parcelAllocation: Random Allocation of Items to Parcels in a Structural Equation Model

Description

This function generates a given number of randomly generated item-to-parcel allocations, fits a model to each allocation, and provides averaged results over all allocations.

Usage

parcelAllocation(model, data, parcel.names, item.syntax, nAlloc = 100,
  fun = "sem", alpha = 0.05, fit.measures = c("chisq", "df", "cfi",
  "tli", "rmsea", "srmr"), ..., show.progress = FALSE, iseed = 12345,
  do.fit = TRUE, return.fit = FALSE, warn = FALSE)

Value

Estimates: A data.frame containing results related to parameter estimates with columns corresponding to their names; average and standard deviation across allocations; minimum, maximum, and range across allocations; and the proportion of allocations in which each parameter estimate was significant.
SE: A data.frame containing results similar to Estimates, but related to the standard errors of parameter estimates.
Fit: A data.frame containing results related to model fit, with columns corresponding to fit index names; their average and standard deviation across allocations; the minimum, maximum, and range across allocations; and (if the test statistic or RMSEA is included in fit.measures) the proportion of allocations in which each test of (exact or close) fit was significant.
Model: A lavaan::lavaanList object containing results of the model fitted to each parcel allocation. Only returned if return.fit = TRUE.

Arguments

model: lavaan::lavaan() model syntax specifying the model fit to (at least some) parceled data. Note that there can be a mixture of items and parcels (even within the same factor), in case certain items should never be parceled. Can be a character string or parameter table. Also see lavaan::lavaanify() for more details.
data: A data.frame containing all observed variables appearing in the model, as well as those in the item.syntax used to create parcels. If the data have missing values, multiple imputation before parceling is recommended: submit a stacked data set (with a variable for the imputation number, so they can be separateed later) and set do.fit = FALSE to return the list of data.frames (one per allocation), each of which is a stacked, imputed data set with parcels.
parcel.names: character vector containing names of all parcels appearing as indicators in model.
item.syntax: lavaan::model.syntax() specifying the model that would be fit to all of the unparceled items, including items that should be randomly allocated to parcels appearing in model.
nAlloc: The number of random items-to-parcels allocations to generate.
fun: character string indicating the name of the lavaan::lavaan() function used to fit model to data. Can only take the values "lavaan", "sem", "cfa", or "growth".
alpha: Alpha level used as criterion for significance.
fit.measures: character vector containing names of fit measures to request from each fitted lavaan::lavaan() model. See the output of lavaan::fitMeasures() for a list of available measures.
...: Additional arguments to be passed to lavaan::lavaanList(). See also lavaan::lavOptions()
show.progress: If TRUE, show a utils::txtProgressBar() indicating how fast the model-fitting iterates over allocations.
iseed: (Optional) Random seed used for parceling items. When the same random seed is specified and the program is re-run, the same allocations will be generated. Using the same iseed argument will ensure the any model is fit to the same parcel allocations. Note: When using parallel options, you must first type RNGkind("L'Ecuyer-CMRG") into the R Console, so that the seed will be controlled across cores.
do.fit: If TRUE (default), the model is fitted to each parceled data set, and the summary of results is returned (see the Value section below). If FALSE, the items are randomly parceled, but the model is not fit; instead, the list of data.frames is returned (so assign it to an object).
return.fit: If TRUE, a lavaan::lavaanList object is returned with the list of results across allocations
warn: Whether to print warnings when fitting model to each allocation

Author

Terrence D. Jorgensen (University of Amsterdam; TJorgensen314@gmail.com)

Details

This function implements the random item-to-parcel allocation procedure described in Sterba (2011) and Sterba and MacCallum (2010). The function takes a single data set with item-level data, randomly assigns items to parcels, fits a structural equation model to the parceled data using lavaan::lavaanList(), and repeats this process for a user-specified number of random allocations. Results from all fitted models are summarized in the output. For further details on the benefits of randomly allocating items to parcels, see Sterba (2011) and Sterba and MacCallum (2010).

