Mediation analysis with missing data using bootstrap

Description

Four methods for mediation analysis with missing data: Listwise deletion, Pairwise deletion, Multiple imputation, and Two Stage Maximum Likelihood algorithm. For MI and TS-ML, auxiliary variables can be included. Bootstrap confidence intervals for mediation effects are obtained. The robust method is also implemented for TS-ML. Since version 1.4, bmem adds the capability to conduct power analysis for mediation models. Details about the methods used can be found in these articles. Zhang and Wang (2003) <doi:10.1007/s11336-012-9301-5>. Zhang (2014) <doi:10.3758/s13428-013-0424-0>.

Details

Author(s)

Zhiyong Zhang and Lijuan Wang

Maintainer: Zhiyong Zhang <zhiyongzhang@nd.edu>

Mediation analysis based on bootstrap

Description

Mediation analysis based on bootstrap

Usage

bmem(x, ram, indirect, v, method='tsml', ci='bc', cl=.95, 
     boot=1000, m=10, varphi=.1, st='i', robust=FALSE, 
     max_it=500, moment=FALSE, ...)

Arguments

Details

The indirect effect can be specified using equations such as a*b, a*b+c, and a*b*c+d*e+f. A vector of indirect effects can be used indirect=c('a*b', 'a*b+c').

Value

The on-screen output includes the parameter estimates, bootstrap standard errors, and CIs.

Author(s)

Zhiyong Zhang and Lijuan Wang

References

Zhang, Z., & Wang, L. (2013). Methods for mediation analysis with missing data. Psychometrika, 78(1), 154-184.

Bootstrap but using the Bollen-Stine method

Description

The same as bmem but using the Bollen-Stine method

Usage

bmem.bs(x, ram, indirect, v, ci='bc', cl=.95, 
        boot=1000, max_it=500, ...)

Arguments

Value

The on-screen output includes the parameter estimates, bootstrap standard errors, and CIs.

Author(s)

Zhiyong Zhang and Lijuan Wang

References

Zhang, Z. & Wang, L. (2011) Four methods for mediation analysis with missing data.

Zhang, Z. (2011) Robust mediation analysis with missing data and auxiliary variables.

See Also

bmem, bmem.sobel, bmem.plot

Bias-corrected confidence intervals

Description

Bias-corrected confidence intervals

Usage

bmem.ci.bc(par.boot, par0, cl=.95)

Arguments

Value

BC confidence intervals. The output includes - estimates, bootstrap standard errors, and confidence intervals.

Author(s)

Zhiyong Zhang and Lijuan Wang

See Also

bmem.ci.norm, bmem.ci.p, bmem.ci.bca

Bias-corrected confidence intervals (for a single variable)

Description

Bias-corrected confidence intervals (for a single variable)

Usage

bmem.ci.bc1(x, b, cl = 0.95)

Arguments

Author(s)

Zhiyong Zhang and Lijuan Wang

See Also

bmem.ci.norm, bmem.ci.p, bmem.ci.bca

Bias-corrected and accelerated confidence intervals

Description

Bias-corrected and accelerated confidence intervals

Usage

bmem.ci.bca(par.boot, par0, jack, cl = 0.95)

Arguments

Value

BCa confidence intervals. The output includes - estimates, bootstrap standard errors, and confidence intervals.

Author(s)

Zhiyong Zhang and Lijuan Wang

See Also

bmem.ci.norm, bmem.ci.p, bmem.ci.bc, bmem.list.jack, bmem.pair.jack, bmem.mi.jack, bmem.em.jack,

BCa for a single variable

Description

BCa for a single variable

Usage

bmem.ci.bca1(x, b, jack, cl = 0.95)

Arguments

Confidence interval based on normal approximation

Description

Confidence interval based on normal approximation

Usage

bmem.ci.norm(par.boot, par0, cl = 0.95)

Arguments

Value

Normal confidence intervals. The output includes - estimates, bootstrap standard errors, and confidence intervals.

