Anthony Raborn 2021-05-18
An R package which utilizes metaheuristic algorithms to simultaneously find the best-fitting model for various factor structures and select which factor structure has the highest fit. Currently, simulated annealing is the only metaheuristic algorithm in use, but ant colony optimization may be incorporated in the future.
To install this package, you must have devtools installed! It is only
found on GitHub at the moment.
require(devtools)
devtools::install_github("AnthonyRaborn/mecfa") # automatically installs stable branchThe goal of mecfa is to find the best-fitting confirmatory factor
analysis from a range of possible latent factors. (If you are unsure of
what this means, here is an article which talks about the
basics).
It fits these CFA models using the lavaan software.
To start, you need a dataset, some initial models, and the mecfa
package.
sessionInfo()## R version 4.0.5 (2021-03-31)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 19041)
##
## Matrix products: default
##
## locale:
## [1] LC_COLLATE=English_United States.1252
## [2] LC_CTYPE=English_United States.1252
## [3] LC_MONETARY=English_United States.1252
## [4] LC_NUMERIC=C
## [5] LC_TIME=English_United States.1252
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## loaded via a namespace (and not attached):
## [1] compiler_4.0.5 magrittr_2.0.1 tools_4.0.5 htmltools_0.5.1.1
## [5] yaml_2.2.1 stringi_1.6.1 rmarkdown_2.8 knitr_1.33
## [9] stringr_1.4.0 xfun_0.22 digest_0.6.27 rlang_0.4.11
## [13] evaluate_0.14
library(mecfa)## Loading required package: lavaan
## This is lavaan 0.6-8
## lavaan is FREE software! Please report any bugs.
# sample data to use
testData <-
lavaan::HolzingerSwineford1939The lavaan Holzinger-Swineford dataset is a 9-item test of mental
ability for 7th and 8th-grade children. It also includes other variables
which may be of interest for structural equation modeling, but we will
ignore these for now.
The test items are labeled x1 thru x9, so we can use these as our
item names when we create the different initial models. While the
generally-accepted model has 3 factors, we will investigate 2, 3, and 4
factors for this example.
factorsNames <-
c("visual", "textual", "speed", "accuracy")
itemNames <-
paste0("x", 1:9)
initialModels <-
createInitialModels(
maxFactors = factorsNames,
items = itemNames)
cat(
paste(
initialModels,
collapse = "\n\n"
)
)## visual =~ x2 + x4 + x6 + x8
## textual =~ x1 + x3 + x5 + x7 + x9
##
## visual =~ x3 + x6 + x9
## textual =~ x2 + x5 + x8
## speed =~ x1 + x4 + x7
##
## visual =~ x4 + x8
## textual =~ x3 + x7
## speed =~ x2 + x6
## accuracy =~ x1 + x5 + x9
maxSteps <-
750
fitStatistic <-
"rmsea"
maximize <-
FALSE
lavaan.model.specs <-
list(
model.type = "cfa",
auto.var = TRUE,
estimator = "default",
ordered = NULL,
int.ov.free = TRUE,
int.lv.free = FALSE,
std.lv = TRUE,
auto.fix.first = FALSE,
auto.fix.single = TRUE,
auto.cov.lv.x = TRUE,
auto.th = TRUE,
auto.delta = TRUE,
auto.cov.y = TRUE,
auto.efa = TRUE,
missing = "listwise"
)
maxChanges <-
2
temperatureFunction <-
"quadratic"example <-
exploratorySA(
initialModels = initialModels,
originalData = testData,
maxSteps = maxSteps,
fitStatistic = fitStatistic,
maximize = maximize,
lavaan.model.specs = lavaan.model.specs,
temperature = temperatureFunction
)## discovered package(s):
