maintainer:	Davood Tofighi <dtofighi@gmail.com>
Description:	Computes confidence intervals for nonlinear functions of model parameters (e.g., product of k coefficients) in single-level and multilevel structural equation models. Methods include the distribution of the product, Monte Carlo simulation, and bootstrap methods. It also performs the Model-Based Constrained Optimization (MBCO) procedure for hypothesis testing of indirect effects. References: Tofighi, D., and MacKinnon, D. P. (2011). RMediation: An R package for mediation analysis confidence intervals. Behavior Research Methods, 43, 692-700. <doi:10.3758/s13428-011-0076-x>; Tofighi, D., and Kelley, K. (2020). Improved inference in mediation analysis: Introducing the model-based constrained optimization procedure. Psychological Methods, 25(4), 496-515. <doi:10.1037/met0000259>; Tofighi, D. (2020). Bootstrap Model-Based Constrained Optimization Tests of Indirect Effects. Frontiers in Psychology, 10, 2989. <doi:10.3389/fpsyg.2019.02989>.
License:	GPL (≥ 3) | file LICENSE
URL:	https://data-wise.github.io/rmediation/, https://github.com/data-wise/rmediation
BugReports:	https://github.com/data-wise/rmediation/issues
Depends:	R (≥ 4.1.0)
Imports:	checkmate (≥ 2.1.0), graphics (≥ 4.1.0), grDevices (≥ 4.1.0), lavaan (≥ 0.5-20), MASS (≥ 7.3), methods, S7
Suggests:	knitr, medfit (≥ 0.2.0), OpenMx (≥ 2.13), rmarkdown, testthat (≥ 3.0.0)
VignetteBuilder:	knitr
Encoding:	UTF-8
LazyData:	true
RoxygenNote:	7.3.3
Config/testthat/edition:	3
Config/Needs/website:	pkgdown, quarto
NeedsCompilation:	no
Packaged:	2026-06-19 18:09:15 UTC; dt
Repository:	CRAN
Date/Publication:	2026-06-20 02:40:02 UTC

RMediation: Mediation Analysis Confidence Intervals

Description

Computes confidence intervals for nonlinear functions of model parameters (e.g., product of k coefficients) in single-level and multilevel structural equation models. Methods include the distribution of the product, Monte Carlo simulation, and bootstrap methods. It also performs the Model-Based Constrained Optimization (MBCO) procedure for hypothesis testing of indirect effects. References: Tofighi, D., and MacKinnon, D. P. (2011). RMediation: An R package for mediation analysis confidence intervals. Behavior Research Methods, 43, 692-700. doi:10.3758/s13428-011-0076-x; Tofighi, D., and Kelley, K. (2020). Improved inference in mediation analysis: Introducing the model-based constrained optimization procedure. Psychological Methods, 25(4), 496-515. doi:10.1037/met0000259; Tofighi, D. (2020). Bootstrap Model-Based Constrained Optimization Tests of Indirect Effects. Frontiers in Psychology, 10, 2989. doi:10.3389/fpsyg.2019.02989.

Author(s)

Maintainer: Davood Tofighi dtofighi@gmail.com (ORCID)

See Also

Useful links:

• https://data-wise.github.io/rmediation/

• https://github.com/data-wise/rmediation

• Report bugs at https://github.com/data-wise/rmediation/issues

CI for a nonlinear function of coefficients estimates

Description

This function returns a confidence interval (CI) at significance level \alpha for a well-defined nonlinear function of the coefficients in single-level and multilevel structural equation models. The ci function uses the Monte Carlo (type="MC") and the asymptotic normal theory (type="asymp") with the multivariate delta standard error (Asymptotic–Delta) method (Sobel, 1982) to compute a CI. In addition, for each of the methods, when a user specifies plot=TRUE and plotCI=TRUE, a plot of the sampling distribution of the quantity of interest in the quant argument and an overlaid plot of the CI will be produced. When type="all" and plot=TRUE, two overlaid plots of the sampling distributions corresponding to each method will be produced; when plotCI=TRUE, then the overlaid plots of the CIs for both methods will be displayed as well.

