antcolony.lavaan: A function to implement the ant colony optimization algorithm...

In ShortForm: Automatic Short Form Creation

A function to implement the ant colony optimization algorithm for short form specification searches with the package lavaan.

Description

The Ant Colony Optimization (ACO) algorithm (Dorigo & Stutzle, 2004) can produce short forms of scales that are optimized with respect to characteristics selected by the developer, such as model fit and predictive relationships with other variables. The algorithm is based on the foraging behavior of a group of ants, which start searching for food in a variety of directions and then eventually all ants converge to the shortest distance to the food source. This behavior occurs because ants leave a pheronome trail behind as they search for food and ants in shorter paths leave stronger pheronome trails, which are detected by other ants and that will lead them to follow the shortest trail.

Usage

antcolony.lavaan(
  data = NULL,
  sample.cov = NULL,
  sample.nobs = NULL,
  ants = 20,
  evaporation = 0.9,
  antModel,
  list.items = NULL,
  full = NULL,
  i.per.f = NULL,
  factors = NULL,
  bifactor = NULL,
  steps = 50,
  lavaan.model.specs = list(model.type = "cfa", auto.var = T, estimator = "default",
    ordered = NULL, int.ov.free = TRUE, int.lv.free = FALSE, auto.fix.first = TRUE,
    auto.fix.single = TRUE, auto.cov.lv.x = TRUE, auto.th = TRUE, auto.delta = TRUE,
    auto.cov.y = TRUE, std.lv = F, group = NULL, group.label = NULL, group.equal =
    "loadings", group.partial = NULL, group.w.free = FALSE),
  pheromone.calculation = "gamma",
  fit.indices = c("cfi", "tli", "rmsea"),
  fit.statistics.test = "(cfi > 0.95)&(tli > 0.95)&(rmsea < 0.06)",
  summaryfile = NULL,
  feedbackfile = NULL,
  max.run = 1000,
  parallel = T
)

Arguments

data	The data being used in data frame format. Default value is null. Only one of data or sample.cov should be used.
sample.cov	The sample covariance matrix. See lavaan for the specific format needed. Default value is null. Only one of data or sample.cov should be used.
sample.nobs	A numeric value indicating the number of observations in the sample covariance matrix. If sample.cov is used, this must be filled in. Default value is null.
ants	A numeric value indicating the number of ants to send (e.g., number of short forms to evaluate) per iteration. Default value is 20.
evaporation	A numeric value which sets the percentage of the pheremone that is retained after evaporation between steps of the algorithm. Default value is 0.9, indicating 10 (0,1), exclusive.
antModel	The lavaan formatted model. See lavaan for more details. Defaults to the default lavaan values.
list.items	A list containing one or more character vectors of item names for each factor, where each factor is a separate element of the list. The items should be input in the order in which the factors are input in i.per.f and factors.
full	A numeric value indicating the total number of unique items in the test or scale.
i.per.f	Vector with number of items per factor (e.g. target number), in the same order of list.items and factors.
factors	Character vector with names of factors in the same order of list.items and i.per.f.
bifactor	Either the name of the factor that all of the chosen items will load on (as character), or 'NULL' if the model is not a bifactor model.
steps	A numeric value that sets the stopping rule, which is the number of ants in a row for which the model does not change.
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.
pheromone.calculation	A character string specifying the method for calculating the pheromone strength. Must be one of "gamma" (standardized latent regression coefficients), "beta" (standardized observed regression coefficients), "regression" (both latent and observed regression coefficients, if they exist) or "variance" (proportion of variance explained by model). You must specify the entire string. Default is gamma.
fit.indices	The fit indices (in lavaan format) extracted for model optimization. See lavaan for more details.
fit.statistics.test	A character vector of the logical test being used for model optimization. The default is "(cfi > 0.95)&(tli > 0.95)&(rmsea < 0.06)". The format for the logical test should match 1) the names of the indices being used in lavaan and 2) the default provided above. At least one fit index must be included.
summaryfile	The name of the summary file generated. A .txt file is suggested. Default is "summary.txt" and writes into the current working directory. This file writes a line for each ant within each step and includes (a) a vector of a 0/1 value for each item indicating whether the item was selected by that ant, (b) the run number, (c) the count number, (d) the ant number, and (e) the current pheromone level.
feedbackfile	The name of the feedback file generated. An .html file is suggested. Default is "iteration.html" and writes into the current working directory. This file saves the result of each run, which includes (a) the run number, (b) the count number, (c) the ant number, (d) the step number (if the current run is successful) or "Failure" (if the current run is unsuccessful), and for successful runs (f) the chosen fit statistics (from fit.indices), the average of the gammas and betas (standardized regression coefficients), and the overall variance explained of the current run.
max.run	The maximum number of ants to run before the algorithm stops. This includes failed iterations as well. Default is 1000.
parallel	An option for using parallel processing. If TRUE, the function will utilize all available cores (up to the number of ants). Default is TRUE.

Details

This function sends a specified number of ants per iteration, which randomly select items to build a model, then evaluates the model based on pheromone levels. The pheromone levels are updated after each iteration according to the best-fitting model of that iteration. The algorithm's stopping rule is to end the search when a certain solution is the same for a given number of ants in a row.

