sim: Run a Monte Carlo simulation with a structural equation...
In simsem: SIMulated Structural Equation Modeling
Description
Usage
Arguments
Details
Value
Author(s)
See Also
Examples
Description
This function can be used to generate data, analyze the generated data, and summarized into a result object where parameter estimates, standard errors, fit indices, and other characteristics of each replications are saved.
Usage
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sim(nRep, model, n, generate = NULL, ..., rawData = NULL, miss = NULL, datafun=NULL,
lavaanfun = "lavaan", outfun=NULL, outfundata = NULL, pmMCAR = NULL,
pmMAR = NULL, facDist = NULL, indDist = NULL, errorDist = NULL,
sequential = FALSE, saveLatentVar = FALSE, modelBoot = FALSE, realData = NULL,
covData = NULL, maxDraw = 50, misfitType = "f0", misfitBounds = NULL,
averageNumMisspec = FALSE, optMisfit=NULL, optDraws = 50,
createOrder = c(1, 2, 3), aux = NULL, group = NULL, mxFit = FALSE,
mxMixture = FALSE, citype = NULL, cilevel = 0.95, seed = 123321, silent = FALSE,
multicore = options('simsem.multicore')[[1]], cluster = FALSE,
numProc = NULL, paramOnly = FALSE, dataOnly=FALSE, smartStart=FALSE,
previousSim = NULL, completeRep = FALSE, stopOnError = FALSE)
Arguments
nRep
Number of replications. If any of the n, pmMCAR, or pmMAR arguments are specified as lists, the number of replications will default to the length of the list(s), and nRep need not be specified (can be set NULL).
model
There are three options for this argument: 1. SimSem object created by model, 2. lavaan script, lavaan parameter table, fitted lavaan object matching the analysis model, or a list that contains all argument that users use to run lavaan (including cfa, sem, lavaan), 3. MxModel object from the OpenMx package, or 4. a function that takes a data set and return a list of coef, se, and converged (see details below). For the SimSem object, if the generate argument is not specified, then the object in the model argument will be used for both data generation and analysis. If generate is specified, then the model argument will be used for data analysis only.
n
Sample size(s). In single-group models, either a single integer, or a vector of integers to vary sample size across replications. In multigroup models, either a list of single integers (for constant group sizes across replications) or a list of vectors (to vary group sizes across replications).
Any non-integers will be rounded.
generate
There are four options for this argument: 1. SimSem object created by model, 2. lavaan script, lavaan parameter table (for data generation; see simulateData), fitted lavaan object that estimated all nonzero population parameters, or a list that contains all argument that users use to run simulateData, 3. MxModel object with population parameters specified in the starting values of all matrices in the model, 4. a function that take only one sample size argument (by integer for single-group model or by a vector of integers for multiple-group model). The generate argument cannot be specified the same time as the rawData argument.
rawData
There are two options for this argument: 1. a list of data frames to be used in simulations or 2. a population data. If a list of data frames is specified, the nRep and n arguments must not be specified. If a population data frame is specified, the nRep and n arguments are required.
miss
A missing data template created using the miss function.
datafun
A function to be applied to each generated data set across replications.
lavaanfun
The character of the function name used in running lavaan model ("cfa", "sem", "growth", "lavaan"). This argument is required only when lavaan script or a list of arguments is specified in the model argument.
outfun
A function to be applied to the lavaan output at each replication. Output from this function in each replication will be saved in the simulation output (SimResult), and can be obtained using the getExtraOutput function.
outfundata
A function to be applied to the lavaan output and the generated data at each replication. Users can get the characteristics of the generated data and also compare the characteristics with the generated output. The output from this function in each replication will be saved in the simulation output (SimResult), and can be obtained using the getExtraOutput function.
pmMCAR
The percentage of data completely missing at random (0 <= pmMCAR < 1). Either a single value or a vector of values in order to vary pmMCAR across replications (with length equal to nRep or a divisor of nRep). The objMissing argument is only required when specifying complex missing value data generation, or when using multiple imputation.
pmMAR
The percentage of data missing at random (0 <= pmCAR < 1). Either a single value or a vector of values in order to vary pmCAR across replications (with length equal to nRep or a divisor of nRep). The objMissing argument is only required when specifying complex missing value data generation, or when using multiple imputation.
facDist
Factor distributions. Either a list of SimDataDist objects or a single SimDataDist object to give all factors the same distribution. Use when sequential is TRUE.
indDist
Indicator distributions. Either a list of SimDataDist objects or a single SimDataDist object to give all indicators the same distribution. Use when sequential is FALSE.
errorDist
An object or list of objects of type SimDataDist indicating the distribution of errors. If a single SimDataDist is specified, each error will be genrated with that distribution.
sequential
If TRUE, a sequential method is used to generate data in which factor data is generated first, and is subsequently applied to a set of equations to obtain the indicator data. If FALSE, data is generated directly from model-implied mean and covariance of the indicators.
saveLatentVar
If TRUE, the generated latent variable scores and measurement error scores are also provided as the attribute of the generated data. Users can use the outfundata to compare the latent variable scores with the estimated output. The sequential argument must be TRUE in order to use this option.
modelBoot
When specified, a model-based bootstrap is used for data generation (for use with the realData argument). See draw for further information.
realData
A data.frame containing real data. Generated data will follow the distribution of this data set.
covData
A data.frame containing covariate data, which can have any distributions. This argument is required when users specify GA or KA matrices in the model template (SimSem).
maxDraw
The maximum number of attempts to draw a valid set of parameters (no negative error variance, standardized coefficients over 1).
misfitType
Character vector indicating the fit measure used to assess the misfit of a set of parameters. Can be "f0", "rmsea", "srmr", or "all".
misfitBounds
Vector that contains upper and lower bounds of the misfit measure. Sets of parameters drawn that are not within these bounds are rejected.
averageNumMisspec
If TRUE, the provided fit will be divided by the number of misspecified parameters.
optMisfit
Character vector of either "min" or "max" indicating either maximum or minimum optimized misfit. If not null, the set of parameters out of the number of draws in "optDraws" that has either the maximum or minimum misfit of the given misfit type will be returned.
optDraws
Number of parameter sets to draw if optMisfit is not null. The set of parameters with the maximum or minimum misfit will be returned.
createOrder
The order of 1) applying equality/inequality constraints, 2) applying misspecification, and 3) fill unspecified parameters (e.g., residual variances when total variances are specified). The specification of this argument is a vector of different orders of 1 (constraint), 2 (misspecification), and 3 (filling parameters). For example, c(1, 2, 3) is to apply constraints first, then add the misspecification, and finally fill all parameters. See the example of how to use it in the draw function.
aux
The names of auxiliary variables saved in a vector.
group
The name of the group variable. This argument is used when lavaan script or MxModel is used in the model only. When generating data from a multigroup population model, the grouping variable in each generated data set will be named "group", so when additionally using a multigroup analysis model, users must specify this argument as group="group".
mxFit
A logical whether to find an extensive list of fit measures (which will be slower). This argument is applicable when MxModel is used in the model argument only.
mxMixture
A logical whether to the analysis model is a mixture model. This argument is applicable when MxModel is used in the model argument only.
citype
Type of confidence interval. For the current version, this argument will be forwarded to the "boot.ci.type" argument in the parameterEstimates function from the lavaan package. This argument is not active when the OpenMx package is used.
cilevel
Confidence level. For the current version, this argument will be forwarded to the "level" argument in the parameterEstimates function from the lavaan package. This argument is not active when the OpenMx package is used.
