Package 'RMediation' reference manual

Title:	Mediation Analysis Confidence Intervals
Description:	We provide functions to compute confidence intervals for a well-defined nonlinear function of the model parameters (e.g., product of k coefficients) in single--level and multilevel structural equation models. It also computes a chi-square test statistic for a function of indirect effects. '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. (2020). Bootstrap Model-Based Constrained Optimization Tests of Indirect Effects. Frontiers in Psychology, 10, 2989. <doi:10.3389/fpsyg.2019.02989>.
Authors:	Davood Tofighi [aut, cre]
Maintainer:	Davood Tofighi <[email protected]>
License:	GPL (>= 3)
Version:	2.0.0
Built:	2024-10-30 03:46:14 UTC
Source:	https://github.com/quantpsych/rmediation

CI for a nonlinear function of coefficients estimates

Description

This function returns a ( $1-\alpha$ )% confidence interval (CI) 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(
  mu,
  Sigma,
  quant,
  alpha = 0.05,
  type = "MC",
  plot = FALSE,
  plotCI = FALSE,
  n.mc = 1e+06,
  H0 = FALSE,
  mu0 = NULL,
  Sigma0 = NULL,
  ...
)
ci(
  mu,
  Sigma,
  quant,
  alpha = 0.05,
  type = "MC",
  plot = FALSE,
  plotCI = FALSE,
  n.mc = 1e+06,
  H0 = FALSE,
  mu0 = NULL,
  Sigma0 = NULL,
  ...
)

Arguments

`mu`	(1) a vector of means (e.g., coefficient estimates) for the normal random variables. A user can assign a name to each mean value, e.g., `mu=c(b1=.1,b2=3)`; otherwise, the coefficient names are assigned automatically as follows: `b1,b2,...`. Or, (2) a lavaan object.
`Sigma`	either a covariance matrix or a vector that stacks all the columns of the lower triangle variance–covariance matrix one underneath the other.
`quant`	quantity of interest, which is a nonlinear/linear function of the model parameters. Argument `quant` is a formula that must start with the symbol "tilde" (`~`): e.g., `~b1b2b3*b4`. The names of coefficients must conform to the names provided in the argument `mu` or to the default names, i.e., `b1,b2,...`.
`alpha`	significance level for the CI. The default value is .05.
`type`	method used to compute a CI. It takes on the values `"MC"` (default) for Monte Carlo, `"asymp"` for Asymptotic–Delta, or `"all"` that produces CIs using both methods.
`plot`	when `TRUE`, plot the approximate sampling distribution of the quantity of interest using the specified method(s) in the argument `type`. The default value is `FALSE`. When `type="all"`, superimposed density plots generated by both methods are displayed.
`plotCI`	when `TRUE`, overlays a CI plot with error bars on the density plot of the sampling distribution of `quant`. When `type="all"`, the superimposed CI plots generated by both methods are added to the density plots. Note that to obtain a CI plot, one must also specify `plot="TRUE"`. The default value is `FALSE`.
`n.mc`	Monte Carlo sample size. The default sample size is 1e+6.
`H0`	False. If `TRUE`, it will estimate the sampling distribution of $H_{0}:f(\bm b)=0$ . See the arguments `mu0` and `Sigma0`.
`mu0`	a vector of means (e.g., coefficient estimates) for the normal random variables that satisfy the null hypothesis $H_{0}:f(\bm b)=0$ . If it is not provided, smallest z value of `mu` is zet to zero.
`Sigma0`	either a covariance matrix or a vector that stacks all the columns of the lower triangle variance–covariance matrix one underneath the other. If it is not provided, then `Sigma` is used instead.
`...`	additional arguments.

Value

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

`(\eqn{1-\alpha})% CI`	a vector of lower and upper confidence limits,
`Estimate`	a point estimate of the quantity of interest,
`SE`	standard error of the quantity of interest,
`MC Error`	When `type="MC"`, error of the Monte Carlo estimate.

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.