References

Sterba, S. K. (2011). Implications of parcel-allocation variability for comparing fit of item-solutions and parcel-solutions. Structural Equation Modeling, 18(4), 554--577. tools:::Rd_expr_doi("10.1080/10705511.2011.607073")

Sterba, S. K. & MacCallum, R. C. (2010). Variability in parameter estimates and model fit across random allocations of items to parcels. Multivariate Behavioral Research, 45(2), 322--358. tools:::Rd_expr_doi("10.1080/00273171003680302")

Sterba, S. K., & Rights, J. D. (2016). Accounting for parcel-allocation variability in practice: Combining sources of uncertainty and choosing the number of allocations. Multivariate Behavioral Research, 51(2--3), 296--313. tools:::Rd_expr_doi("10.1080/00273171.2016.1144502")

Sterba, S. K., & Rights, J. D. (2017). Effects of parceling on model selection: Parcel-allocation variability in model ranking. Psychological Methods, 22(1), 47--68. tools:::Rd_expr_doi("10.1037/met0000067")

Examples

Run this code


## Fit 2-factor CFA to simulated data. Each factor has 9 indicators.

## Specify the item-level model (if NO parcels were created)
item.syntax <- c(paste0("f1 =~ f1item", 1:9),
                 paste0("f2 =~ f2item", 1:9))
cat(item.syntax, sep = "\n")
## Below, we reduce the size of this same model by
## applying different parceling schemes


## 3-indicator parcels
mod.parcels <- '
f1 =~ par1 + par2 + par3
f2 =~ par4 + par5 + par6
'
## names of parcels
(parcel.names <- paste0("par", 1:6))

# \donttest{
## override default random-number generator to use parallel options
RNGkind("L'Ecuyer-CMRG")

parcelAllocation(mod.parcels, data = simParcel, nAlloc = 100,
                 parcel.names = parcel.names, item.syntax = item.syntax,
               # parallel = "multicore",  # parallel available in Mac/Linux
                 std.lv = TRUE)           # any addition lavaan arguments



## POOL RESULTS by treating parcel allocations as multiple imputations
## Details provided in Sterba & Rights (2016); see ?poolMAlloc.

## save list of data sets instead of fitting model yet
dataList <- parcelAllocation(mod.parcels, data = simParcel, nAlloc = 100,
                             parcel.names = parcel.names,
                             item.syntax = item.syntax,
                             do.fit = FALSE)
## now fit the model to each data set
library(lavaan.mi)
fit.parcels <- cfa.mi(mod.parcels, data = dataList, std.lv = TRUE)
summary(fit.parcels)        # pooled using Rubin's rules
anova(fit.parcels)          # pooled test statistic
help(package = "lavaan.mi") # find more methods for pooling results
# }


## multigroup example
simParcel$group <- 0:1 # arbitrary groups for example
mod.mg <- '
f1 =~ par1 + c(L2, L2)*par2 + par3
f2 =~ par4 + par5 + par6
'
## names of parcels
(parcel.names <- paste0("par", 1:6))

parcelAllocation(mod.mg, data = simParcel, parcel.names, item.syntax,
                 std.lv = TRUE, group = "group", group.equal = "loadings",
                 nAlloc = 20, show.progress = TRUE)



## parcels for first factor, items for second factor
mod.items <- '
f1 =~ par1 + par2 + par3
f2 =~ f2item2 + f2item7 + f2item8
'
## names of parcels
(parcel.names <- paste0("par", 1:3))

parcelAllocation(mod.items, data = simParcel, parcel.names, item.syntax,
                 nAlloc = 20, std.lv = TRUE)



## mixture of 1- and 3-indicator parcels for second factor
mod.mix <- '
f1 =~ par1 + par2 + par3
f2 =~ f2item2 + f2item7 + f2item8 + par4 + par5 + par6
'
## names of parcels
(parcel.names <- paste0("par", 1:6))

parcelAllocation(mod.mix, data = simParcel, parcel.names, item.syntax,
                 nAlloc = 20, std.lv = TRUE)

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