Usage

.ci_core(
  mu,
  Sigma,
  quant,
  alpha = 0.05,
  type = "MC",
  plot = FALSE,
  plotCI = FALSE,
  n.mc = 1e+05,
  H0 = FALSE,
  mu0 = NULL,
  Sigma0 = NULL,
  ...
)

Arguments

Value

When type is "MC" or "asymp", ci returns a list that contains:

When type="all", ci returns a list of two objects, each of which a list that contains the results produced by each method as described above.

Author(s)

Davood Tofighi dtofighi@gmail.com

References

Tofighi, D. and MacKinnon, D. P. (2011). RMediation: An R package for mediation analysis confidence intervals. Behavior Research Methods, 43, 692–700. doi:10.3758/s13428-011-0076-x

See Also

medci RMediation-package

Examples

ci(
  mu = c(b1 = 1, b2 = .7, b3 = .6, b4 = .45),
  Sigma = c(.05, 0, 0, 0, .05, 0, 0, .03, 0, .03),
  quant = ~ b1 * b2 * b3 * b4, type = "all", plot = TRUE, plotCI = TRUE
)
# An Example of Conservative Null Sampling Distribution
ci(c(b1 = .3, b2 = .4, b3 = .3), c(.01, 0, 0, .01, 0, .02),
  quant = ~ b1 * b2 * b3, type = "MC", plot = TRUE, plotCI = TRUE,
   H0 = TRUE, mu0 = c(b1 = .3, b2 = .4, b3 = 0)
)
# An Example of Less Conservative Null Sampling Distribution
ci(c(b1 = .3, b2 = .4, b3 = .3), c(.01, 0, 0, .01, 0, .02),
  quant = ~ b1 * b2 * b3, type = "MC", plot = TRUE, plotCI = TRUE,
  H0 = TRUE, mu0 = c(b1 = 0, b2 = .4, b3 = 0.1)
)

Internal: Compute CDF using Distribution of Product

Description

Computes the cumulative distribution function P(XY \le q) for the product of two normal random variables using numerical integration (Meeker & Escobar, 1994).

Usage

.compute_cdf_dop(object, q)

Arguments

Value

Probability P(XY \le q)

Internal: Compute CDF using Monte Carlo

Description

Computes the cumulative distribution function P(XY \le q) for the product of normal random variables using Monte Carlo simulation. Works for any number of variables.

Usage

.compute_cdf_mc(object, q, n.mc = 1e+05)

Arguments

Value

Probability P(XY \le q)

Internal: Compute CI using Asymptotic method (Delta method)

Description

Computes asymptotic confidence intervals using normal approximation (Sobel test). The standard error is computed using Craig's (1936) formula:

SE = \sqrt{\sigma_y^2\mu_x^2 + \sigma_x^2\mu_y^2 + 2\mu_x\mu_y\rho\sigma_x\sigma_y + \sigma_x^2\sigma_y^2 + \sigma_x^2\sigma_y^2\rho^2}

and the CI is Estimate \pm z_{1-\alpha/2} \times SE, where z_{1-\alpha/2} is the standard normal quantile.

Usage

.compute_ci_asymp(object, alpha = 0.05)

Arguments

Value

List with CI, Estimate, SE

Internal: Compute CI using Distribution of Product (Meeker & Escobar 1994)

Description

Computes confidence intervals for the product of two normal random variables using the exact distribution method. The point estimate is \mu_x\mu_y + \sigma_{xy} and the standard error follows Craig (1936):

SE = \sqrt{\sigma_y^2\mu_x^2 + \sigma_x^2\mu_y^2 + 2\mu_x\mu_y\rho\sigma_x\sigma_y + \sigma_x^2\sigma_y^2 + \sigma_x^2\sigma_y^2\rho^2}

Usage

.compute_ci_dop(object, alpha = 0.05)