## automatically exporting the following variables from the local environment:
## bifactor, fitStatistic, initialModels, Kirkpatrick, lavaan.model.specs, maxChanges, maximize, maximumConsecutive, maxSteps, originalData, randomNeighbor, restartCriteria, temperature
## explicitly exporting package(s):
## numValues: 3, numResults: 0, stopped: TRUE
## numValues: 3, numResults: 1, stopped: TRUE
## returning status FALSE
## numValues: 3, numResults: 2, stopped: TRUE
## returning status FALSE
## numValues: 3, numResults: 3, stopped: TRUE
## calling combine function
## evaluating call object to combine results:
## fun(accum, result.1, result.2, result.3)
## returning status TRUE
# show/print method
example## ECFA Algorithm: Simulated Annealing
## Total Run Time: 5.809 mins
## ECFA Function Call:
## exploratorySA(initialModels = initialModels, originalData = testData, maxSteps =
## maxSteps, fitStatistic = fitStatistic, maximize = maximize, lavaan.model.specs
## = lavaan.model.specs, temperature = temperatureFunction)
##
## Best Model Function Call:
## ecfaSA(initialModel = lavaan::cfa(model = initialModels[chain], data =
## originalData, model.type = model.type, estimator = estimator, ordered =
## ordered, int.ov.free = int.ov.free, int.lv.free = int.lv.free, auto.fix.first
## = auto.fix.first, std.lv = std.lv, auto.fix.single = auto.fix.single, auto.var
## = auto.var, auto.cov.lv.x = auto.cov.lv.x, auto.efa = auto.efa, auto.th =
## auto.th, auto.delta = auto.delta, auto.cov.y = auto.cov.y, missing = missing),
## originalData = originalData, maxSteps = maxSteps, fitStatistic = fitStatistic,
## temperature = temperature, maximize = maximize, Kirkpatrick = Kirkpatrick,
## randomNeighbor = randomNeighbor, lavaan.model.specs = lavaan.model.specs,
## maxChanges = maxChanges, restartCriteria = restartCriteria, maximumConsecutive
## = maximumConsecutive, bifactor = bifactor)
##
## Final Model Syntax:
## accuracy =~ x4 + x5 + x6
## speed =~ x1 + x2
## textual =~ x7 + x8
## visual =~ x3 + x9
## speed ~~ accuracy
## textual ~~ accuracy + speed
## visual ~~ accuracy + speed + textual
## Best Model Fit Using rmsea: 0.086
# summary method
summary(example)## lavaan 0.6-8 ended normally after 28 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 24
##
## Number of observations 301
##
## Model Test User Model:
##
## Test statistic 68.168
## Degrees of freedom 21
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## accuracy =~
## x4 0.990 0.057 17.487 0.000
## x5 1.102 0.063 17.598 0.000
## x6 0.916 0.054 17.068 0.000
## speed =~
## x1 0.821 0.088 9.291 0.000
## x2 0.496 0.076 6.516 0.000
## textual =~
## x7 0.658 0.076 8.647 0.000
## x8 0.813 0.079 10.299 0.000
## visual =~
## x3 0.585 0.072 8.127 0.000
## x9 0.639 0.067 9.521 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## speed ~~
## accuracy 0.547 0.076 7.224 0.000
## textual ~~
## accuracy 0.208 0.071 2.926 0.003
## speed 0.302 0.091 3.310 0.001
## visual ~~
## accuracy 0.375 0.080 4.654 0.000
## speed 1.001 0.105 9.505 0.000
## textual 0.710 0.085 8.332 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## accuracy 1.000
## speed 1.000
## textual 1.000
## visual 1.000
## .x1 0.684 0.123 5.577 0.000
## .x2 1.136 0.101 11.269 0.000
## .x3 0.932 0.089 10.520 0.000
## .x4 0.371 0.048 7.788 0.000
## .x5 0.445 0.058 7.640 0.000
## .x6 0.358 0.043 8.316 0.000
## .x7 0.750 0.091 8.281 0.000
## .x8 0.360 0.106 3.389 0.001
## .x9 0.607 0.073 8.257 0.000
# plot method
plot(example)
It took a total of 5.83 mins to compile this document.