Author(s)

Zhiyong Zhang and Lijuan Wang

See Also

bmem.ci.bca, bmem.ci.p, bmem.ci.bc

Percentile confidence interval

Description

Percentile confidence interval

Usage

bmem.ci.p(par.boot, par0, cl = 0.95)

Arguments

Value

Percentile confidence intervals. The output includes - estimates, bootstrap standard errors, and confidence intervals.

Author(s)

Zhiyong Zhang and Lijuan Wang

See Also

bmem.ci.bca, bmem.ci.norm, bmem.ci.bc

Calculate the covariance matrix based on a given ram model

Description

Can be used to simulated data for an SEM model.

Usage

bmem.cov(ram,obs.variables,moment=FALSE, debug=FALSE)

Arguments

Estimate a mediation model based on EM covariance matrix

Description

Estimate a mediation model based on EM covariance matrix

Usage

bmem.em(x, ram, indirect, v, robust = FALSE, 
        varphi = 0.1, st= "i", moment = FALSE, 
        max_it = 500, ...)

Arguments

Bootstrap for EM

Description

Bootstrap for EM

Usage

bmem.em.boot(x, ram, indirect, v, robust = FALSE, 
             varphi = 0.1, st= "i", boot = 1000, 
             moment = FALSE, max_it = 500, ...)

Arguments

Details

The indirect effect can be specified using equations such as a*b, a*b+c, and a*b*c+d*e+f. A vector of indirect effects can be used indirect=c('a*b', 'a*b+c').

Value

Author(s)

Zhiyong Zhang and Lijuan Wang

Covariance matrix from EM

Description

Covariance matrix from EM

Usage

bmem.em.cov(xmis, moment = FALSE, max_it = 500)

Arguments

Jackknife estimate using EM

Description

Jackknife estimate using EM

Usage

bmem.em.jack(x, ram, indirect, v, robust = FALSE, 
             varphi = 0.1, st= "i", moment = FALSE, 
             max_it = 500, ...)

Arguments

Estimation of robust covariance matrix

Description

Estimation of robust covariance matrix

Usage

bmem.em.rcov(xmis, varphi=.1, moment=FALSE, max_it=1000, st='i')

Arguments

Value

An interval function to calculate the robust covaraince matrix

Author(s)

Zhiyong Zhang and Lijuan Wang

Estimate a mediaiton model based on listwise deletion

Description

Estimate a mediaiton model based on listwise deletion

Usage

bmem.list(x, ram, indirect, moment = FALSE, ...)

Arguments

Bootstrap for listwise deletion method

Description

Bootstrap for listwise deletion method

Usage

bmem.list.boot(x, ram, indirect, boot = 1000, moment = FALSE, ...)

Arguments

Covariance matrix for listwise deletion

Description

Covariance matrix for listwise deletion

Usage

bmem.list.cov(x, moment = FALSE)

Arguments

Jackknife for listwise deletion

Description

Jackknife for listwise deletion

Usage

bmem.list.jack(x, ram, indirect, moment = FALSE, ...)

Arguments

Estimate a mediation model based on multiple imputation

Description

Estimate a mediation model based on multiple imputation

Usage

bmem.mi(x, ram, indirect, v, m = 10, moment = FALSE, ...)

Arguments

Bootstrap for multiple imputation

Description

Bootstrap for multiple imputation

Usage

bmem.mi.boot(x, ram, indirect, v, m = 10, boot = 1000, 
             moment = FALSE, ...)

Arguments

Covariance estimation for multiple imputation

Description

Covariance estimation for multiple imputation

Usage

bmem.mi.cov(x, m = 10, moment = FALSE)

Arguments

Jackknife for multiple imputation

Description

Jackknife for multiple imputation

Usage

bmem.mi.jack(x, ram, indirect, v, m = 10, moment = FALSE, ...)

Arguments

Calculate the moments of a data set

Description

Calculate the moments of a data set using either listwise deletion or pairwise deletion

Usage

bmem.moments(x, type=0)

Arguments

Estimate a mediaiton model based on pairwise deletion

Description

Estimate a mediaiton model based on pairwise deletion

Usage

bmem.pair(x, ram, indirect, moment = FALSE, ...)