Arguments

Value

List with CI, Estimate, SE

Internal: Compute CI using Monte Carlo method

Description

Internal: Compute CI using Monte Carlo method

Usage

.compute_ci_mc(object, alpha = 0.05, n.mc = 1e+05)

Arguments

Value

List with CI, Estimate, SE, MC.Error

Internal: Compute quantile using Distribution of Product

Description

Internal: Compute quantile using Distribution of Product

Usage

.compute_quantile_dop(object, p, lower.tail = TRUE)

Arguments

Value

Quantile value

Internal: Compute quantile using Meeker & Escobar (1994) algorithm

Description

Internal: Compute quantile using Meeker & Escobar (1994) algorithm

Usage

.compute_quantile_dop_internal(
  p,
  mu.x,
  mu.y,
  se.x,
  se.y,
  rho = 0,
  lower.tail = TRUE
)

Internal: Compute quantile using Monte Carlo

Description

Internal: Compute quantile using Monte Carlo

Usage

.compute_quantile_mc(object, p, n.mc = 1e+05, lower.tail = TRUE)

Arguments

Value

Quantile value

Helper to format S7 result to legacy list format

Description

Helper to format S7 result to legacy list format

Usage

.format_medci_result(s7_result, alpha)

MBCO Result Class

Description

A class representing the results of a Model-Based Constrained Optimization (MBCO) test.

Usage

MBCOResult(
  statistic = integer(0),
  df = integer(0),
  p_value = integer(0),
  type = character(0)
)

Arguments

ProductNormal Class

Description

Represents the distribution of the product of normal random variables.

Usage

ProductNormal(mu = integer(0), Sigma = integer(0))

Arguments

Enhanced ProductNormal constructor with better validation

Description

Enhanced ProductNormal constructor with better validation

Usage

ProductNormal2(mu, Sigma, validate = TRUE)

Arguments

Utility function to create ProductNormal from lavaan parameter estimates

Description

Utility function to create ProductNormal from lavaan parameter estimates

Usage

ProductNormal_from_lavaan(lavaan_model, param_names)

Arguments

Value

A ProductNormal object

Cumulative Distribution Function

Description

Generic function for computing cumulative distribution function.

Usage

cdf(object, ...)

Arguments

Confidence Interval

Description

Generic function for computing confidence intervals.

Usage

ci(mu, ...)

Arguments

Confidence Interval for MediationData Objects

Description

Computes confidence intervals for the indirect effect from a medfit MediationData object using RMediation's methods (DOP, Monte Carlo, etc.).

Usage

ci_mediation_data(mu, level = 0.95, type = "dop", n.mc = 1e+05, ...)

ci_serial_mediation_data(mu, level = 0.95, type = "MC", n.mc = 1e+05, ...)

Arguments

Details

This method extracts the a and b path coefficients from the MediationData object, along with their standard errors and covariance, and computes confidence intervals using RMediation's methods.

Method Options

• "dop": Distribution of Product method. Uses the exact or approximate distribution of the product of two normal random variables. Recommended for most applications.

• "MC": Monte Carlo simulation. Samples from the joint distribution of a and b to estimate the CI. Use n.mc to control precision.

• "asymp": Asymptotic normal approximation using the delta method. Fast but may be inaccurate for small samples or non-normal distributions.

Value

A list with components:

See Also

ci for the generic function, MediationData for the input class, ProductNormal for the underlying distribution class

Examples

## Not run: 
library(medfit)
library(RMediation)

# Fit mediation models
fit_m <- lm(M ~ X + C, data = mydata)
fit_y <- lm(Y ~ X + M + C, data = mydata)

# Extract mediation structure
med_data <- extract_mediation(fit_m, model_y = fit_y,
                               treatment = "X", mediator = "M")

# Compute CI using Distribution of Product
ci(med_data, type = "dop")

# Compute CI using Monte Carlo
ci(med_data, type = "MC", n.mc = 10000)

## End(Not run)

Distribution Quantile Function

Description

Compute quantiles for distribution objects. This function computes quantiles for product normal distributions, not data quantiles (use stats::quantile for data).