seed
Random number seed. Note that the seed number is always fixed in the simsem so that users can always replicate the same simulatin or can be confidence that the same data set are generated. Reproducibility across multiple cores or clusters is ensured using R'Lecuyer package.
silent
If TRUE, suppress warnings.
multicore
Users may put TRUE or FALSE. If TRUE, multiple processors within a computer will be utilized. The default value is FALSE. Users may permanently change the default value by assigning the following line: options('simsem.multicore' = TRUE)
cluster
Not applicable now. Used to specify nodes in hpc in order to be parallelizable.
numProc
Number of processors for using multiple processors. If it is NULL, the package will find the maximum number of processors.
paramOnly
If TRUE, only the parameters from each replication will be returned.
dataOnly
If TRUE, only the raw data generated from each replication will be returned.
smartStart
Defaults to FALSE. If TRUE, population parameter values that are real numbers will be used as starting values. When tested in small models, the time elapsed when using population values as starting values was greater than the time reduced during analysis, and convergence rates were not affected.
previousSim
A result object that users wish to add the results of the current simulation in
completeRep
If TRUE, the function will run until the number of convergent replication equal to the specified nRep.
stopOnError
If TRUE, stop running the simulation when the error occurs during the data analysis on any replications.
...
Additional arguments to be passed to lavaan. See also lavOptions
Details
This function is executed as follows: 1. parameters are drawn from the specified data-generation model (applicable only simsem model template, SimSem, only), 2. the drawn (or the specified) parameters are used to create data, 3. data can be transformed using the datafun argument, 4. specified missingness (if any) is imposed, 5. data are analyzed using the specified analysis model, 6. parameter estimates, standard errors, fit indices, and other characteristics of a replication are extracted, 7. additional outputs (if any) are extracted using the outfun argument, and 8. results across replications are summarized in a result object, SimResult).
There are six ways to provide or generate data in this function:
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SimSem can be used as a template to generate data, which can be created by the model function. The SimSem can be specified in the generate argument.
-
lavaan script, parameter table for the lavaan package, or a list of arguments for the simulateData function. The lavaan script can be specified in the generate argument.
-
MxModel object from the OpenMx package. The MxModel object can be specified in the generate argument.
A list of raw data for each replication can be provided for the rawData argument. The sim function will analyze each data and summarize the result. Note that the generate, n and nRep could not be specified if the list of raw data is provided.
Population data can be provided for the rawData argument. The sim function will randomly draw sample data sets and analyze data. Note that the n and nRep must be specified if the population data are provided. The generate argument must not be specified.
A function can be used to generate data. The function must take sample size in a numeric format (or a vector of numerics for multiple groups) and return a data frame of the generated data set. Note that parameter values and their standardized values can be provided by using the attributes of the resulting data set. That is, users can assign parameter values and standardized parameter values to attr(data, "param") and attr(data, "stdparam").
Note that all generated or provided data can be transformed based on Bollen-Stine approach by providing a real data in the realData argument if any of the first three methods are used.
There are four ways to analyze the data sets for each replication by setting the model argument as
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SimSem can be used as a template for data analysis.
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lavaan script, parameter table for the lavaan package, or a list of arguments for the lavaan, sem, cfa, or growth function. Note that if the desired function to analyze data can be specified in the lavaanfun argument, which the default is the lavaan function
-
MxModel object from the OpenMx package. The object does not need to have data inside. Note that if users need an extensive fit indices, the mxFit argument should be specified as TRUE. If users wish to analyze by mixture model, the mxMixture argument should be TRUE such that the sim function knows how to handle the data.
A function that takes a data set and returns a list. The list must contain at least three objects: a vector of parameter estimates (coef), a vector of standard error (se), and the convergence status as TRUE or FALSE (converged). There are seven optional objects in the list: a vector of fit indices (fit), a vector of standardized estimates (std), a vector of standard errors of standardized estimates (stdse), fraction missing type I (FMI1), fraction missing type II (FMI2), lower bounds of confidence intervals (cilower), and upper bounds of confidence intervals (ciupper). Note that the coef, se, std, stdse, FMI1, FMI2, cilower, and ciupper must be a vector with names. The name of those vectors across different objects must be the same. Users may optionally specify other objects in the list; however, the results of the other objects will not be automatically combined. Users need to specify the outfun argument to get the extra objects. For example, researchers may specify residuals in the list. The outfun argument should have the function as follows: function(obj) obj$residuals.
Any combination of data-generation methods and data-analysis methods are valid. For example, data can be simulated using lavaan script and analyzed by MxModel. Paralleled processing can be enabled using the multicore argument.
Value
A result object (SimResult)
Author(s)
Patrick Miller (University of Notre Dame; pmille13@nd.edu)
Sunthud Pornprasertmanit (psunthud@gmail.com)
See Also
-
SimResult for the resulting output description
Examples
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# Please go to https://simsem.org/ for more examples in the Vignettes.
## Example of using simsem model template
library(lavaan)
loading <- matrix(0, 6, 2)
loading[1:3, 1] <- NA
loading[4:6, 2] <- NA
LY <- bind(loading, 0.7)
latent.cor <- matrix(NA, 2, 2)
diag(latent.cor) <- 1
RPS <- binds(latent.cor, 0.5)
RTE <- binds(diag(6))
VY <- bind(rep(NA,6),2)
CFA.Model <- model(LY = LY, RPS = RPS, RTE = RTE, modelType = "CFA")
# In reality, more than 5 replications are needed.
Output <- sim(5, CFA.Model, n=200)
summary(Output)
## Example of using lavaan model syntax
popModel <- "
f1 =~ 0.7*y1 + 0.7*y2 + 0.7*y3
f2 =~ 0.7*y4 + 0.7*y5 + 0.7*y6
f1 ~~ 1*f1
f2 ~~ 1*f2
f1 ~~ 0.5*f2
y1 ~~ 0.49*y1
y2 ~~ 0.49*y2
y3 ~~ 0.49*y3
y4 ~~ 0.49*y4
y5 ~~ 0.49*y5
y6 ~~ 0.49*y6
"
analysisModel <- "
f1 =~ y1 + y2 + y3
f2 =~ y4 + y5 + y6
"
Output <- sim(5, model=analysisModel, n=200, generate=popModel, std.lv=TRUE, lavaanfun = "cfa")
summary(Output)
## Example of using raw data as the population
pop <- data.frame(y1 = rnorm(100000, 0, 1), y2 = rnorm(100000, 0, 1))
covModel <- " y1 ~~ y2 "
Output <- sim(5, model=covModel, n=200, rawData=pop, lavaanfun = "cfa")
summary(Output)
## Example of user-defined functions:
# data-transformation function: Transforming to standard score
fun1 <- function(data) {
temp <- scale(data)
as.data.frame(temp)
}
# additional-output function: Extract modification indices from lavaan
fun2 <- function(out) {
inspect(out, "mi")
}
# In reality, more than 5 replications are needed.
Output <- sim(5, CFA.Model,n=200,datafun=fun1, outfun=fun2)
summary(Output)
# Get modification indices
getExtraOutput(Output)
## Example of additional output: Comparing latent variable correlation
outfundata <- function(out, data) {
predictcor <- lavInspect(out, "est")$psi[2, 1]
latentvar <- attr(data, "latentVar")[,c("f1", "f2")]
latentcor <- cor(latentvar)[2,1]
latentcor - predictcor
}
Output <- sim(5, CFA.Model, n=200, sequential = TRUE, saveLatentVar = TRUE,
outfundata = outfundata)
getExtraOutput(Output)
## Example of analyze using a function
analyzeFUN <- function(data) {
out <- lm(y2 ~ y1, data=data)
coef <- coef(out)
se <- sqrt(diag(vcov(out)))
fit <- c(loglik = as.numeric(logLik(out)))
converged <- TRUE # Assume to be convergent all the time
return(list(coef = coef, se = se, fit = fit, converged = converged))
}
Output <- sim(5, model=analyzeFUN, n=200, rawData=pop, lavaanfun = "cfa")
summary(Output)
Example output
Loading required package: lavaan
This is lavaan 0.6-7
lavaan is BETA software! Please report any bugs.