Note

A shiny web application for Monte Carlo method of this function is available at https://amplab.shinyapps.io/MEDMC/

Author(s)

Davood Tofighi [email protected]

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

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)
)
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)
)

Function to check if lavaan model syntax is valid

Description

This function checks if the lavaan model syntax is valid. It does so by attempting to parse and fit the model in a safe environment. If the model syntax is invalid, the function will return an error message.

Usage

is_valid_lav_syntax(model, data = NULL)
is_valid_lav_syntax(model, data = NULL)

Arguments

`model`	A character string representing the lavaan model to be fitted.
`data`	A data frame containing the observed variables.

Value

A logical value indicating whether the model syntax is valid.

Author(s)

Davood Tofighi [email protected]

Examples

bad_model <- "y ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9"
data(HolzingerSwineford1939, package = "lavaan")
is_valid_lav_syntax(bad_model, HolzingerSwineford1939)
good_model <- "visual =~ x1 + x2 + x3
textual =~ x4 + x5 + x6
speed =~ x7 + x8 + x9
visual ~ speed
textual ~ speed"
is_valid_lav_syntax(good_model, HolzingerSwineford1939)
bad_model <- "y ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9"
data(HolzingerSwineford1939, package = "lavaan")
is_valid_lav_syntax(bad_model, HolzingerSwineford1939)
good_model <- "visual =~ x1 + x2 + x3
textual =~ x4 + x5 + x6
speed =~ x7 + x8 + x9
visual ~ speed
textual ~ speed"
is_valid_lav_syntax(good_model, HolzingerSwineford1939)

Fit SEM Model to Each Dataset in a MIDS Object Without Pooling

Description

Fits a SEM model to each dataset in a mids object without pooling the results. This function is an extension for the lavaan::sem() function to handle mice::mids objects from the mice package. It allows for both a SEM model syntax as a character string or a pre-fitted lavaan model object.

Usage

lav_mice(model, mids, ...)
lav_mice(model, mids, ...)

Arguments

`model`	Either a character string representing the SEM model to be fitted or a pre-fitted lavaan model object.
`mids`	A `mids` object from the mice package.
`...`	Additional arguments to be passed to `lavaan::sem()`.

Value

A list of lavaan model fits, one for each imputed dataset.

Author(s)

Davood Tofighi [email protected]

Examples

## Not run: 
# library(mice)
# library(lavaan)
# Load Holzinger and Swineford (1939) dataset
data("HolzingerSwineford1939", package = "lavaan")
# Introduce missing data
df_complete <- na.omit(HolzingerSwineford1939)
amp <- mice::ampute(df_complete, prop = 0.2, mech = "MAR")
data_with_missing <- amp$amp

# Perform multiple imputation
imputed_data <- mice::mice(data_with_missing, m = 3, maxit = 5, seed = 12345, printFlag = FALSE)

# fit the Holzinger and Swineford (1939) example model
HS_model <- " visual  =~ x1 + x2 + x3
             textual =~ x4 + x5 + x6
             speed   =~ x7 + x8 + x9 "
# Fit the SEM model without running
fit_HS <- lavaan::sem(HS_model, data = data_with_missing, do.fit = FALSE)
# Fit the SEM model without pooling to each imputed dataset
fit_list1 <- lav_mice(HS_model, imputed_data)
# 'fit_list1' now contains a list of lavaan objects, one for each imputed dataset
# Fit the SEM model without pooling to each imputed dataset using a pre-fitted model object
fit_list2 <- lav_mice(fit_HS, imputed_data)
# 'fit_list2' now contains a list of lavaan objects, one for each imputed dataset

## End(Not run)
## Not run: 
# library(mice)
# library(lavaan)
# Load Holzinger and Swineford (1939) dataset
data("HolzingerSwineford1939", package = "lavaan")
# Introduce missing data
df_complete <- na.omit(HolzingerSwineford1939)
amp <- mice::ampute(df_complete, prop = 0.2, mech = "MAR")
data_with_missing <- amp$amp

# Perform multiple imputation
imputed_data <- mice::mice(data_with_missing, m = 3, maxit = 5, seed = 12345, printFlag = FALSE)

