This function can be used to generate random data based on the 1. '>SimSem objects created with the model function, 2. lavaan script or parameter tables, or 3. an MxModel object from the OpenMx package. Some notable features include fine control of misspecification and misspecification optimization (for '>SimSem only), as well as the ability to generate non-normal data. When using simsem for simulations, this function is used internally to generate data in the function sim, and can be helpful for debugging, or in creating data for use with other analysis programs.
generate(model, n, maxDraw=50, misfitBounds=NULL, misfitType="f0",
averageNumMisspec=FALSE, optMisfit=NULL, optDraws=50,
createOrder = c(1, 2, 3), indDist=NULL, sequential=FALSE,
facDist=NULL, errorDist=NULL, saveLatentVar = FALSE, indLab=NULL,
modelBoot=FALSE, realData=NULL, covData=NULL, params=FALSE, group = NULL,
empirical = FALSE, ...)Integer of sample size.
Integer specifying the maximum number of attempts to draw a valid set of parameters (no negative error variance, standardized coefficients over 1).
Vector that contains upper and lower bounds of the misfit measure. Sets of parameters drawn that are not within these bounds are rejected.
Character vector indicating the fit measure used to assess the misfit of a set of parameters. Can be "f0", "rmsea", "srmr", or "all".
If TRUE, the provided fit will be divided by the number of misspecified parameters.
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.
Number of parameter sets to draw if optMisfit is not null. The set of parameters with the maximum or minimum misfit will be returned.
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.
If TRUE, use a sequential method to create data such that the data from factor are generated first and apply to a set of equations to obtain the data of indicators. If FALSE, create data directly from model-implied mean and covariance of indicators.
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.
If TRUE, the total latent variable scores, residual latent variable scores, and measurement error scores are also provided as the "latentVar" attribute of the generated data by the following line: attr(generatedData, "latentVar"). The sequential argument must be TRUE in order to use this option.
A vector of indicator labels. When not specified, the variable names are x1, x2, ... xN.
When specified, a model-based bootstrap is used for data generation. See details for further information. This argument requires real data to be passed to realData.
A data.frame containing real data. The data generated will follow the distribution of this data set.
If TRUE, return the parameters drawn along with the generated data set. Default is FALSE.
The label of the grouping variable
Logical. If TRUE, the specified parameters are treated as sample statistics and data are created to get the specified sample statistics. This argument is applicable when multivariate normal distribution is specified only.
Additional arguments for the simulateData function.
A data.frame containing simulated data from the data generation template. A variable "group" is appended indicating group membership.
If the lavaan script or the MxModel are provided, the model-implied covariance matrix will be computed and internally use createData function to generate data. The data-generation method is based on whether the indDist argument is specified. For the lavaan script, the code for data generation is modified from the simulateData function.
If the '>SimSem object is specified, it will check whether there are any random parameters or trivial misspecification in the model. If so, real or misspecified parameters are drawn via the draw function. Next, there are two methods to generate data. First, the function will calculate the model-implied covariance matrix (including model misspecification) and generate data similar to the lavaan script or the MxModel object. The second method is referred to as the sequential method, which can be used by specifying the sequential argument as TRUE. This function will create data based on the chain of equations in structural equation modeling such that independent variables and errors are generated and added as dependent variables and the dependent variables will be treated as independent variables in the next equation. For example, in the model with factor A and B are independent variables, factor C are dependent variables, factors A and B are generated first. Then, residual in factor C are created and added with factors A and B. This current step has all factor scores. Then, measurement errors are created and added with factor scores to create indicator scores. During each step, independent variables and errors can be nonnormal by setting facDist or errorDist arguments. The data generation in each step is based on the createData function.
For the model-based bootstrap (providing the realData argument), the transformation proposed by Yung & Bentler (1996) is used. This procedure is the expansion from the Bollen and Stine (1992) bootstrap including a mean structure. The model-implied mean vector and covariance matrix with trivial misspecification will be used in the model-based bootstrap if misspec is specified. See page 133 of Bollen and Stine (1992) for a reference.
Bollen, K. A., & Stine, R. A. (1992). Bootstrapping goodness-of-fit measures in structural equation models. Sociological Methods and Research, 21, 205-229.
Yung, Y.-F., & Bentler, P. M. (1996). Bootstrapping techniques in analysis of mean and covariance structures. In G. A. Marcoulides & R. E. Schumacker (Eds.), Advanced structural equation modeling: Issues and techniques (pp. 195-226). Mahwah, NJ: Erlbaum.
draw To draw parameters using the '>SimSem template.
createData To generate random data using a set of parameters from draw
# NOT RUN {
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")
dat <- generate(CFA.Model, 200)
# Get the latent variable scores
dat2 <- generate(CFA.Model, 20, sequential = TRUE, saveLatentVar = TRUE)
dat2
attr(dat2, "latentVar")
# }
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