PREPARATORY STEPS: For the ACO algorithm implementation for short for selection, the following decisions are needed:

1. Determine the target size for the short form.

2. Determine which characteristics should be optimized.

3. Define how the pheronome level will be computed: This is a function of the characteristics of the short form that will be optimized. In Leite, Huang and Marcoulides (2008), the pheronomone level was zero if model fit indices did not meet Hu and Bentler's (1999) suggested thresholds, and equal to the sum of path coefficients of a predictor variable if model fit indices met thresholds. Currently, the package only implements pheromone calculation based on regression coefficients or variance explained, with user-selected model fit index thresholds.

4. Define how many short forms should be evaluated before the best-so-far pheronome level is examined. Leite, Huang and Marcoulides (2008) used 10 short forms.

5. Define the percentage of pheronome evaporation, if any. Leite, Huang and Marcoulides (2008) used 5%.

6. Define convergence criterion. Leite, Huang and Marcoulides (2008) set the algorithm to converge if the short form did not improve in 100 x number of short forms in step 4.

IMPLEMENTATION: Once these decisions are made, the ACO algorithm selects short forms with the following steps:

Step 1. All items are assigned an initial weight of 1.

Step 2. A set of n short forms is selected by sampling with probability proportional to the item weights.

Step 3. Fit the latent variable model to the n short forms.

Step 4. Calculate the pheromone levels for the n short forms. Define the best-so-far pheronome level (if iteration 1) or compare the current best pheronome from the set of n short forms to the best-so-far pheronome.

Step 5. If the pheromone level of the best short form from step 4 exceeds the best-so-far pheronome level, update the best-so-far pheromone level and add it to the current weight of the items of the best short form.

Step 6. Return to step 2 until convergence criterion is reached.

Value

A list with four elements: the first containing a named matrix with final model's best fit indices, the final pheromone level (either the mean of the standardized regression coefficients (gammas, betas, or both), or the mean variance explained), and a series of 0/1 values indicating the items selected in the final solution, the second element containing tbe summary matrix of the best fit statistic value(s) for each run, the items chosen for said best fit, the mean gamma, beta, and variance explained for the best fit, and the item pheromone levels after each run, the third containing the best-fitting lavaan model object, and the fourth containing the best-fitting model syntax.

Author(s)

Anthony W Raborn, [e-mail]

See Also

antcolony.mplus

Other Ant Colony Algorithms: antcolony.mplus()

Examples

# a 3-factor example using the HolzingerSwineford1939 data from `lavaan`

# some changes to the default values
# notice that in this example we are recreating the original model
abilityShortForm <- antcolony.lavaan(
  data = lavaan::HolzingerSwineford1939,
  ants = 2, evaporation = 0.7,
  antModel = " visual  =~ x1 + x2 + x3
             textual =~ x4 + x5 + x6
             speed   =~ x7 + x8 + x9 ",
  list.items = list(c(
    "x1",
    "x2", "x3"
  ), c("x4", "x5", "x6"), c("x7", "x8", "x9")), full = 9, i.per.f =
    c(3, 3, 3), factors = c("visual", "textual", "speed"), steps = 2, fit.indices =
    c("cfi"), fit.statistics.test = "(cfi > 0.6)", summaryfile =
    NULL, feedbackfile = NULL, max.run = 2, parallel = FALSE
)
## Not run: 
# using simulated test data and the default values for lavaan.model.specs
# first, read in the original or "full" model
data(exampleAntModel) # a character vector for a lavaan model

# then, create the list of the items by the factors
# in this case, all items load onto the general 'Ability' factor
list.items <- list(c(
  "Item1", "Item2", "Item3", "Item4", "Item5",
  "Item6", "Item7", "Item8", "Item9", "Item10",
  "Item11", "Item12", "Item13", "Item14", "Item15",
  "Item16", "Item17", "Item18", "Item19", "Item20",
  "Item21", "Item22", "Item23", "Item24", "Item25",
  "Item26", "Item27", "Item28", "Item29", "Item30",
  "Item31", "Item32", "Item33", "Item34", "Item35",
  "Item36", "Item37", "Item38", "Item39", "Item40",
  "Item41", "Item42", "Item43", "Item44", "Item45",
  "Item46", "Item47", "Item48", "Item49", "Item50",
  "Item51", "Item52", "Item53", "Item54", "Item55", "Item56"
))

# load the data
data(simulated_test_data)

# finally, call the function with some minor changes to the default values.
abilityShortForm <- antcolony.lavaan(
  data = simulated_test_data,
  ants = 5, evaporation = 0.7, antModel = exampleAntModel,
  list.items = list.items, full = 56, i.per.f = 20,
  factors = "Ability", steps = 3, fit.indices = c("cfi", "rmsea"),
  fit.statistics.test = "(cfi > 0.95)&(rmsea < 0.05)",
  summaryfile = "summary.txt",
  feedbackfile = "iteration.html",
  max.run = 500
)

abilityShortForm # print the results of the final short form

## End(Not run)

ShortForm documentation built on March 31, 2023, 6:04 p.m.