# fit the Holzinger and Swineford (1939) example model
HS_model <- " visual  =~ x1 + x2 + x3
             textual =~ x4 + x5 + x6
             speed   =~ x7 + x8 + x9 "
# Fit the SEM model without running
fit_HS <- lavaan::sem(HS_model, data = data_with_missing, do.fit = FALSE)
# Fit the SEM model without pooling to each imputed dataset
fit_list1 <- lav_mice(HS_model, imputed_data)
# 'fit_list1' now contains a list of lavaan objects, one for each imputed dataset
# Fit the SEM model without pooling to each imputed dataset using a pre-fitted model object
fit_list2 <- lav_mice(fit_HS, imputed_data)
# 'fit_list2' now contains a list of lavaan objects, one for each imputed dataset

## End(Not run)

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 = NULL,
  h1 = NULL,
  R = 10L,
  type = "asymp",
  alpha = 0.05,
  checkHess = "No",
  checkSE = "No",
  optim = "SLSQP",
  precision = 1e-09
)
mbco(
  h0 = NULL,
  h1 = NULL,
  R = 10L,
  type = "asymp",
  alpha = 0.05,
  checkHess = "No",
  checkSE = "No",
  optim = "SLSQP",
  precision = 1e-09
)

Arguments

`h0`	An `OpenMx` model estimated under a null hypothesis, which is a more constrained model
`h1`	An `OpenMx` model estimated under an alternative hypothesis, which is a less constrained model. This is usually a model hypothesized by a researcher.
`R`	The number of bootstrap draws.
`type`	If 'asymp' (default), the asymptotic MBCO chi-squares test comparing fit of h0 and h1. If 'parametric', the parametric bootstrap MBCO chi-squared test is computed. If 'semi', the semi-parametric MBCO chi-squared is computed.
`alpha`	Significance level with the default value of .05
`checkHess`	If 'No' (default), the Hessian matrix would not be calculated.
`checkSE`	if 'No' (default), the standard errors would not be calculated.
`optim`	Choose optimizer available in OpenMx. The default optimizer is "SLSQP". Other optimizer choices are available. See mxOption for more details.
`precision`	Functional precision. The default value is set to 1e-9. See mxOption for more details.

Value

A list that contains

`chisq`	asymptotic chi-squared test statistic value
`df`	chi-squared df
`p`	chi-squared p-value computed based on the method specified by the argument `type`

Author(s)

Davood Tofighi [email protected]

References

Tofighi, D., & Kelley, K. (2020). Indirect effects in sequential mediation models: Evaluating methods for hypothesis testing and confidence interval formation. Multivariate Behavioral Research, 55, 188–210. doi:10.1080/00273171.2019.1618545

Tofighi, D. (2020). Bootstrap Model-Based Constrained Optimization Tests of Indirect Effects. Frontiers in Psychology, 10, 2989. doi:10.3389/fpsyg.2019.02989

