Package 'bmemLavaan'

Mediation analysis based on bootstrap

Description

Mediation analysis based on bootstrap

Usage

bmem(data, model, v, method='list', ci='perc', cl=.95, 
     boot=1000, m=10, varphi=.1, st='i', robust=FALSE, 
     max_it=500, parallel=FALSE, ncore=1,  ...)

Arguments

data	A data set
model	RAM path for the mediaiton model
v	Indices of variables used in the mediation model. If omitted, all variables are used.
method	list: listwise deletion, pair: pairwise deletion, mi: multiple imputation, em: EM algorithm.
ci	norm: normal approximation CI, perc: percentile CI, bc: bias-corrected CI, bca: BCa
cl	Confidence level. Can be a vector.
boot	Number of bootstraps
m	Number of imputations
varphi	Percent of data to be downweighted in robust method
st	Starting values
robust	Whether to use roubst method
max_it	Maximum number of iterations in EM
parallel	Whether to use parallel method to calculate.
ncore	Number of cores for parallel method.
...	Other options for sem function can be used.

Details

The indirect effect can be specified using equations such as a*b, a*b+c, and a*b*c+d*e+f, which can be defined in 'model' parameter.

Value

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

Author(s)

Zhiyong Zhang, Shuigen Ming and Lijuan Wang

References

Zhang, Z., & Wang, L. (2013). Methods for mediation analysis with missing data. Psychometrika, 78(1), 154-184. doi:10.1007/s11336-012-9301-5

Yuan, KH., Zhang, Z. Robust Structural Equation Modeling with Missing Data and Auxiliary Variables. Psychometrika 77, 803-826 (2012). doi:10.1007/s11336-012-9282-4

Examples

data("PoliticalDemocracy")

model_l <- '
ind60 =~ x1 + g*x2 + h*x3
dem60 =~ y1 + d*y2 + e*y3 + f*y4
dem65 =~ y5 + d*y6 + e*y7 + f*y8

dem60 ~ a * ind60
dem65 ~ c * ind60 + b * dem60

y1 ~~ y5
y2 ~~ y4 + y6
y3 ~~ y7
y4 ~~ y8
y6 ~~ y8
ind := a*b
'

fit_l <- bmem(data=PoliticalDemocracy, model = model_l, method='list', 
      ci='perc', boot=50, parallel = TRUE, ncore = 8)
summary(fit_l)

---

Parents' education levels and adolescent mathematics achievement of 76 families in 1986

Description

A dataset containing the mothers' education level, children's mathematical achievement and other attributes of 76 families.

Usage

data("Math")

Format

A data frame with 76 observations on the following 4 variables.

ME

mothers' education level

HE

home environment

MATH

children's mathematical achievement

READ

reading recognition ability

Details

Data used in this example are randomly sampled from the National Longitudinal Survey of Youth, the 1979 cohort, which were collected in 1986.

Source

https://www.nlsinfo.org/content/cohorts/nlsy79-children/using-and-understanding-the-data/childyoung-adult-documentation

References

Center for Human Resource Research (2006). NLSY79 child & young adult data users guide: a guide to the 1986-2004 child data (Computer software manual). Columbus.

Examples

data(Math)

---

Conducting power analysis

Description

A comprehensive power analysis function, it can conduct power analysis based on normal, bootstrap and robust Huber-type confidence intervals.

Usage

power.bmem(model, method="normal", nobs = 100, nrep = 1000, nboot = 1000, 
alpha = 0.95, skewness = NULL, kurtosis = NULL, ovnames = NULL,  
ci='perc', boot.type='default', 
se = "default", estimator = "default", parallel = FALSE, 
ncore = 1, verbose=TRUE, ...)

Arguments

model	A model specified using lavaan notation and above. See model.syntax for basic model specification. For the power analysis, the population parameter values should be provided in the following way. For example, the coefficient between math and HE is .39. Then it is specified as start(.39). If the parameter will be referred in the mediation effect, a label should be given as a modifier as b*HE+start(.39)*HE. It also specify the indirect or other composite effects using lavaan notation. model<-' math ~ c*ME+start(0)*ME + b*HE+start(.39)*HE HE ~ a*ME+start(.39)*ME ab := a*b abc := a*b + c '
method	Type of confidence intervals based on. Must be "normal", "boot" or "robust", which correspond to the normal, bootstrap or robust Huber-type confidence interval, respectively.
nobs	Number of observations for power analysis. If it is a vector, multiple group analysis will be conducted.
nrep	Number of replications for Monte Carlo simulation. At least 1,000 is recommended.
nboot	Number of bootstrap replicates. It's only required when bootstrap method is used.
alpha	The alpha level is used to obtain the confidence interval for model parameters.
skewness	A vector to give the skewness for the observed variables.
kurtosis	A vector to give the kurtosis for the observed variables.
ovnames	A vector to give the variable names for the observed variables. This is only needed when the skewness and kurtosis are provided. The skewness, kurtosis and variable names should be in the same order.
se	How to calculate the standard error, for example, robust standard error can be specified using se="robust".
estimator	Estimation methods to be used here.
parallel	Whether to use parallel method to calculate.
ncore	Number of cores to be used in parallel.
ci	Type of bootstrap confidence intervals. By default, the percentile one is used. otherwise get the bias-corrected one. It's only required when bootstrap method is used.
boot.type	Type of bootstrap method. By default, the nonparametric one is used. Changing it to "BS" to use the Bollen-Stine method. It's only required when bootstrap method is used.
verbose	Whether to print power information.
...	Other named arguments for lavaan can be passed here.