#################################################################
This is simsem 0.5-15
simsem is BETA software! Please report any bugs.
simsem was first developed at the University of Kansas Center for
Research Methods and Data Analysis, under NSF Grant 1053160.
#################################################################
Attaching package: ‘simsem’
The following object is masked from ‘package:lavaan’:
inspect
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RESULT OBJECT
Model Type
[1] "cfa"
========= Fit Indices Cutoffs ============
Alpha
Fit Indices 0.1 0.05 0.01 0.001 Mean SD
chisq 16.166 17.613 18.770 19.031 8.543 6.920
aic 3145.232 3152.617 3158.525 3159.855 3113.358 36.958
bic 3207.900 3215.285 3221.193 3222.523 3176.026 36.958
rmsea 0.069 0.076 0.082 0.083 0.026 0.038
cfi 0.973 0.969 0.965 0.964 0.990 0.016
tli 0.950 0.941 0.934 0.933 1.000 0.047
srmr 0.038 0.041 0.044 0.044 0.025 0.012
========= Parameter Estimates and Standard Errors ============
Estimate Average Estimate SD Average SE Power (Not equal 0) Std Est
f1=~y1 0.718 0.033 0.074 1.0 0.724
f1=~y2 0.654 0.084 0.072 1.0 0.675
f1=~y3 0.688 0.114 0.075 1.0 0.683
f2=~y4 0.656 0.045 0.072 1.0 0.676
f2=~y5 0.707 0.104 0.074 1.0 0.702
f2=~y6 0.708 0.100 0.073 1.0 0.719
f1~~f2 0.439 0.157 0.081 1.0 0.439
y1~~y1 0.470 0.095 0.078 1.0 0.474
y2~~y2 0.503 0.071 0.074 1.0 0.540
y3~~y3 0.522 0.036 0.079 1.0 0.529
y4~~y4 0.510 0.057 0.073 1.0 0.542
y5~~y5 0.503 0.055 0.077 1.0 0.505
y6~~y6 0.455 0.039 0.074 1.0 0.480
y1~1 0.024 0.064 0.070 0.0 0.024
y2~1 0.029 0.110 0.068 0.2 0.030
y3~1 0.016 0.126 0.071 0.2 0.012
y4~1 -0.068 0.071 0.069 0.2 -0.070
y5~1 -0.029 0.056 0.071 0.0 -0.031
y6~1 -0.018 0.086 0.069 0.0 -0.018
Std Est SD Std Ave SE Average Param Average Bias Coverage
f1=~y1 0.047 0.055 0.70 0.018 1.0
f1=~y2 0.073 0.057 0.70 -0.046 0.8
f1=~y3 0.074 0.056 0.70 -0.012 0.8
f2=~y4 0.035 0.056 0.70 -0.044 1.0
f2=~y5 0.057 0.055 0.70 0.007 0.8
f2=~y6 0.061 0.055 0.70 0.008 0.8
f1~~f2 0.157 0.081 0.50 -0.061 0.6
y1~~y1 0.069 0.080 0.51 -0.040 0.8
y2~~y2 0.096 0.076 0.51 -0.007 1.0
y3~~y3 0.096 0.077 0.51 0.012 1.0
y4~~y4 0.048 0.075 0.51 0.000 1.0
y5~~y5 0.082 0.077 0.51 -0.007 1.0
y6~~y6 0.083 0.078 0.51 -0.055 1.0
y1~1 0.064 0.071 0.00 0.024 1.0
y2~1 0.113 0.071 0.00 0.029 0.8
y3~1 0.126 0.071 0.00 0.016 0.8
y4~1 0.072 0.071 0.00 -0.068 0.8
y5~1 0.058 0.071 0.00 -0.029 1.0
y6~1 0.087 0.071 0.00 -0.018 1.0
========= Correlation between Fit Indices ============
chisq aic bic rmsea cfi tli srmr
chisq 1.000 -0.021 -0.021 0.980 -0.970 -0.991 0.966
aic -0.021 1.000 1.000 -0.059 0.097 0.027 0.176
bic -0.021 1.000 1.000 -0.059 0.097 0.027 0.176
rmsea 0.980 -0.059 -0.059 1.000 -0.976 -0.951 0.937
cfi -0.970 0.097 0.097 -0.976 1.000 0.933 -0.954
tli -0.991 0.027 0.027 -0.951 0.933 1.000 -0.944
srmr 0.966 0.176 0.176 0.937 -0.954 -0.944 1.000
================== Replications =====================
Number of replications = 5
Number of converged replications = 5
Number of nonconverged replications:
1. Nonconvergent Results = 0
2. Nonconvergent results from multiple imputation = 0
3. At least one SE were negative or NA = 0
4. At least one variance estimates were negative = 0
5. At least one correlation estimates were greater than 1 or less than -1 = 0
6. Model-implied covariance matrices of any groups of latent variables are not positive definite = 0
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RESULT OBJECT
Model Type
[1] "lavaan"
========= Fit Indices Cutoffs ============
Alpha
Fit Indices 0.1 0.05 0.01 0.001 Mean SD
chisq 17.320 18.701 19.806 20.054 12.645 4.598
aic 3101.268 3112.605 3121.674 3123.715 3063.279 40.642
bic 3144.146 3155.483 3164.552 3166.593 3106.157 40.642
rmsea 0.075 0.081 0.086 0.087 0.048 0.027
cfi 0.972 0.967 0.964 0.963 0.985 0.014
tli 0.947 0.938 0.932 0.930 0.973 0.026
srmr 0.047 0.050 0.052 0.052 0.038 0.009
========= Parameter Estimates and Standard Errors ============
Estimate Average Estimate SD Average SE Power (Not equal 0) Std Est
f1=~y1 0.658 0.085 0.071 1 0.678
f1=~y2 0.635 0.049 0.068 1 0.684
f1=~y3 0.737 0.043 0.070 1 0.762
f2=~y4 0.667 0.058 0.073 1 0.678
f2=~y5 0.701 0.130 0.072 1 0.709
f2=~y6 0.728 0.064 0.076 1 0.709
y1~~y1 0.503 0.098 0.072 1 0.536
y2~~y2 0.459 0.074 0.065 1 0.531
y3~~y3 0.391 0.034 0.072 1 0.419
y4~~y4 0.525 0.085 0.075 1 0.539
y5~~y5 0.467 0.106 0.074 1 0.489
y6~~y6 0.523 0.107 0.082 1 0.495
f1~~f2 0.481 0.112 0.078 1 0.481
Std Est SD Std Ave SE Average Param Average Bias Coverage
f1=~y1 0.071 0.054 0.70 -0.042 1.0
f1=~y2 0.049 0.054 0.70 -0.065 1.0
f1=~y3 0.031 0.051 0.70 0.037 1.0
f2=~y4 0.034 0.056 0.70 -0.033 1.0
f2=~y5 0.098 0.054 0.70 0.001 0.6
f2=~y6 0.064 0.055 0.70 0.028 1.0
y1~~y1 0.095 0.073 0.49 0.013 0.8
y2~~y2 0.067 0.073 0.49 -0.031 0.8
y3~~y3 0.046 0.078 0.49 -0.099 1.0
y4~~y4 0.047 0.076 0.49 0.035 1.0
y5~~y5 0.134 0.075 0.49 -0.023 1.0
y6~~y6 0.095 0.077 0.49 0.033 1.0
f1~~f2 0.112 0.078 0.50 -0.019 0.8
========= Correlation between Fit Indices ============
chisq aic bic rmsea cfi tli srmr
chisq 1.000 0.111 0.111 0.980 -0.996 -0.996 0.948
aic 0.111 1.000 1.000 0.220 -0.152 -0.152 0.322
bic 0.111 1.000 1.000 0.220 -0.152 -0.152 0.322
rmsea 0.980 0.220 0.220 1.000 -0.975 -0.975 0.916
cfi -0.996 -0.152 -0.152 -0.975 1.000 1.000 -0.964
tli -0.996 -0.152 -0.152 -0.975 1.000 1.000 -0.964
srmr 0.948 0.322 0.322 0.916 -0.964 -0.964 1.000
================== Replications =====================
Number of replications = 5
Number of converged replications = 5
Number of nonconverged replications:
1. Nonconvergent Results = 0
2. Nonconvergent results from multiple imputation = 0
3. At least one SE were negative or NA = 0
4. At least one variance estimates were negative = 0
5. At least one correlation estimates were greater than 1 or less than -1 = 0
6. Model-implied covariance matrices of any groups of latent variables are not positive definite = 0