Usage

dist_quantile(object, ...)

Arguments

Method to check if ProductNormal object is properly specified for computation

Description

Method to check if ProductNormal object is properly specified for computation

Usage

is_valid_for_computation(object)

Arguments

Value

TRUE if object is valid for computation methods

Model-based Constrained Optimization (MBCO) Chi-squared Test

Description

This function computes asymptotic MBCO chi-squared test for a smooth function of model parameters including a function of indirect effects.

Usage

mbco(h0, h1, ...)

Arguments

Value

An object of class MBCOResult containing

Author(s)

Davood Tofighi dtofighi@gmail.com

Examples

## Not run: 
data(memory_exp)
memory_exp$x <- as.numeric(memory_exp$x)-1 # manually creating dummy codes
endVar <- c('x', 'repetition', 'imagery', 'recall')
manifests <- c('x', 'repetition', 'imagery', 'recall')
full_model <- OpenMx::mxModel(
 "memory_example",
 type = "RAM",
 manifestVars = manifests,
 OpenMx::mxPath(
   from = "x",
   to = endVar,
   arrows = 1,
   free = TRUE,
   values = .2,
   labels = c("a1", "a2", "cp")
 ),
 OpenMx::mxPath(
   from = 'repetition',
  to = 'recall',
  arrows = 1,
   free = TRUE,
   values = .2,
   labels = 'b1'
 ),
 OpenMx::mxPath(
   from = 'imagery',
 to = 'recall',
 arrows = 1,
 free = TRUE,
 values = .2,
 labels = "b2"
),
OpenMx::mxPath(
 from = manifests,
 arrows = 2,
 free = TRUE,
 values = .8
),
OpenMx::mxPath(
 from = "one",
 to = endVar,
 arrows = 1,
 free = TRUE,
 values = .1
),
OpenMx::mxAlgebra(a1 * b1, name = "ind1"),
OpenMx::mxAlgebra(a2 * b2, name = "ind2"),
OpenMx::mxCI("ind1", type = "both"),
OpenMx::mxCI("ind2", type = "both"),
OpenMx::mxData(observed = memory_exp, type = "raw")
)
## Reduced  Model for indirect effect: a1*b1
null_model1 <- OpenMx::mxModel(
model= full_model,
name = "Null Model 1",
OpenMx::mxConstraint(ind1 == 0, name = "ind1_eq0_constr")
)
full_model <- OpenMx::mxTryHard(full_model, checkHess=FALSE, silent = TRUE )
null_model1 <- OpenMx::mxTryHard(null_model1, checkHess=FALSE, silent = TRUE )
mbco(null_model1,full_model)

## End(Not run)

Confidence Interval for the Mediated Effect

Description

Produces confidence intervals for the mediated effect and the product of two normal random variables

Produces confidence intervals for the mediated effect and the product of two normal random variables

Usage

medci(
  mu.x,
  mu.y,
  se.x,
  se.y,
  rho = 0,
  alpha = 0.05,
  type = "dop",
  plot = FALSE,
  plotCI = FALSE,
  n.mc = 1e+05,
  ...
)

medci(
  mu.x,
  mu.y,
  se.x,
  se.y,
  rho = 0,
  alpha = 0.05,
  type = "dop",
  plot = FALSE,
  plotCI = FALSE,
  n.mc = 1e+05,
  ...
)

Arguments

Details

This function returns a confidence interval at significance level \alpha for the mediated effect (product of two normal random variables). To obtain a confidence interval using a specific method, the argument type should be specified. The default is type="dop", which uses the code we wrote in R to implement the distribution of product of the coefficients method described by Meeker and Escobar (1994) to evaluate the CDF of the distribution of product. type="MC" uses the Monte Carlo approach to compute the confidence interval (Tofighi & MacKinnon, 2011). type="asymp" produces the asymptotic normal confidence interval. Note that except for the Monte Carlo method, the standard error for the indirect effect is based on the analytical results by Craig (1936):

SE = \sqrt{\sigma_y^2 \mu_x^2 + \sigma_x^2 \mu_y^2 + 2\mu_x\mu_y\rho\sigma_x\sigma_y + \sigma_x^2\sigma_y^2 + \sigma_x^2\sigma_y^2\rho^2}

where \sigma_x and \sigma_y are the standard errors of x and y, respectively. In addition, the estimate of the indirect effect is \mu_x\mu_y + \sigma_{xy}, where \sigma_{xy} is the covariance between x and y. The argument type="all" prints confidence intervals using all available methods.