Examples

library(OpenMx)
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 <- mxModel(
  "memory_example",
  type = "RAM",
  manifestVars = manifests,
  mxPath(
    from = "x",
    to = endVar,
    arrows = 1,
    free = TRUE,
    values = .2,
    labels = c("a1", "a2", "cp")
  ),
  mxPath(
    from = "repetition",
    to = "recall",
    arrows = 1,
    free = TRUE,
    values = .2,
    labels = "b1"
  ),
  mxPath(
    from = "imagery",
    to = "recall",
    arrows = 1,
    free = TRUE,
    values = .2,
    labels = "b2"
  ),
  mxPath(
    from = manifests,
    arrows = 2,
    free = TRUE,
    values = .8
  ),
  mxPath(
    from = "one",
    to = endVar,
    arrows = 1,
    free = TRUE,
    values = .1
  ),
  mxAlgebra(a1 * b1, name = "ind1"),
  mxAlgebra(a2 * b2, name = "ind2"),
  mxCI("ind1", type = "both"),
  mxCI("ind2", type = "both"),
  mxData(observed = memory_exp, type = "raw")
)
## Reduced  Model for indirect effect: a1*b1
null_model1 <- mxModel(
  model = full_model,
  name = "Null Model 1",
  mxConstraint(ind1 == 0, name = "ind1_eq0_constr")
)
full_model <- mxTryHard(full_model, checkHess = FALSE, silent = TRUE)
null_model1 <- mxTryHard(null_model1, checkHess = FALSE, silent = TRUE)
mbco(null_model1, full_model)
library(OpenMx)
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 <- mxModel(
  "memory_example",
  type = "RAM",
  manifestVars = manifests,
  mxPath(
    from = "x",
    to = endVar,
    arrows = 1,
    free = TRUE,
    values = .2,
    labels = c("a1", "a2", "cp")
  ),
  mxPath(
    from = "repetition",
    to = "recall",
    arrows = 1,
    free = TRUE,
    values = .2,
    labels = "b1"
  ),
  mxPath(
    from = "imagery",
    to = "recall",
    arrows = 1,
    free = TRUE,
    values = .2,
    labels = "b2"
  ),
  mxPath(
    from = manifests,
    arrows = 2,
    free = TRUE,
    values = .8
  ),
  mxPath(
    from = "one",
    to = endVar,
    arrows = 1,
    free = TRUE,
    values = .1
  ),
  mxAlgebra(a1 * b1, name = "ind1"),
  mxAlgebra(a2 * b2, name = "ind2"),
  mxCI("ind1", type = "both"),
  mxCI("ind2", type = "both"),
  mxData(observed = memory_exp, type = "raw")
)
## Reduced  Model for indirect effect: a1*b1
null_model1 <- mxModel(
  model = full_model,
  name = "Null Model 1",
  mxConstraint(ind1 == 0, name = "ind1_eq0_constr")
)
full_model <- mxTryHard(full_model, checkHess = FALSE, silent = TRUE)
null_model1 <- mxTryHard(null_model1, checkHess = FALSE, silent = TRUE)
mbco(null_model1, full_model)

Confidence Interval for the Mediated Effect

Description

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

`mu.x`	mean of $x$
`mu.y`	mean of $y$
`se.x`	standard error (deviation) of $x$
`se.y`	standard error (deviation) of $y$
`rho`	correlation between $x$ and $y$ , where -1 <`rho` < 1. The default value is 0.
`alpha`	significance level for the confidence interval. The default value is .05.
`type`	method used to compute confidence interval. It takes on the values `"dop"` (default), `"MC"`, `"asymp"` or `"all"`
`plot`	when `TRUE`, plots the distribution of `n.mc` data points from the distribution of product of two normal random variables using the density estimates provided by the function `density`. The default value is `FALSE`.
`plotCI`	when `TRUE`, overlays a confidence interval with error bars on the plot for the mediated effect. Note that to obtain the CI plot, one must also specify `plot="TRUE"`. The default value is `FALSE`.
`n.mc`	when `type="MC"`, `n.mc` determines the sample size for the Monte Carlo method. The default sample size is 1E5.
`...`	additional arguments to be passed on to the function.

Details

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:

`(\eqn{1-\alpha})% CI`	a vector of lower and upper confidence limits,
`Estimate`	a point estimate of the quantity of interest,
`SE`	standard error of the quantity of interest,
`MC Error`	When `type="MC"`, error of the Monte Carlo estimate.

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 [email protected]

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

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)

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)
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 on a 1 to 9 scale
recall: Total words recalled out of 20 words
imagery: Use of imagery rehearsal technique on a 1 to 9 scale
x: A factor with two levels: repetition or primary rehearsal = 0, imagery or secondary rehearsal = 1

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

Fit OpenMx model to multiply imputed datasets

Description

This function fits an OpenMx model to each imputed dataset in a 'mids' object from the 'mice' package. The function returns a list of OpenMx model fits.

Usage

mx_mice(model, mids, ...)
mx_mice(model, mids, ...)

Arguments

`model`	An OpenMx model object.
`mids`	A 'mids' object from the 'mice' package.
`...`	Additional arguments to be passed to 'mxRun'.

Value

A list of OpenMx model fits.