Value

power	power for all parameters and required ones in the model
coverage	coverage probability
pop.value	Population parameter values
results	A list to give all intermediate results
data	The last data set generated for checking purpose

Author(s)

Zhiyong Zhang, Shuigen Ming and Lijuan Wang

References

Zhang, Z. Monte Carlo based statistical power analysis for mediation models: methods and software. Behav Res 46, 1184-1198 (2014). doi:10.3758/s13428-013-0424-0

Examples

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

N <- 50

system.time(power_normal <- power.bmem(ex1model, method = "normal", nobs = N, 
  nrep=100, parallel=TRUE, skewness=c(-.3, -.7, 1.3), 
  kurtosis=c(1.5, 0, 5), ovnames=c('ME', 'HE', 'math'), ncore=8))
summary(power_normal)

---

Generate a power curve

Description

Generate a power curve either based on Sobel test or bootstrap

Usage

power.curve(model, nobs=seq(100, 2000, 200), method='normal', nrep=1000, 
nboot=1000, alpha=.95, skewness=NULL, kurtosis=NULL, ovnames=NULL,  
ci='perc', boot.type='default', 
se="default", estimator="default", parallel=FALSE, 
ncore=1, interactive=TRUE, ...)

Arguments

model	A model specified using lavaan notation and above. See model.syntax for basic model specification. For the power analysis, the population parameter values should be provided in the following way. For example, the coefficient between math and HE is .39. Then it is specified as start(.39). If the parameter will be referred in the mediation effect, a label should be given as a modifier as b*HE+start(.39)*HE. It also specify the indirect or other composite effects using lavaan notation. model<-' math ~ c*ME+start(0)*ME + b*HE+start(.39)*HE HE ~ a*ME+start(.39)*ME ab := a*b abc := a*b + c '
method	Type of confidence intervals based on. Must be "normal", "boot" or "robust", which correspond to the normal, bootstrap or robust Huber-type confidence interval, respectively.
nobs	Number of observations for power analysis. It is typically should be a vector for single group analysis. For multiple group analysis, it should be a matrix.
nrep	Number of replications for Monte Carlo simulation. At least 1,000 is recommended.
nboot	Number of bootstraps to conduct.
alpha	The alpha level is used to obtain the confidence interval for model parameters.
skewness	A vector to give the skewness for the observed variables.
kurtosis	A vector to give the kurtosis for the observed variables.
ovnames	A vector to give the variable names for the observed variables. This is only needed when the skewness and kurtosis are provided. The skewness, kurtosis and variable names should be in the same order.
se	How to calculate the standard error, for example, robust standard error can be specified using se="robust".
estimator	Estimation methods to be used here.
parallel	Parallel methods, snow or multicore, can be used here.
ncore	Number of cores to be used in parallel. By default, the maximum number of cores are used.
ci	Type of bootstrap confidence intervals. By default, the percentile one is used. To get the bias-corrected one, use ci='BC'
boot.type	Type of bootstrap method. By default, the nonparametric one is used. Changing it to "BS" to use the Bollen-Stine method.
interactive	Whether to get the figure interactively.
...	Other named arguments for lavaan can be passed here.

Value

Generate the nobs-power curves for all relationships given in the model.

Examples

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

nobs <- seq(50, 200, by=50)

power.curve(model=ex1model, nobs=nobs, method='normal', 
nrep = 100, parallel=TRUE, ncore=8)

---

Sumarize the results of function 'bmem'

Description

Sumarize the results of function 'bmem'

Usage

## S3 method for class 'bmem'
summary(object, estimates=TRUE,...)

Arguments

object	An output object from the function bmem
estimates	Whether output a more detailed results of parameters and values of statistics
...	other options can be used for the generic summary function.

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.

Examples

data("PoliticalDemocracy")

model_l <- '
ind60 =~ x1 + g*x2 + h*x3
dem60 =~ y1 + d*y2 + e*y3 + f*y4
dem65 =~ y5 + d*y6 + e*y7 + f*y8

dem60 ~ a * ind60
dem65 ~ c * ind60 + b * dem60

y1 ~~ y5
y2 ~~ y4 + y6
y3 ~~ y7
y4 ~~ y8
y6 ~~ y8
ind := a*b'

fit_l <- bmem(data=PoliticalDemocracy, model = model_l, method='list',
    ci='perc', boot=30, parallel = TRUE, ncore = 8)
summary.bmem(fit_l)

---

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

object	Output from the function either power.bmem.
...	Other options

Value

The on-screen output includes the basic information of this power analysis, parameters' true values, parameter estimates, average bootstrap standard error, standard deviation of the parameter estimates, powers, standard error of the estimated powers and empirical coverage probability of the constructed CIs.

Examples

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

N <- 50

system.time(power_robust <- power.bmem(ex1model, method = "robust", nobs = N,
        nrep=100, parallel=TRUE, ncore=8))
summary.power(power_robust)

---