Arguments

Bootstrap for pairwise deletion

Description

Bootstrap for pairwise deletion

Usage

bmem.pair.boot(x, ram, indirect, boot = 1000, moment = FALSE, ...)

Arguments

Covariance matrix estimation based on pairwise deletion

Description

Covariance matrix estimation based on pairwise deletion

Usage

bmem.pair.cov(x, moment = FALSE)

Arguments

Jackknife for pairwise deletion

Description

Jackknife for pairwise deletion

Usage

bmem.pair.jack(x, ram, indirect, moment = FALSE, ...)

Arguments

Obtain missing data pattern information

Description

Obtain missing data pattern information

Usage

bmem.pattern(x)

Arguments

Plot of the bootstrap distribution. This function is replaced by plot.

Description

Plot of the bootstrap distribution

Usage

bmem.plot(x, par,...)

Arguments

Value

A plot

Author(s)

Zhiyong Zhang and Lijuan Wang

References

Zhang, Z. & Wang, L. (2011) Four methods for mediation analysis with missing data.

Zhang, Z. (2011) Robust mediation analysis with missing data and auxiliary variables.

See Also

bmem, bmem.sobel, bmem.plot

Convert a raw moment matrix to covariance matrix

Description

Convert a raw moment matrix to covariance matrix

Usage

bmem.raw2cov(x)

Arguments

Value

A covariance matrix

Author(s)

Zhiyong Zhang and Lijuan Wang

References

Zhang, Z. & Wang, L. (2011) Four methods for mediation analysis with missing data.

Zhang, Z. (2011) Robust mediation analysis with missing data and auxiliary variables.

See Also

bmem, bmem.sobel, bmem.plot

Estimate a mediaiton model using SEM technique

Description

Estimate a mediaiton model using SEM technique

Usage

bmem.sem(x, ram, N, indirect, moment=FALSE, ...)

Arguments

See Also

bmem.list.cov, bmem.pair.cov, bmem.mi.cov, bmem.em.cov

Mediation analysis using sobel test (for complete data only)

Description

Mediation analysis using sobel test (for complete data only)

Usage

bmem.sobel(x, ram, indirect, moment=FALSE, ...)

Arguments

Value

The on-screen output includes the parameter estimates and sobel standard errors.

Author(s)

Zhiyong Zhang and Lijuan Wang

References

Zhang, Z. & Wang, L. (2011) Four methods for mediation analysis with missing data.

Zhang, Z. (2011) Robust mediation analysis with missing data and auxiliary variables.

See Also

bmem, bmem.sobel, bmem.plot

Mediation analysis using sobel test for one indirect effect

Description

Internal function

Usage

bmem.sobel.ind(sem.object, ind)

Arguments

Value

Internal output

Author(s)

Zhiyong Zhang and Lijuan Wang

References

Zhang, Z. & Wang, L. (2011) Four methods for mediation analysis with missing data.

Zhang, Z. (2011) Robust mediation analysis with missing data and auxiliary variables.

See Also

bmem, bmem.sobel, bmem.plot

Sum square of a matrix

Description

Sum square of a matrix

Usage

bmem.ssq(x)

Arguments

Select data according to a vector of indices

Description

Select data according to a vector of indices

Usage

bmem.v(x, v, moment = FALSE)

Arguments

Plot of the bootstrap distribution

Description

Plot of the bootstrap distribution

Usage

## S3 method for class 'bmem'
plot(x, par, ...)

Arguments

Value

Generate the bootstrap histogram for a chosen parameter.

Author(s)

Zhiyong Zhang and Lijuan Wang

References

Zhang, Z. & Wang, L. (2011) Four methods for mediation analysis with missing data.

Zhang, Z. (2011) Robust mediation analysis with missing data and auxiliary variables.

See Also

bmem, bmem.sobel, bmem.plot

Get the population parameter values

Description

Get the population parameter values including both direct and indirect effects in a model

Usage

popPar(object)

Arguments

Conducting power analysis based on Sobel test

Description

Different from power.boot, this function conduct power analysis based on the Sobel test.