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RESULT OBJECT
Model Type
[1] "lavaan"
========= Fit Indices Cutoffs ============
Alpha
Fit Indices 0.1 0.05 0.01 0.001 Mean SD
chisq 0.000 0.000 0.000 0.000 0.000 0.000
aic 1142.098 1145.983 1149.090 1149.790 1121.339 19.069
bic 1151.993 1155.878 1158.985 1159.685 1131.234 19.069
rmsea 0.000 0.000 0.000 0.000 0.000 0.000
cfi 1.000 1.000 1.000 1.000 1.000 0.000
tli 1.000 1.000 1.000 1.000 1.000 0.000
srmr 0.000 0.000 0.000 0.000 0.000 0.000
========= Parameter Estimates and Standard Errors ============
Estimate Average Estimate SD Average SE Power (Not equal 0) Std Est
y1~~y2 -0.078 0.091 0.068 0.2 -0.079
y1~~y1 0.900 0.100 0.090 1.0 1.000
y2~~y2 1.026 0.067 0.103 1.0 1.000
Std Est SD Std Ave SE Average Param Average Bias Coverage
y1~~y2 0.094 0.07 0 -0.078 0.8
y1~~y1 0.000 0.00 1 -0.100 0.8
y2~~y2 0.000 0.00 1 0.026 1.0
========= Correlation between Fit Indices ============
chisq aic bic cfi srmr
chisq 1.000 -0.535 -0.535 -1.000 0.989
aic -0.535 1.000 1.000 0.535 -0.610
bic -0.535 1.000 1.000 0.535 -0.610
cfi -1.000 0.535 0.535 1.000 -0.989
srmr 0.989 -0.610 -0.610 -0.989 1.000
================== Replications =====================
Number of replications = 5
Number of converged replications = 5
Number of nonconverged replications:
1. Nonconvergent Results = 0
2. Nonconvergent results from multiple imputation = 0
3. At least one SE were negative or NA = 0
4. At least one variance estimates were negative = 0
5. At least one correlation estimates were greater than 1 or less than -1 = 0
6. Model-implied covariance matrices of any groups of latent variables are not positive definite = 0
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RESULT OBJECT
Model Type
[1] "cfa"
========= Fit Indices Cutoffs ============
Alpha
Fit Indices 0.1 0.05 0.01 0.001 Mean SD
chisq 16.166 17.613 18.770 19.031 8.543 6.920
aic 3183.866 3198.673 3210.518 3213.184 3144.952 40.195
bic 3246.534 3261.341 3273.186 3275.852 3207.620 40.195
rmsea 0.069 0.076 0.082 0.083 0.026 0.038
cfi 0.973 0.969 0.965 0.964 0.990 0.016
tli 0.950 0.941 0.934 0.933 1.000 0.047
srmr 0.038 0.041 0.044 0.044 0.025 0.012
========= Parameter Estimates and Standard Errors ============
Estimate Average Estimate SD Average SE Power (Not equal 0) Std Est
f1=~y1 0.722 0.046 0.074 1 0.724
f1=~y2 0.673 0.073 0.075 1 0.675
f1=~y3 0.682 0.074 0.074 1 0.683
f2=~y4 0.674 0.035 0.074 1 0.676
f2=~y5 0.700 0.057 0.074 1 0.702
f2=~y6 0.718 0.061 0.074 1 0.719
f1~~f2 0.439 0.157 0.081 1 0.439
y1~~y1 0.471 0.068 0.079 1 0.474
y2~~y2 0.537 0.095 0.078 1 0.540
y3~~y3 0.526 0.096 0.078 1 0.529
y4~~y4 0.539 0.048 0.077 1 0.542
y5~~y5 0.502 0.082 0.077 1 0.505
y6~~y6 0.477 0.083 0.077 1 0.480
y1~1 0.000 0.000 0.071 0 0.000
y2~1 0.000 0.000 0.071 0 0.000
y3~1 0.000 0.000 0.071 0 0.000
y4~1 0.000 0.000 0.071 0 0.000
y5~1 0.000 0.000 0.071 0 0.000
y6~1 0.000 0.000 0.071 0 0.000
Std Est SD Std Ave SE Average Param Average Bias Coverage
f1=~y1 0.047 0.055 0.70 0.022 1.0
f1=~y2 0.073 0.057 0.70 -0.027 1.0
f1=~y3 0.074 0.056 0.70 -0.018 1.0
f2=~y4 0.035 0.056 0.70 -0.026 1.0
f2=~y5 0.057 0.055 0.70 0.000 1.0
f2=~y6 0.061 0.055 0.70 0.018 1.0
f1~~f2 0.157 0.081 0.50 -0.061 0.6
y1~~y1 0.069 0.080 0.51 -0.039 1.0
y2~~y2 0.096 0.076 0.51 0.027 0.8
y3~~y3 0.096 0.077 0.51 0.016 0.8
y4~~y4 0.048 0.075 0.51 0.029 1.0
y5~~y5 0.082 0.077 0.51 -0.008 1.0
y6~~y6 0.083 0.078 0.51 -0.033 1.0
y1~1 0.000 0.071 0.00 0.000 1.0
y2~1 0.000 0.071 0.00 0.000 1.0
y3~1 0.000 0.071 0.00 0.000 1.0
y4~1 0.000 0.071 0.00 0.000 1.0
y5~1 0.000 0.071 0.00 0.000 1.0
y6~1 0.000 0.071 0.00 0.000 1.0
========= Correlation between Fit Indices ============
chisq aic bic rmsea cfi tli srmr
chisq 1.000 -0.371 -0.371 0.980 -0.970 -0.991 0.966
aic -0.371 1.000 1.000 -0.196 0.188 0.489 -0.324
bic -0.371 1.000 1.000 -0.196 0.188 0.489 -0.324
rmsea 0.980 -0.196 -0.196 1.000 -0.976 -0.951 0.937
cfi -0.970 0.188 0.188 -0.976 1.000 0.933 -0.954
tli -0.991 0.489 0.489 -0.951 0.933 1.000 -0.944
srmr 0.966 -0.324 -0.324 0.937 -0.954 -0.944 1.000
================== Replications =====================
Number of replications = 5
Number of converged replications = 5
Number of nonconverged replications:
1. Nonconvergent Results = 0
2. Nonconvergent results from multiple imputation = 0
3. At least one SE were negative or NA = 0
4. At least one variance estimates were negative = 0
5. At least one correlation estimates were greater than 1 or less than -1 = 0
6. Model-implied covariance matrices of any groups of latent variables are not positive definite = 0
[[1]]
NULL
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NULL
[[3]]
NULL
[[4]]
NULL
[[5]]
NULL
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[[1]]
[1] -0.01218423
[[2]]
[1] -0.1084645
[[3]]
[1] 0.1592328
[[4]]
[1] 0.07325282
[[5]]
[1] 0.01852426
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RESULT OBJECT
Model Type
[1] "function"
========= Fit Indices Cutoffs ============
Alpha
Fit Indices 0.1 0.05 0.01 0.001 Mean SD
loglik -280.369 -280.261 -280.175 -280.155 -284.848 5.572
========= Parameter Estimates and Standard Errors ============
Estimate Average Estimate SD Average SE Power (Not equal 0)
(Intercept) 0.056 0.081 0.072 0.2
y1 -0.085 0.104 0.076 0.2
Average Param Average Bias Coverage
(Intercept) 0.002 0.054 0.8
y1 -0.002 -0.083 0.8
================== Replications =====================
Number of replications = 5
Number of converged replications = 5
Number of nonconverged replications:
1. Nonconvergent Results = 0
2. Nonconvergent results from multiple imputation = 0
3. At least one SE were negative or NA = 0
4. At least one variance estimates were negative = 0
5. At least one correlation estimates were greater than 1 or less than -1 = 0
6. Model-implied covariance matrices of any groups of latent variables are not positive definite = 0
simsem documentation built on March 29, 2021, 1:07 a.m.
