The goal of noisemaker is to provide functions to make it easy to
generate population correlation matrices that fit a common factor
analysis model imperfectly. In particular, the noisemaker() function
provides an interface to three methods for generating population
correlation matrices with RMSEA and/or CFI values that are close to
user-specified target values.
You can install the development version from GitHub with:
# install.packages("devtools")
devtools::install_github("JustinKracht/noisemaker")To also build the vignette when the package is installed (highly recommended), you can use:
devtools::install_github("JustinKracht/noisemaker", build_vignettes = TRUE)In this example, the factor model has two factors, each with three
salient items. I’ll demonstrate using the noisemaker() function to
generate a population correlation matrix with model error (Σ) such
that RMSEA(Σ, Ω) = 0.05, where Ω is the model-implied correlation
matrix. For this first example, I’ll use the method described by Cudeck
and Browne (1992).
library(noisemaker)
library(fungible)
# Generate a simple factor model with two factors and six items
mod <- simFA(Model = list(NFac = 2, NItemPerFac = 3),
Seed = 42)
(Omega <- mod$Rpop) # the model-implied correlation matrix
#> V1 V2 V3 V4 V5 V6
#> V1 1.0000000 0.4493845 0.2759954 0.0000000 0.0000000 0.0000000
#> V2 0.4493845 1.0000000 0.2796873 0.0000000 0.0000000 0.0000000
#> V3 0.2759954 0.2796873 1.0000000 0.0000000 0.0000000 0.0000000
#> V4 0.0000000 0.0000000 0.0000000 1.0000000 0.4493845 0.2759954
#> V5 0.0000000 0.0000000 0.0000000 0.4493845 1.0000000 0.2796873
#> V6 0.0000000 0.0000000 0.0000000 0.2759954 0.2796873 1.0000000
set.seed(42)
# Generate a population correlation matrix with model error (Sigma) using the
# Cudeck and Browne (1992) method
noisemaker(mod, method = "CB", target_rmsea = 0.05)
#> $Sigma
#> V1 V2 V3 V4 V5 V6
#> V1 1.000000000 0.449384535 0.27599542 -0.032181331 -0.028744381 0.009662973
#> V2 0.449384535 1.000000000 0.27968729 -0.007370352 -0.004001275 0.035583143
#> V3 0.275995418 0.279687285 1.00000000 0.047067522 0.051613664 0.070785224
#> V4 -0.032181331 -0.007370352 0.04706752 1.000000000 0.449384535 0.275995418
#> V5 -0.028744381 -0.004001275 0.05161366 0.449384535 1.000000000 0.279687285
#> V6 0.009662973 0.035583143 0.07078522 0.275995418 0.279687285 1.000000000
#>
#> $rmsea
#> [1] 0.04999999
#>
#> $cfi
#> [1] 0.9854324
#>
#> $v
#> [1] NA
#>
#> $eps
#> [1] NAThe noisemaker() function implements a method for simulating
correlation matrices with RMSEA values close to a target value based on
the adventitious error framework developed by Wu and Browne
(2015).
noisemaker(mod, method = "WB", target_rmsea = 0.05)
#> Warning in .recacheSubclasses(def@className, def, env): undefined subclass
#> "numericVector" of class "Mnumeric"; definition not updated
#> $Sigma
#> V1 V2 V3 V4 V5 V6
#> V1 1.00000000 0.440586099 0.276744840 -0.01252130 -0.028274417 -0.029007137
#> V2 0.44058610 1.000000000 0.293893396 -0.02663021 0.033773948 0.001035131
#> V3 0.27674484 0.293893396 1.000000000 -0.01450089 0.008299116 -0.006544648
#> V4 -0.01252130 -0.026630207 -0.014500889 1.00000000 0.457114670 0.295925028
#> V5 -0.02827442 0.033773948 0.008299116 0.45711467 1.000000000 0.320625627
#> V6 -0.02900714 0.001035131 -0.006544648 0.29592503 0.320625627 1.000000000
#>
#> $rmsea
#> [1] 0.04924298
#>
#> $cfi
#> [1] 0.9864878
#>
#> $v
#> [1] NA
#>
#> $eps
#> [1] NAFinally, the noisemaker() function implements a procedure that
optimizes the values of the parameters for the Tucker, Koopman, and
Linn (1969) method
to produce a Σ matrix that has both RMSEA and CFI values close to the
user-specified targets:
noisemaker(mod, method = "TKL",
target_rmsea = 0.05,
target_cfi = 0.95,
tkl_ctrl = list(optim_type = "optim"))
#> $Sigma
#> V1 V2 V3 V4 V5 V6
#> V1 1.000000000 0.500756146 0.25597318 0.003608341 -0.01291235 -0.02667746
#> V2 0.500756146 1.000000000 0.24647748 0.004715913 -0.02456718 -0.01490170
#> V3 0.255973178 0.246477477 1.00000000 0.012761126 0.04327002 -0.05487096
#> V4 0.003608341 0.004715913 0.01276113 1.000000000 0.42463583 0.25647774
#> V5 -0.012912352 -0.024567176 0.04327002 0.424635833 1.00000000 0.24572421
#> V6 -0.026677455 -0.014901702 -0.05487096 0.256477745 0.24572421 1.00000000
#>
#> $rmsea
#> [1] 0.0679774
#>
#> $cfi
#> [1] 0.9726869
#>
#> $v
#> [1] 0.1006799
#>
#> $eps
#> [1] 0.4196303