Usage

power.basic(model, indirect = NULL, nobs, nrep = 1000, alpha = 0.95, 
skewness = NULL, kurtosis = NULL, ovnames = NULL, se = "default", 
estimator = "default", parallel = "no", ncore = 1,  ...)

Arguments

Value

Examples

ex1model<-'
math ~ c*ME+start(0)*ME + b*HE+start(0.39)*HE
HE ~ a*ME+start(0.39)*ME
'

indirect<-'ab:=a*b'

N<-50

## change nrep to at least 1000 in real analysis

system.time(non.normal<-power.basic(ex1model, indirect, N, 
 nrep=30, skewness=c(-.3, -.7, 1.3), 
 kurtosis=c(1.5, 0, 5), ovnames=c('ME', 'HE', 'math')))
 
summary(non.normal)

Conducting power analysis based on bootstrap

Description

Different from power.basic, this function conduct power analysis based on the bootstrap method.

Usage

power.boot(model, indirect = NULL, nobs, nrep = 1000, nboot = 1000, 
alpha = 0.95, skewness = NULL, kurtosis = NULL, ovnames = NULL,  
ci='default', boot.type='default', 
se = "default", estimator = "default", parallel = "no", 
ncore = 1,  ...)

Arguments

Value

Examples

ex1model<-'
math ~ c*ME+start(0)*ME + b*HE+start(0.39)*HE
HE ~ a*ME+start(0.39)*ME
'

indirect<-'ab:=a*b'

N<-50

## change nrep and nboot to at least 1000 in real analysis
system.time(boot.non.normal<-power.boot(ex1model, indirect, N, 
 nrep=100, nboot=100, skewness=c(-.3, -.7, 1.3), 
 kurtosis=c(1.5, 0, 5), ovnames=c('ME', 'HE', 'math'),  ci='percent', boot.type='simple'))
summary(boot.non.normal)

Generate a power curve

Description

Generate a power curve either based on Sobel test or bootstrap

Usage

power.curve(model, indirect=NULL, nobs=100, type='basic', nrep=1000, 
nboot=1000, alpha=.95, skewness=NULL, kurtosis=NULL, ovnames=NULL,  
ci='default', boot.type='default', 
se="default", estimator="default", parallel="no", 
ncore=1, interactive=TRUE, ...)

Arguments

Value

Examples

ex2model<-'
 ept ~ start(.4)*hvltt + b*hvltt + start(0)*age + start(0)*edu + start(2)*R
 hvltt ~ start(-.35)*age + a*age + c*edu + start(.5)*edu
 R ~ start(-.06)*age + start(.2)*edu
 R =~ 1*ws + start(.8)*ls + start(.5)*lt
 age ~~ start(30)*age
 edu ~~ start(8)*edu
 age ~~ start(-2.8)*edu
 hvltt ~~ start(23)*hvltt
 R ~~ start(14)*R
 ws ~~ start(3)*ws
 ls ~~ start(3)*ls
 lt ~~ start(3)*lt
 ept ~~ start(3)*ept 
'

indirect<-'ind1 := a*b + c*b'

nobs <- seq(100, 200, by=100)

## change nrep and nboot to at least 1000 in real analysis
power.curve(model=ex2model, indirect=indirect, nobs=nobs, 
type='boot', nrep=30, nboot=30, ci='percent', 
boot.type='simple', interactive=FALSE)

Calculate bootstrap confidence intervals

Description

Calculate bootstrap confidence intervals

Usage

## S3 method for class 'bmem'
summary(object, ci='bc', cl=.95, ...)

Arguments

Details

The other type of confidence intervals can be constructed from the output of the function bmem. Note if the BCa is required, the ci='BCa' should have been specified in the function bmem.

Value

The on-screen output includes the parameter estimates, bootstrap standard errors, and CIs.

Organize the results into a table

Description

This function is adpated from the lavaan summary function to put the results in a table.

Usage

## S3 method for class 'power'
summary(object,...)

Arguments