justinkracht / noisemaker

An R package with functions for generating population correlation matrices with imperfect model fit

noisemaker

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.

Installation

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)

Examples

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] NA

The 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] NA

Finally, 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