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Description Usage Arguments Details Value Author(s) See Also Examples
Description
This function can be used to generate data, analyze the generated data, and summarized into a result object where parameter estimates, standard errors, fit indices, and other characteristics of each replications are saved.
Usage
1 2 3 4 5 6 7 8 9 10 11 | sim(nRep, model, n, generate = NULL, ..., rawData = NULL, miss = NULL, datafun=NULL,
lavaanfun = "lavaan", outfun=NULL, outfundata = NULL, pmMCAR = NULL,
pmMAR = NULL, facDist = NULL, indDist = NULL, errorDist = NULL,
sequential = FALSE, saveLatentVar = FALSE, modelBoot = FALSE, realData = NULL,
covData = NULL, maxDraw = 50, misfitType = "f0", misfitBounds = NULL,
averageNumMisspec = FALSE, optMisfit=NULL, optDraws = 50,
createOrder = c(1, 2, 3), aux = NULL, group = NULL, mxFit = FALSE,
mxMixture = FALSE, citype = NULL, cilevel = 0.95, seed = 123321, silent = FALSE,
multicore = options('simsem.multicore')[[1]], cluster = FALSE,
numProc = NULL, paramOnly = FALSE, dataOnly=FALSE, smartStart=FALSE,
previousSim = NULL, completeRep = FALSE, stopOnError = FALSE)
|
Arguments
nRep |
Number of replications. If any of the |
model |
There are three options for this argument: 1. |
n |
Sample size(s). In single-group models, either a single |
generate |
There are four options for this argument: 1. |
rawData |
There are two options for this argument: 1. a list of data frames to be used in simulations or 2. a population data. If a list of data frames is specified, the |
miss |
A missing data template created using the |
datafun |
A function to be applied to each generated data set across replications. |
lavaanfun |
The character of the function name used in running lavaan model ( |
outfun |
A function to be applied to the |
outfundata |
A function to be applied to the |
pmMCAR |
The percentage of data completely missing at random (0 <= pmMCAR < 1). Either a single value or a vector of values in order to vary pmMCAR across replications (with length equal to nRep or a divisor of nRep). The |
pmMAR |
The percentage of data missing at random (0 <= pmCAR < 1). Either a single value or a vector of values in order to vary pmCAR across replications (with length equal to nRep or a divisor of nRep). The |
facDist |
Factor distributions. Either a list of |
indDist |
Indicator distributions. Either a list of |
errorDist |
An object or list of objects of type |
sequential |
If |
saveLatentVar |
If |
modelBoot |
When specified, a model-based bootstrap is used for data generation (for use with the |
realData |
A data.frame containing real data. Generated data will follow the distribution of this data set. |
covData |
A data.frame containing covariate data, which can have any distributions. This argument is required when users specify |
maxDraw |
The maximum number of attempts to draw a valid set of parameters (no negative error variance, standardized coefficients over 1). |
misfitType |
Character vector indicating the fit measure used to assess the misfit of a set of parameters. Can be "f0", "rmsea", "srmr", or "all". |
misfitBounds |
Vector that contains upper and lower bounds of the misfit measure. Sets of parameters drawn that are not within these bounds are rejected. |
averageNumMisspec |
If |
optMisfit |
Character vector of either "min" or "max" indicating either maximum or minimum optimized misfit. If not null, the set of parameters out of the number of draws in "optDraws" that has either the maximum or minimum misfit of the given misfit type will be returned. |
optDraws |
Number of parameter sets to draw if optMisfit is not null. The set of parameters with the maximum or minimum misfit will be returned. |
createOrder |
The order of 1) applying equality/inequality constraints, 2) applying misspecification, and 3) fill unspecified parameters (e.g., residual variances when total variances are specified). The specification of this argument is a vector of different orders of 1 (constraint), 2 (misspecification), and 3 (filling parameters). For example, |
aux |
The names of auxiliary variables saved in a vector. |
group |
The name of the group variable. This argument is used when |
mxFit |
A logical whether to find an extensive list of fit measures (which will be slower). This argument is applicable when |
mxMixture |
A logical whether to the analysis model is a mixture model. This argument is applicable when |
citype |
Type of confidence interval. For the current version, this argument will be forwarded to the |
cilevel |
Confidence level. For the current version, this argument will be forwarded to the |
seed |
Random number seed. Note that the seed number is always fixed in the |
silent |
If |
multicore |
Users may put |
cluster |
Not applicable now. Used to specify nodes in hpc in order to be parallelizable. |
numProc |
Number of processors for using multiple processors. If it is |
paramOnly |
If |
dataOnly |
If |
smartStart |
Defaults to FALSE. If TRUE, population parameter values that are real numbers will be used as starting values. When tested in small models, the time elapsed when using population values as starting values was greater than the time reduced during analysis, and convergence rates were not affected. |
previousSim |
A result object that users wish to add the results of the current simulation in |
completeRep |
If |
stopOnError |
If |
... |
Additional arguments to be passed to |
Details
This function is executed as follows: 1. parameters are drawn from the specified data-generation model (applicable only simsem model template, SimSem, only), 2. the drawn (or the specified) parameters are used to create data, 3. data can be transformed using the datafun argument, 4. specified missingness (if any) is imposed, 5. data are analyzed using the specified analysis model, 6. parameter estimates, standard errors, fit indices, and other characteristics of a replication are extracted, 7. additional outputs (if any) are extracted using the outfun argument, and 8. results across replications are summarized in a result object, SimResult).