This function returns a (1-\alpha)% confidence interval for the mediated effect (product of two normal random variables). To obtain a confidence interval using a specific method, the argument type should be specified. The default is type="dop", which uses the code we wrote in R to implement the distribution of product of the coefficients method described by Meeker and Escobar (1994) to evaluate the CDF of the distribution of product. type="MC" uses the Monte Carlo approach to compute the confidence interval (Tofighi & MacKinnon, 2011). type="asymp" produces the asymptotic normal confidence interval. Note that except for the Monte Carlo method, the standard error for the indirect effect is based on the analytical results by Craig (1936):

\sqrt(se.y^2 \mu.x^2+se.x^2 \mu.y^2+2 \mu.x \mu.y \rho se.x se.y+ se.x^2 se.y^2+se.x^2 se.y^2 \rho^2)

. In addition, the estimate of indirect effect is \mu.x \mu.y +\sigma.xy ; type="all" prints confidence intervals using all four options.

Value

A vector of lower confidence limit and upper confidence limit. When type is "prodclin" (default), "DOP", "MC" or "asymp", medci returns a list that contains:

Note that when type="all", medci returns a list of four objects, each of which a list that contains the results produced by each method as described above.

A vector of lower confidence limit and upper confidence limit. When type is "prodclin" (default), "DOP", "MC" or "asymp", medci returns a list that contains:

Note that when type="all", medci returns a list of four objects, each of which a list that contains the results produced by each method as described above.

Author(s)

Davood Tofighi dtofighi@gmail.com

References

Craig, C. C. (1936). On the frequency function of xy. The Annals of Mathematical Statistics, 7, 1–15.

MacKinnon, D. P., Fritz, M. S., Williams, J., and Lockwood, C. M. (2007). Distribution of the product confidence limits for the indirect effect: Program PRODCLIN. Behavior Research Methods, 39, 384–389.

Meeker, W. and Escobar, L. (1994). An algorithm to compute the CDF of the product of two normal random variables. Communications in Statistics: Simulation and Computation, 23, 271–280.

Tofighi, D. and MacKinnon, D. P. (2011). RMediation: An R package for mediation analysis confidence intervals. Behavior Research Methods, 43, 692–700. doi:10.3758/s13428-011-0076-x

Craig, C. C. (1936). On the frequency function of xy. The Annals of Mathematical Statistics, 7, 1–15.

MacKinnon, D. P., Fritz, M. S., Williams, J., and Lockwood, C. M. (2007). Distribution of the product confidence limits for the indirect effect: Program PRODCLIN. Behavior Research Methods, 39, 384–389.

Meeker, W. and Escobar, L. (1994). An algorithm to compute the CDF of the product of two normal random variables. Communications in Statistics: Simulation and Computation, 23, 271–280.

Tofighi, D. and MacKinnon, D. P. (2011). RMediation: An R package for mediation analysis confidence intervals. Behavior Research Methods, 43, 692–700. doi:10.3758/s13428-011-0076-x

See Also

qprodnormal pprodnormal ci RMediation-package

qprodnormal pprodnormal ci RMediation-package

Examples

## Example 1
res <- medci(
  mu.x = .2, mu.y = .4, se.x = 1, se.y = 1, rho = 0, alpha = .05,
  type = "dop", plot = TRUE, plotCI = TRUE
)
## Example 2
res <- medci(mu.x = .2, mu.y = .4, se.x = 1, se.y = 1, rho = 0,
 alpha = .05, type = "all", plot = TRUE, plotCI = TRUE)
## Example 1
res <- medci(
  mu.x = .2, mu.y = .4, se.x = 1, se.y = 1, rho = 0, alpha = .05,
  type = "dop", plot = TRUE, plotCI = TRUE
)
## Example 2
res <- medci(mu.x = .2, mu.y = .4, se.x = 1, se.y = 1, rho = 0,
 alpha = .05, type = "all", plot = TRUE, plotCI = TRUE)