Author(s)

Davood Tofighi [email protected]

Examples

## Not run: 
# library(OpenMx)
# library(mice)
# Fit a model to multiply imputed datasets
data("HolzingerSwineford1939", package = "lavaan")
# Introduce missing data
df_complete <- na.omit(HolzingerSwineford1939)
amp <- mice::ampute(df_complete, prop = 0.2, mech = "MAR")
df_incomplete <- amp$amp
# Perform multiple imputation
imputed_data <- mice(df_incomplete, m = 3, method = "pmm", maxit = 5, seed = 12345)
# Simple SEM model specification with OpenMx
manifestVars <- paste0("x", 1:9)
latVar <- c("visual", "textual", "speed")
model <- mxModel("Simple SEM",
  type = "RAM",
  manifestVars = manifestVars,
  latentVars = latVar,
  mxPath(from = "visual", to = c("x1", "x2", "x3")),
  mxPath(from = "textual", to = c("x4", "x5", "x6")),
  mxPath(from = "speed", to = c("x7", "x8", "x9")),
  mxPath(from = manifestVars, arrows = 2),
  mxPath(from = latVar, arrows = 2, free = FALSE, values = 1.0),
  mxPath(from = "one", to = manifestVars, arrows = 1, free = TRUE, values = 1.0),
  mxPath(from = "one", to = latVar, arrows = 1, free = FALSE, values = 0),
  mxData(df_complete, type = "raw")
)
# Assuming mx_mice is correctly defined in your environment
fits <- mx_mice(model, imputed_data)
summary(fits[[1]])

## End(Not run)
## Not run: 
# library(OpenMx)
# library(mice)
# Fit a model to multiply imputed datasets
data("HolzingerSwineford1939", package = "lavaan")
# Introduce missing data
df_complete <- na.omit(HolzingerSwineford1939)
amp <- mice::ampute(df_complete, prop = 0.2, mech = "MAR")
df_incomplete <- amp$amp
# Perform multiple imputation
imputed_data <- mice(df_incomplete, m = 3, method = "pmm", maxit = 5, seed = 12345)
# Simple SEM model specification with OpenMx
manifestVars <- paste0("x", 1:9)
latVar <- c("visual", "textual", "speed")
model <- mxModel("Simple SEM",
  type = "RAM",
  manifestVars = manifestVars,
  latentVars = latVar,
  mxPath(from = "visual", to = c("x1", "x2", "x3")),
  mxPath(from = "textual", to = c("x4", "x5", "x6")),
  mxPath(from = "speed", to = c("x7", "x8", "x9")),
  mxPath(from = manifestVars, arrows = 2),
  mxPath(from = latVar, arrows = 2, free = FALSE, values = 1.0),
  mxPath(from = "one", to = manifestVars, arrows = 1, free = TRUE, values = 1.0),
  mxPath(from = "one", to = latVar, arrows = 1, free = FALSE, values = 0),
  mxData(df_complete, type = "raw")
)
# Assuming mx_mice is correctly defined in your environment
fits <- mx_mice(model, imputed_data)
summary(fits[[1]])

## End(Not run)

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+06, ...)
pMC(q, mu, Sigma, quant, lower.tail = TRUE, n.mc = 1e+06, ...)

Arguments

`q`	quantile
`mu`	a vector of means (e.g., coefficient estimates) for the normal random variables. A user can assign a name to each mean value, e.g., `mu=c(b1=.1,b2=3)`; otherwise, the coefficient names are assigned automatically as follows: `b1,b2,...`.
`Sigma`	either a covariance matrix or a vector that stacks all the columns of the lower triangle variance–covariance matrix one underneath the other.
`quant`	quantity of interest, which is a nonlinear/linear function of the model parameters. Argument `quant` is a formula that must start with the symbol "tilde" (`~`): e.g., `~b1b2b3*b4`. The names of coefficients must conform to the names provided in the argument `mu` or to the default names, i.e., `b1,b2,...`.
`lower.tail`	logical; if `TRUE` (default), the probability is $P[quant < q]$ ; otherwise, $P[quant > q]$
`n.mc`	Monte Carlo sample size. The default sample size is 1e+6.
`...`	additional arguments.