There are six ways to provide or generate data in this function:
-
SimSemcan be used as a template to generate data, which can be created by themodelfunction. TheSimSemcan be specified in thegenerateargument. -
lavaanscript, parameter table for thelavaanpackage, or a list of arguments for thesimulateDatafunction. Thelavaanscript can be specified in thegenerateargument. -
MxModelobject from theOpenMxpackage. TheMxModelobject can be specified in thegenerateargument. A list of raw data for each replication can be provided for the
rawDataargument. Thesimfunction will analyze each data and summarize the result. Note that thegenerate,nandnRepcould not be specified if the list of raw data is provided.Population data can be provided for the
rawDataargument. Thesimfunction will randomly draw sample data sets and analyze data. Note that thenandnRepmust be specified if the population data are provided. Thegenerateargument must not be specified.A function can be used to generate data. The function must take sample size in a numeric format (or a vector of numerics for multiple groups) and return a data frame of the generated data set. Note that parameter values and their standardized values can be provided by using the attributes of the resulting data set. That is, users can assign parameter values and standardized parameter values to
attr(data, "param")andattr(data, "stdparam").
Note that all generated or provided data can be transformed based on Bollen-Stine approach by providing a real data in the realData argument if any of the first three methods are used.
There are four ways to analyze the data sets for each replication by setting the model argument as
-
SimSemcan be used as a template for data analysis. -
lavaanscript, parameter table for thelavaanpackage, or a list of arguments for thelavaan,sem,cfa, orgrowthfunction. Note that if the desired function to analyze data can be specified in thelavaanfunargument, which the default is thelavaanfunction -
MxModelobject from theOpenMxpackage. The object does not need to have data inside. Note that if users need an extensive fit indices, themxFitargument should be specified asTRUE. If users wish to analyze by mixture model, themxMixtureargument should beTRUEsuch that thesimfunction knows how to handle the data. A function that takes a data set and returns a list. The list must contain at least three objects: a vector of parameter estimates (
coef), a vector of standard error (se), and the convergence status asTRUEorFALSE(converged). There are seven optional objects in the list: a vector of fit indices (fit), a vector of standardized estimates (std), a vector of standard errors of standardized estimates (stdse), fraction missing type I (FMI1), fraction missing type II (FMI2), lower bounds of confidence intervals (cilower), and upper bounds of confidence intervals (ciupper). Note that thecoef,se,std,stdse,FMI1,FMI2,cilower, andciuppermust be a vector with names. The name of those vectors across different objects must be the same. Users may optionally specify other objects in the list; however, the results of the other objects will not be automatically combined. Users need to specify theoutfunargument to get the extra objects. For example, researchers may specifyresidualsin the list. The outfun argument should have the function as follows:function(obj) obj$residuals.
Any combination of data-generation methods and data-analysis methods are valid. For example, data can be simulated using lavaan script and analyzed by MxModel. Paralleled processing can be enabled using the multicore argument.
Value
A result object (SimResult)
Author(s)
Patrick Miller (University of Notre Dame; pmille13@nd.edu) Sunthud Pornprasertmanit (psunthud@gmail.com)
See Also
-
SimResultfor the resulting output description
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 | # Please go to https://simsem.org/ for more examples in the Vignettes.
## Example of using simsem model template
library(lavaan)
loading <- matrix(0, 6, 2)
loading[1:3, 1] <- NA
loading[4:6, 2] <- NA
LY <- bind(loading, 0.7)
latent.cor <- matrix(NA, 2, 2)
diag(latent.cor) <- 1
RPS <- binds(latent.cor, 0.5)
RTE <- binds(diag(6))
VY <- bind(rep(NA,6),2)
CFA.Model <- model(LY = LY, RPS = RPS, RTE = RTE, modelType = "CFA")
# In reality, more than 5 replications are needed.
Output <- sim(5, CFA.Model, n=200)
summary(Output)
## Example of using lavaan model syntax
popModel <- "
f1 =~ 0.7*y1 + 0.7*y2 + 0.7*y3
f2 =~ 0.7*y4 + 0.7*y5 + 0.7*y6
f1 ~~ 1*f1
f2 ~~ 1*f2
f1 ~~ 0.5*f2
y1 ~~ 0.49*y1
y2 ~~ 0.49*y2
y3 ~~ 0.49*y3
y4 ~~ 0.49*y4
y5 ~~ 0.49*y5
y6 ~~ 0.49*y6
"
analysisModel <- "
f1 =~ y1 + y2 + y3
f2 =~ y4 + y5 + y6
"
Output <- sim(5, model=analysisModel, n=200, generate=popModel, std.lv=TRUE, lavaanfun = "cfa")
summary(Output)
## Example of using raw data as the population
pop <- data.frame(y1 = rnorm(100000, 0, 1), y2 = rnorm(100000, 0, 1))
covModel <- " y1 ~~ y2 "
Output <- sim(5, model=covModel, n=200, rawData=pop, lavaanfun = "cfa")
summary(Output)
## Example of user-defined functions:
# data-transformation function: Transforming to standard score
fun1 <- function(data) {
temp <- scale(data)
as.data.frame(temp)
}
# additional-output function: Extract modification indices from lavaan
fun2 <- function(out) {
inspect(out, "mi")
}
# In reality, more than 5 replications are needed.
Output <- sim(5, CFA.Model,n=200,datafun=fun1, outfun=fun2)
summary(Output)
# Get modification indices
getExtraOutput(Output)
## Example of additional output: Comparing latent variable correlation
outfundata <- function(out, data) {
predictcor <- lavInspect(out, "est")$psi[2, 1]
latentvar <- attr(data, "latentVar")[,c("f1", "f2")]
latentcor <- cor(latentvar)[2,1]
latentcor - predictcor
}
Output <- sim(5, CFA.Model, n=200, sequential = TRUE, saveLatentVar = TRUE,
outfundata = outfundata)
getExtraOutput(Output)
## Example of analyze using a function
analyzeFUN <- function(data) {
out <- lm(y2 ~ y1, data=data)
coef <- coef(out)
se <- sqrt(diag(vcov(out)))
fit <- c(loglik = as.numeric(logLik(out)))
converged <- TRUE # Assume to be convergent all the time
return(list(coef = coef, se = se, fit = fit, converged = converged))
}
Output <- sim(5, model=analyzeFUN, n=200, rawData=pop, lavaanfun = "cfa")
summary(Output)
|
Example output
Loading required package: lavaan
This is lavaan 0.6-7
lavaan is BETA software! Please report any bugs.
#################################################################
This is simsem 0.5-15
simsem is BETA software! Please report any bugs.
simsem was first developed at the University of Kansas Center for
Research Methods and Data Analysis, under NSF Grant 1053160.