Confidence Interval for the Mediated Effect (PROTOTYPE S7 Wrapper)

Description

Confidence Interval for the Mediated Effect (PROTOTYPE S7 Wrapper)

Usage

medci_prototype(
  mu.x,
  mu.y,
  se.x,
  se.y,
  rho = 0,
  alpha = 0.05,
  type = "dop",
  plot = FALSE,
  plotCI = FALSE,
  n.mc = 1e+05,
  ...
)

Arguments

Memory Experiment Data Description from MacKinnon et al., 2018

Description

Data were obtained from eight replicated experiments. The data were collected on the first day of class as part of the first Dr. MacKinnon's (2018) classroom teaching. The pedagogical value of the experiment was that students would have first-hand knowledge of the experiment thereby increasing their understanding of course concepts. Permission to use the data was obtained from the university Institutional Review Board.

Usage

data(memory_exp)

Format

A data frame with 369 rows and 5 variables:

study

Replication ID, ranges from 1 to 8

repetition

Use of repetition rehearsal technique, ranges from 1 to 12

recall

Total words recalled out of 20 words, ranges from 3 to 20

imagery

Use of imagery rehearsal technique on a 1 to 9 scale

x

A factor with two levels: "repetition" (primary rehearsal) or "imagery" (secondary rehearsal)

Note

If you use the data set, please cite the original article by MacKinnon et al. (2018) cited below.

Source

doi:10.1037/met0000174.supp

References

MacKinnon, D. P., Valente, M. J., & Wurpts, I. C. (2018). Benchmark validation of statistical models: Application to mediation analysis of imagery and memory. Psychological Methods, 23, 654–671. doi:10.1037/met0000174

Probability (percentile) for the Monte Carlo Sampling Distribution of a nonlinear function of coefficients estimates

Description

This function returns a probability corresponding to the quantile q.

Usage

pMC(q, mu, Sigma, quant, lower.tail = TRUE, n.mc = 1e+05, ...)

Arguments

Value

scalar probability value.

Author(s)

Davood Tofighi dtofighi@gmail.com

References

Tofighi, D. and MacKinnon, D. P. (2011). RMediation: An R package for mediation analysis confidence intervals. Behavior Research Methods, 43, 692–700. doi:10.3758/s13428-011-0076-x

Examples

pMC(.2,
  mu = c(b1 = 1, b2 = .7, b3 = .6, b4 = .45), Sigma = c(.05, 0, 0, 0, .05, 0, 0, .03, 0, .03),
  quant = ~ b1 * b2 * b3 * b4
)

Percentile for the Distribution of Product of Two Normal Variables

Description

Generates percentiles (100 based quantiles) for the distribution of product of two normal random variables and the mediated effect

Usage

pprodnormal(
  q,
  mu.x,
  mu.y,
  se.x = 1,
  se.y = 1,
  rho = 0,
  lower.tail = TRUE,
  type = "dop",
  n.mc = 1e+05
)

Arguments

Details

This function returns the percentile (probability) and the associated error for the distribution of product of mediated effect (two normal random variables). To obtain a percentile using a specific method, the argument type should be specified. The default method is type="dop", which is based on the method described by Meeker and Escobar (1994) to evaluate the CDF of the distribution of product of two normal random variables. type="MC" uses the Monte Carlo approach (Tofighi & MacKinnon, 2011). type="all" prints percentiles using all three options. For the method type="dop", the error is the modulus of absolute error for the numerical integration (for more information see Meeker and Escobar, 1994). For type="MC", the error refers to the Monte Carlo error.

