tabuShortForm {ShortForm}

Short Form Tabu Search

Description

Given an initial (full) lavaan model string, the original data, a criterion function to minimize, and some additional specifications, performs a Tabu model specification search. Currently only supports neighbors that are 1 move away from the current model.

Usage

tabuShortForm(
  originalData,
  initialModel,
  numItems,
  criterion = function(x) {
     tryCatch(-lavaan::fitmeasures(object = x, fit.measures =
    "cfi"), error = function(e) Inf)
 },
  niter = 20,
  tabu.size = 5,
  lavaan.model.specs = list(int.ov.free = TRUE, int.lv.free = FALSE, std.lv = TRUE,
    auto.fix.first = FALSE, auto.fix.single = TRUE, auto.var = TRUE, auto.cov.lv.x =
    TRUE, auto.th = TRUE, auto.delta = TRUE, auto.cov.y = TRUE, ordered = NULL,
    model.type = "cfa", estimator = "default"),
  bifactor = FALSE,
  verbose = FALSE,
  parallel = T
)

Arguments

originalData

The original data frame with variable names.

initialModel

The initial model (typically the full form) as a character vector with lavaan model.syntax.

numItems

A numeric vector indicating the number of items to retain for each factor.

criterion

A function calculating the objective criterion to minimize. Default is to use the built-in 'rmsea' value from 'lavaan::fitmeasures()'.

niter

A numeric value indicating the number of iterations (model specification selections) to perform. Default is 50.

tabu.size

A numeric value indicating the size of Tabu list. Default is 5.

lavaan.model.specs

A list which contains the specifications for the lavaan model. The default values are the defaults for lavaan to perform a CFA. See lavaan for more details.

bifactor

Logical. Indicates if the latent model is a bifactor model. If 'TRUE', assumes that the last latent variable in the provided model syntax is the bifactor (i.e., all of the retained items will be set to load on the last latent variable).

verbose

Logical. If 'TRUE', prints out the initial short form and the selected short form at the end of each iteration.

parallel

An option for using parallel processing. If TRUE, the function will utilize all available cores. Default is TRUE.

Value

A named list with the best value of the objective function ('best.obj') and the best lavaan model object ('best.mod').

Examples

shortAntModel <- "
Ability =~ Item1 + Item2 + Item3 + Item4 + Item5 + Item6 + Item7 + Item8
Ability ~ Outcome
"

data(simulated_test_data)
tabuResult <- tabuShortForm(
  initialModel = shortAntModel,
  originalData = simulated_test_data, numItems = 7,
  niter = 1, tabu.size = 3, parallel = FALSE
)
summary(tabuResult) # shows the resulting model
## Not run: 
# create simulation data from the `psych` package
# four factors, 12 items each, 48 total items
# factor loading matrix - not quite simple structure
fxMatrix <-
  matrix(
    data = c(
      rep(x = c(.9, .7, .5, .3), times = 3),
      rep(0.2, times = 3 * 4 * 3), # first factor loadings

      rep(0.2, times = 3 * 4),
      rep(x = c(.9, .7, .5, .3), times = 3),
      rep(0.2, times = 3 * 4 * 2), # second factor loadings

      rep(0.2, times = 3 * 4 * 2),
      rep(x = c(.9, .7, .5, .3), times = 3),
      rep(0.2, times = 3 * 4), # third factor loadings

      rep(0.2, times = 3 * 4 * 3),
      rep(x = c(.9, .7, .5, .3), times = 3) # fourth factor loadings
    ),
    ncol = 4
  )
# factor correlation matrix - all factors uncorrelated
PhiMatrix <-
  matrix(data = c(
    1, 0, 0, 0,
    0, 1, 0, 0,
    0, 0, 1, 0,
    0, 0, 0, 1
  ), ncol = 4)
tabuData <-
  psych::sim(
    fx = fxMatrix,
    Phi = PhiMatrix,
    n = 1000,
    raw = TRUE
  )$observed # observed is the simulated observed data

# NOTE: you must specify the model such that each factor is on a single line!
# otherwise, the algorithm will not work correctly!
tabuModel <- "
Trait1 =~ Item1 + Item2 + Item3 + Item4 + Item5 + Item6 +
Item7 + Item8 + Item9 + Item10 + Item11 + Item12
Trait2 =~ Item13 + Item14 + Item15 + Item16 + Item17 +
Item18 + Item19 + Item20 + Item21 + Item22 + Item23 + Item24
Trait3 =~ Item25 + Item26 + Item27 + Item28 + Item29 + Item30 +
Item31 + Item32 + Item33 + Item34 + Item35 + Item36
Trait4 =~ Item37 + Item38 + Item39 + Item40 + Item41 +
Item42 + Item43 + Item44 + Item45 + Item46 + Item47 + Item48
"

colnames(tabuData) <- paste0("Item", 1:48)
# specify the criterion function that the Tabu Search minimizes
# wrap this in a tryCatch in case a model does not converge!
# specify an appropriate error value: if minimizing, error value must be large
tabuCriterion <- function(x) {
  tryCatch(lavaan::fitmeasures(object = x, fit.measures = "chisq"),
    error = function(e) Inf
  )
}

# use the tabuShortForm function
# reduce form to the best 12 items
tabuShort <- tabuShortForm(
  initialModel = tabuModel, originalData = tabuData,
  numItems = c(3, 3, 3, 3),
  criterion = tabuCriterion,
  niter = 20, tabu.size = 10
)

## End(Not run)