#################################################################
Attaching package: ‘simsem’
The following object is masked from ‘package:lavaan’:
inspect
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RESULT OBJECT
Model Type
[1] "cfa"
========= Fit Indices Cutoffs ============
Alpha
Fit Indices 0.1 0.05 0.01 0.001 Mean SD
chisq 16.166 17.613 18.770 19.031 8.543 6.920
aic 3145.232 3152.617 3158.525 3159.855 3113.358 36.958
bic 3207.900 3215.285 3221.193 3222.523 3176.026 36.958
rmsea 0.069 0.076 0.082 0.083 0.026 0.038
cfi 0.973 0.969 0.965 0.964 0.990 0.016
tli 0.950 0.941 0.934 0.933 1.000 0.047
srmr 0.038 0.041 0.044 0.044 0.025 0.012
========= Parameter Estimates and Standard Errors ============
Estimate Average Estimate SD Average SE Power (Not equal 0) Std Est
f1=~y1 0.718 0.033 0.074 1.0 0.724
f1=~y2 0.654 0.084 0.072 1.0 0.675
f1=~y3 0.688 0.114 0.075 1.0 0.683
f2=~y4 0.656 0.045 0.072 1.0 0.676
f2=~y5 0.707 0.104 0.074 1.0 0.702
f2=~y6 0.708 0.100 0.073 1.0 0.719
f1~~f2 0.439 0.157 0.081 1.0 0.439
y1~~y1 0.470 0.095 0.078 1.0 0.474
y2~~y2 0.503 0.071 0.074 1.0 0.540
y3~~y3 0.522 0.036 0.079 1.0 0.529
y4~~y4 0.510 0.057 0.073 1.0 0.542
y5~~y5 0.503 0.055 0.077 1.0 0.505
y6~~y6 0.455 0.039 0.074 1.0 0.480
y1~1 0.024 0.064 0.070 0.0 0.024
y2~1 0.029 0.110 0.068 0.2 0.030
y3~1 0.016 0.126 0.071 0.2 0.012
y4~1 -0.068 0.071 0.069 0.2 -0.070
y5~1 -0.029 0.056 0.071 0.0 -0.031
y6~1 -0.018 0.086 0.069 0.0 -0.018
Std Est SD Std Ave SE Average Param Average Bias Coverage
f1=~y1 0.047 0.055 0.70 0.018 1.0
f1=~y2 0.073 0.057 0.70 -0.046 0.8
f1=~y3 0.074 0.056 0.70 -0.012 0.8
f2=~y4 0.035 0.056 0.70 -0.044 1.0
f2=~y5 0.057 0.055 0.70 0.007 0.8
f2=~y6 0.061 0.055 0.70 0.008 0.8
f1~~f2 0.157 0.081 0.50 -0.061 0.6
y1~~y1 0.069 0.080 0.51 -0.040 0.8
y2~~y2 0.096 0.076 0.51 -0.007 1.0
y3~~y3 0.096 0.077 0.51 0.012 1.0
y4~~y4 0.048 0.075 0.51 0.000 1.0
y5~~y5 0.082 0.077 0.51 -0.007 1.0
y6~~y6 0.083 0.078 0.51 -0.055 1.0
y1~1 0.064 0.071 0.00 0.024 1.0
y2~1 0.113 0.071 0.00 0.029 0.8
y3~1 0.126 0.071 0.00 0.016 0.8
y4~1 0.072 0.071 0.00 -0.068 0.8
y5~1 0.058 0.071 0.00 -0.029 1.0
y6~1 0.087 0.071 0.00 -0.018 1.0
========= Correlation between Fit Indices ============
chisq aic bic rmsea cfi tli srmr
chisq 1.000 -0.021 -0.021 0.980 -0.970 -0.991 0.966
aic -0.021 1.000 1.000 -0.059 0.097 0.027 0.176
bic -0.021 1.000 1.000 -0.059 0.097 0.027 0.176
rmsea 0.980 -0.059 -0.059 1.000 -0.976 -0.951 0.937
cfi -0.970 0.097 0.097 -0.976 1.000 0.933 -0.954
tli -0.991 0.027 0.027 -0.951 0.933 1.000 -0.944
srmr 0.966 0.176 0.176 0.937 -0.954 -0.944 1.000
================== Replications =====================
Number of replications = 5
Number of converged replications = 5
Number of nonconverged replications:
1. Nonconvergent Results = 0
2. Nonconvergent results from multiple imputation = 0
3. At least one SE were negative or NA = 0
4. At least one variance estimates were negative = 0
5. At least one correlation estimates were greater than 1 or less than -1 = 0
6. Model-implied covariance matrices of any groups of latent variables are not positive definite = 0
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RESULT OBJECT
Model Type
[1] "lavaan"
========= Fit Indices Cutoffs ============
Alpha
Fit Indices 0.1 0.05 0.01 0.001 Mean SD
chisq 17.320 18.701 19.806 20.054 12.645 4.598
aic 3101.268 3112.605 3121.674 3123.715 3063.279 40.642
bic 3144.146 3155.483 3164.552 3166.593 3106.157 40.642
rmsea 0.075 0.081 0.086 0.087 0.048 0.027
cfi 0.972 0.967 0.964 0.963 0.985 0.014
tli 0.947 0.938 0.932 0.930 0.973 0.026
srmr 0.047 0.050 0.052 0.052 0.038 0.009
========= Parameter Estimates and Standard Errors ============
Estimate Average Estimate SD Average SE Power (Not equal 0) Std Est
f1=~y1 0.658 0.085 0.071 1 0.678
f1=~y2 0.635 0.049 0.068 1 0.684
f1=~y3 0.737 0.043 0.070 1 0.762
f2=~y4 0.667 0.058 0.073 1 0.678
f2=~y5 0.701 0.130 0.072 1 0.709
f2=~y6 0.728 0.064 0.076 1 0.709
y1~~y1 0.503 0.098 0.072 1 0.536
y2~~y2 0.459 0.074 0.065 1 0.531
y3~~y3 0.391 0.034 0.072 1 0.419
y4~~y4 0.525 0.085 0.075 1 0.539
y5~~y5 0.467 0.106 0.074 1 0.489
y6~~y6 0.523 0.107 0.082 1 0.495
f1~~f2 0.481 0.112 0.078 1 0.481
Std Est SD Std Ave SE Average Param Average Bias Coverage
f1=~y1 0.071 0.054 0.70 -0.042 1.0
f1=~y2 0.049 0.054 0.70 -0.065 1.0
f1=~y3 0.031 0.051 0.70 0.037 1.0
f2=~y4 0.034 0.056 0.70 -0.033 1.0
f2=~y5 0.098 0.054 0.70 0.001 0.6
f2=~y6 0.064 0.055 0.70 0.028 1.0
y1~~y1 0.095 0.073 0.49 0.013 0.8
y2~~y2 0.067 0.073 0.49 -0.031 0.8
y3~~y3 0.046 0.078 0.49 -0.099 1.0
y4~~y4 0.047 0.076 0.49 0.035 1.0
y5~~y5 0.134 0.075 0.49 -0.023 1.0
y6~~y6 0.095 0.077 0.49 0.033 1.0
f1~~f2 0.112 0.078 0.50 -0.019 0.8
========= Correlation between Fit Indices ============
chisq aic bic rmsea cfi tli srmr
chisq 1.000 0.111 0.111 0.980 -0.996 -0.996 0.948
aic 0.111 1.000 1.000 0.220 -0.152 -0.152 0.322
bic 0.111 1.000 1.000 0.220 -0.152 -0.152 0.322
rmsea 0.980 0.220 0.220 1.000 -0.975 -0.975 0.916
cfi -0.996 -0.152 -0.152 -0.975 1.000 1.000 -0.964
tli -0.996 -0.152 -0.152 -0.975 1.000 1.000 -0.964
srmr 0.948 0.322 0.322 0.916 -0.964 -0.964 1.000
================== Replications =====================
Number of replications = 5
Number of converged replications = 5
Number of nonconverged replications:
1. Nonconvergent Results = 0
2. Nonconvergent results from multiple imputation = 0
3. At least one SE were negative or NA = 0
4. At least one variance estimates were negative = 0
5. At least one correlation estimates were greater than 1 or less than -1 = 0
6. Model-implied covariance matrices of any groups of latent variables are not positive definite = 0
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RESULT OBJECT
Model Type
[1] "lavaan"
========= Fit Indices Cutoffs ============