Value

An object of the type list that contains the following values:

Author(s)

Davood Tofighi dtofighi@gmail.com

References

Tofighi, D. and MacKinnon, D. P. (2011). RMediation: An R package for mediation analysis confidence intervals. Behavior Research Methods, 43, 692–700. doi:10.3758/s13428-011-0076-x

See Also

medci RMediation-package

Examples

pprodnormal(q = 0, mu.x = .5, mu.y = .3, se.x = 1, se.y = 1, rho = 0, type = "all")

Quantile for the Monte Carlo Sampling Distribution of a nonlinear function of coefficients estimates

Description

This function returns a quantile corresponding to the probability p.

Usage

qMC(p, mu, Sigma, quant, n.mc = 1e+05, ...)

Arguments

Value

scalar quantile value.

Author(s)

Davood Tofighi dtofighi@gmail.com

References

Tofighi, D. and MacKinnon, D. P. (2011). RMediation: An R package for mediation analysis confidence intervals. Behavior Research Methods, 43, 692–700. doi:10.3758/s13428-011-0076-x

Examples

qMC(.05,
  mu = c(b1 = 1, b2 = .7, b3 = .6, b4 = .45), Sigma = c(.05, 0, 0, 0, .05, 0, 0, .03, 0, .03),
  quant = ~ b1 * b2 * b3 * b4
)

Quantile for the Distribution of Product of Two Normal Variables

Description

Generates quantiles for the distribution of product of two normal random variables

Usage

qprodnormal(
  p,
  mu.x,
  mu.y,
  se.x,
  se.y,
  rho = 0,
  lower.tail = TRUE,
  type = "dop",
  n.mc = 1e+05
)

Arguments

Details

This function returns a quantile and the associated error (accuracy) corresponding the requested percentile (probability) p of the distribution of product of mediated effect (product of two normal random variables). To obtain a quantile using a specific method, the argument type should be specified. The default method is type="dop", which uses the method described by Meeker and Escobar (1994) to evaluate the CDF of the distribution of product of two normal variables. type="MC" uses the Monte Carlo approach (Tofighi & MacKinnon, 2011). type="all" prints quantiles using all three options. For the method type="dop", the error is the modulus of absolute error for the numerical integration (for more information see Meeker and Escobar, 1994). For type="MC", the error refers to the Monte Carlo error.

Value

An object of the type list that contains the following values:

Author(s)

Davood Tofighi dtofighi@gmail.com

References

Tofighi, D. and MacKinnon, D. P. (2011). RMediation: An R package for mediation analysis confidence intervals. Behavior Research Methods, 43, 692–700. doi:10.3758/s13428-011-0076-x

See Also

medci RMediation-package

Examples

## lower tail
qprodnormal(
  p = .1, mu.x = .5, mu.y = .3, se.x = 1, se.y = 1, rho = 0,
  lower.tail = TRUE, type = "all"
)
## upper tail
qprodnormal(
  p = .1, mu.x = .5, mu.y = .3, se.x = 1, se.y = 1, rho = 0,
  lower.tail = FALSE, type = "all"
)

Tidy generic function

Description

Tidy generic function

Usage

tidy(x, ...)

Arguments

Value

A tibble or data.frame with tidy output

Creates a data.frame for a log-likelihood object

Description

Creates a data.frame for a log-likelihood object

Usage

## S3 method for class 'logLik'
tidy(x, ...)

Arguments

Value

A data.frame with columns:

term

The term name

estimate

The log-likelihood value

df

The degrees of freedom

Author(s)

Davood Tofighi dtofighi@gmail.com

See Also

logLik

Examples

fit <- lm(mpg ~ wt, data = mtcars)
logLik_fit <- logLik(fit)
tidy(logLik_fit)

Enhanced validation and utility functions for ProductNormal class

Description

Enhanced validation and utility functions for ProductNormal class

Additional validation for ProductNormal objects

Description

Additional validation for ProductNormal objects

Usage

validate_ProductNormal(object, verbose = FALSE)

Arguments

Value

TRUE if valid, throws error if invalid