semTools (version 0.5-1)

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, do.fit = TRUE)

Arguments

model

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 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 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 model. See the output of fitMeasures for a list of available measures.

…

Additional arguments to be passed to lavaanList

show.progress

If TRUE, show a txtProgressBar indicating how fast the model-fitting iterates over allocations.

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).

Value

Estimates

A data frame containing results related to parameter estimates with columns corresponding to parameter names, average parameter estimates across allocations, the standard deviation of parameter estimates across allocations, the minimum parameter estimate across allocations, the maximum parameter estimate across allocations, the range of parameter estimates across allocations, and the proportions of allocations in which the parameter estimate is significant.

SE

A data frame containing results related to standard errors with columns corresponding to parameter names, average standard errors across allocations, the standard deviation of standard errors across allocations, the minimum standard error across allocations, the maximum standard error across allocations, and the range of standard errors across allocations.

Fit

A data frame containing results related to model fit with columns corresponding to fit index names, the average of each index across allocations, the standard deviation of each fit index across allocations, the minimum of each fit index across allocations, the maximum of each fit index across allocations, and the range of each fit index across allocations.

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), 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 the random allocation of itesm to parcels, see Sterba (2011) and Sterba and MccCallum (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. 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. doi:10.1080/00273171003680302

See Also

PAVranking, poolMAlloc

Examples

# NOT RUN {
## 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))

# }
# NOT RUN {
parcelAllocation(mod.parcels, data = simParcel, parcel.names, item.syntax,
                 nAlloc = 20, std.lv = TRUE, parallel = "snow", iseed = 12345)
# }
# NOT RUN {

## 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))

set.seed(12345)
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))

set.seed(12345)
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))

set.seed(12345)
parcelAllocation(mod.mix, data = simParcel, parcel.names, item.syntax,
                 nAlloc = 20, std.lv = TRUE)

# }