Alpha
Fit Indices 0.1 0.05 0.01 0.001 Mean SD
chisq 0.000 0.000 0.000 0.000 0.000 0.000
aic 1142.098 1145.983 1149.090 1149.790 1121.339 19.069
bic 1151.993 1155.878 1158.985 1159.685 1131.234 19.069
rmsea 0.000 0.000 0.000 0.000 0.000 0.000
cfi 1.000 1.000 1.000 1.000 1.000 0.000
tli 1.000 1.000 1.000 1.000 1.000 0.000
srmr 0.000 0.000 0.000 0.000 0.000 0.000
========= Parameter Estimates and Standard Errors ============
Estimate Average Estimate SD Average SE Power (Not equal 0) Std Est
y1~~y2 -0.078 0.091 0.068 0.2 -0.079
y1~~y1 0.900 0.100 0.090 1.0 1.000
y2~~y2 1.026 0.067 0.103 1.0 1.000
Std Est SD Std Ave SE Average Param Average Bias Coverage
y1~~y2 0.094 0.07 0 -0.078 0.8
y1~~y1 0.000 0.00 1 -0.100 0.8
y2~~y2 0.000 0.00 1 0.026 1.0
========= Correlation between Fit Indices ============
chisq aic bic cfi srmr
chisq 1.000 -0.535 -0.535 -1.000 0.989
aic -0.535 1.000 1.000 0.535 -0.610
bic -0.535 1.000 1.000 0.535 -0.610
cfi -1.000 0.535 0.535 1.000 -0.989
srmr 0.989 -0.610 -0.610 -0.989 1.000
================== Replications =====================
Number of replications = 5
Number of converged replications = 5
Number of nonconverged replications:
1. Nonconvergent Results = 0
2. Nonconvergent results from multiple imputation = 0
3. At least one SE were negative or NA = 0
4. At least one variance estimates were negative = 0
5. At least one correlation estimates were greater than 1 or less than -1 = 0
6. Model-implied covariance matrices of any groups of latent variables are not positive definite = 0
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RESULT OBJECT
Model Type
[1] "cfa"
========= Fit Indices Cutoffs ============
Alpha
Fit Indices 0.1 0.05 0.01 0.001 Mean SD
chisq 16.166 17.613 18.770 19.031 8.543 6.920
aic 3183.866 3198.673 3210.518 3213.184 3144.952 40.195
bic 3246.534 3261.341 3273.186 3275.852 3207.620 40.195
rmsea 0.069 0.076 0.082 0.083 0.026 0.038
cfi 0.973 0.969 0.965 0.964 0.990 0.016
tli 0.950 0.941 0.934 0.933 1.000 0.047
srmr 0.038 0.041 0.044 0.044 0.025 0.012
========= Parameter Estimates and Standard Errors ============
Estimate Average Estimate SD Average SE Power (Not equal 0) Std Est
f1=~y1 0.722 0.046 0.074 1 0.724
f1=~y2 0.673 0.073 0.075 1 0.675
f1=~y3 0.682 0.074 0.074 1 0.683
f2=~y4 0.674 0.035 0.074 1 0.676
f2=~y5 0.700 0.057 0.074 1 0.702
f2=~y6 0.718 0.061 0.074 1 0.719
f1~~f2 0.439 0.157 0.081 1 0.439
y1~~y1 0.471 0.068 0.079 1 0.474
y2~~y2 0.537 0.095 0.078 1 0.540
y3~~y3 0.526 0.096 0.078 1 0.529
y4~~y4 0.539 0.048 0.077 1 0.542
y5~~y5 0.502 0.082 0.077 1 0.505
y6~~y6 0.477 0.083 0.077 1 0.480
y1~1 0.000 0.000 0.071 0 0.000
y2~1 0.000 0.000 0.071 0 0.000
y3~1 0.000 0.000 0.071 0 0.000
y4~1 0.000 0.000 0.071 0 0.000
y5~1 0.000 0.000 0.071 0 0.000
y6~1 0.000 0.000 0.071 0 0.000
Std Est SD Std Ave SE Average Param Average Bias Coverage
f1=~y1 0.047 0.055 0.70 0.022 1.0
f1=~y2 0.073 0.057 0.70 -0.027 1.0
f1=~y3 0.074 0.056 0.70 -0.018 1.0
f2=~y4 0.035 0.056 0.70 -0.026 1.0
f2=~y5 0.057 0.055 0.70 0.000 1.0
f2=~y6 0.061 0.055 0.70 0.018 1.0
f1~~f2 0.157 0.081 0.50 -0.061 0.6
y1~~y1 0.069 0.080 0.51 -0.039 1.0
y2~~y2 0.096 0.076 0.51 0.027 0.8
y3~~y3 0.096 0.077 0.51 0.016 0.8
y4~~y4 0.048 0.075 0.51 0.029 1.0
y5~~y5 0.082 0.077 0.51 -0.008 1.0
y6~~y6 0.083 0.078 0.51 -0.033 1.0
y1~1 0.000 0.071 0.00 0.000 1.0
y2~1 0.000 0.071 0.00 0.000 1.0
y3~1 0.000 0.071 0.00 0.000 1.0
y4~1 0.000 0.071 0.00 0.000 1.0
y5~1 0.000 0.071 0.00 0.000 1.0
y6~1 0.000 0.071 0.00 0.000 1.0
========= Correlation between Fit Indices ============
chisq aic bic rmsea cfi tli srmr
chisq 1.000 -0.371 -0.371 0.980 -0.970 -0.991 0.966
aic -0.371 1.000 1.000 -0.196 0.188 0.489 -0.324
bic -0.371 1.000 1.000 -0.196 0.188 0.489 -0.324
rmsea 0.980 -0.196 -0.196 1.000 -0.976 -0.951 0.937
cfi -0.970 0.188 0.188 -0.976 1.000 0.933 -0.954
tli -0.991 0.489 0.489 -0.951 0.933 1.000 -0.944
srmr 0.966 -0.324 -0.324 0.937 -0.954 -0.944 1.000
================== Replications =====================
Number of replications = 5
Number of converged replications = 5
Number of nonconverged replications:
1. Nonconvergent Results = 0
2. Nonconvergent results from multiple imputation = 0
3. At least one SE were negative or NA = 0
4. At least one variance estimates were negative = 0
5. At least one correlation estimates were greater than 1 or less than -1 = 0
6. Model-implied covariance matrices of any groups of latent variables are not positive definite = 0
[[1]]
NULL
[[2]]
NULL
[[3]]
NULL
[[4]]
NULL
[[5]]
NULL
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[[1]]
[1] -0.01218423
[[2]]
[1] -0.1084645
[[3]]
[1] 0.1592328
[[4]]
[1] 0.07325282
[[5]]
[1] 0.01852426
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RESULT OBJECT
Model Type
[1] "function"
========= Fit Indices Cutoffs ============
Alpha
Fit Indices 0.1 0.05 0.01 0.001 Mean SD
loglik -280.369 -280.261 -280.175 -280.155 -284.848 5.572
========= Parameter Estimates and Standard Errors ============
Estimate Average Estimate SD Average SE Power (Not equal 0)
(Intercept) 0.056 0.081 0.072 0.2
y1 -0.085 0.104 0.076 0.2
Average Param Average Bias Coverage
(Intercept) 0.002 0.054 0.8
y1 -0.002 -0.083 0.8
================== Replications =====================
Number of replications = 5
Number of converged replications = 5
Number of nonconverged replications:
1. Nonconvergent Results = 0
2. Nonconvergent results from multiple imputation = 0
3. At least one SE were negative or NA = 0
4. At least one variance estimates were negative = 0
5. At least one correlation estimates were greater than 1 or less than -1 = 0
6. Model-implied covariance matrices of any groups of latent variables are not positive definite = 0
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