Value

scalar probability value.

Author(s)

Davood Tofighi [email protected]

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

Arguments

`q`	quantile or value of the product
`mu.x`	mean of $x$
`mu.y`	mean of $y$
`se.x`	standard error (deviation) of $x$
`se.y`	standard error (deviation) of $y$
`rho`	correlation between $x$ and $y$ , where -1 <`rho` < 1. The default value is 0.
`lower.tail`	logical; if `TRUE` (default), the probability is $P[XY < q]$ ; otherwise, $P[XY > q]$
`type`	method used to compute confidence interval. It takes on the values `"dop"` (default), `"MC"`, `"asymp"` or `"all"`
`n.mc`	when `type="MC"`, `n.mc` determines the sample size for the Monte Carlo method. The default sample size is 1E5.

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:

`p`	probability (percentile) corresponding to quantile `q`
`error`	estimate of the absolute error

Author(s)

Davood Tofighi [email protected]

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

pprodnormal(q = 0, mu.x = .5, mu.y = .3, se.x = 1, se.y = 1, rho = 0, type = "all")
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+06, ...)
qMC(p, mu, Sigma, quant, n.mc = 1e+06, ...)

Arguments

`p`	probability.
`mu`	a vector of means (e.g., coefficient estimates) for the normal random variables. A user can assign a name to each mean value, e.g., `mu=c(b1=.1,b2=3)`; otherwise, the coefficient names are assigned automatically as follows: `b1,b2,...`.
`Sigma`	either a covariance matrix or a vector that stacks all the columns of the lower triangle variance–covariance matrix one underneath the other.
`quant`	quantity of interest, which is a nonlinear/linear function of the model parameters. Argument `quant` is a formula that must start with the symbol "tilde" (`~`): e.g., `~b1b2b3*b4`. The names of coefficients must conform to the names provided in the argument `mu` or to the default names, i.e., `b1,b2,...`.
`n.mc`	Monte Carlo sample size. The default sample size is 1e+6.
`...`	additional arguments.

Value

scalar quantile value.

Author(s)

Davood Tofighi [email protected]

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

Arguments

`p`	probability
`mu.x`	mean of $x$
`mu.y`	mean of $y$
`se.x`	standard error (deviation) of $x$
`se.y`	standard error (deviation) of $y$
`rho`	correlation between $x$ and $y$ , where -1 <`rho` < 1. The default value is 0.
`lower.tail`	logical; if `TRUE` (default), the probability is $P[XY < q]$ ; otherwise, $P[XY > q]$
`type`	method used to compute confidence interval. It takes on the values `"dop"` (default), `"MC"`, `"asymp"` or `"all"`
`n.mc`	when `type="MC"`, `n.mc` determines the sample size for the Monte Carlo method. The default sample size is 1E5.

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:

`q`	quantile corresponding to probability `p`
`error`	estimate of the absolute error

Author(s)

Davood Tofighi [email protected]

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

## 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"
)
## 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"
)

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

Arguments

`x`	x A log-likelihood object, typically returned by logLik.
`...`	Additional arguments (not used)

Value

A data.frame with columns:

term: The term name
estimate: The log-likelihood value
df: The degrees of freedom

Author(s)

Davood Tofighi [email protected]

Examples

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

Package 'RMediation'

Help Index

CI for a nonlinear function of coefficients estimates

Description

Usage

Arguments

Value

Note

Author(s)

References

See Also

Examples

Function to check if lavaan model syntax is valid

Description

Usage

Arguments

Value

Author(s)

Examples

Fit SEM Model to Each Dataset in a MIDS Object Without Pooling

Description

Usage

Arguments

Value

Author(s)

Examples

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

Description

Usage

Arguments

Value

Author(s)

References

Examples

Confidence Interval for the Mediated Effect

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Memory Experiment Data Description from MacKinnon et al., 2018

Description

Usage

Format

Note

Source

References

Fit OpenMx model to multiply imputed datasets

Description

Usage

Arguments

Value

Author(s)

Examples

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

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Percentile for the Distribution of Product of Two Normal Variables

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

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

Description

Usage