Description Usage Arguments Details Value Author(s) References See Also Examples
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.
1 2 3 4 5 6 7  antcolony.mplus(ants = 20, evaporation = 0.95, mplus = NULL,
list.items = NULL, full = NULL, i.per.f = NULL, factors = NULL,
steps = 50, max.run = 1000, resultfile = NULL,
summaryfile = "summary.txt", min.CFI = 0.95, min.TLI = 0.95,
max.RMSEA = 0.06, feedbackfile = "iteration.html", loc.gammas,
loc.variances, predictors, var.predictors, Mplus.Automation = FALSE,
dataOut = "tempModel.dat", modelOut = "tempModel.inp")

ants 
A numeric value indicating the number of ants to send send (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. 
mplus 
When 
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

full 
A numeric value indicating the total number of unique items in the test or scale. 
i.per.f 
A vector with number of items per factor (e.g. target number),
in the same order of 
factors 
A character vector with the names of the factors in the same
order of 
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. 
max.run 
The maximum number of ants to run before the algorithm stops. This includes failed iterations as well. Default is 1000. 
resultfile 
A character vector containing the file path where the MPlus
results for the current ant model is saved. If the file is not in the
current working directery, the full path must be specified. Not used when

summaryfile 
A character vector containing 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. 
min.CFI 
A numeric value indicating the minimum CFI for "acceptable" model fit. Models with CFI less than this value are automatically rejected. Default is 0.95. 
min.TLI 
A numeric value indicating the minimum TLI for "acceptable" model fit. Models with TLI less than this value are automatically rejected. Default is 0.95. 
max.RMSEA 
A numeric value indicating the maximum RMSEA for "acceptable" model fit. Models with RMSEA greater than this value are automatically rejected. Default is 0.06 
feedbackfile 
A character vector containing 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 value of CFI, TLI, and RMSEA fit indices, the average of the gammas (standardized regression coefficients), and the overall variance explained of the current run. 
loc.gammas 
A numeric vector with the line numbers where the regression
coefficients of the MIMIC model start and end (locations). Not used with

loc.variances 
A numeric ector with the line numbers of the residual
variances of the latent factors. Not used with 
predictors 
Character vector with names of predictor variables, if any. 
var.predictors 
A numeric ector with variances of the predictor(s), if
any. Not used with 
Mplus.Automation 
Logical. If 
dataOut 
A character vector specifying the location and name of the data
file generated by 
modelOut 
A character vector specifying the location and name of the
Mplus model file generated by 
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 bestfitting 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. When constructing the mplus dataset
and when Mplus.Automation=FALSE
, make sure that items in 'categorical
are' and 'usevariables' are specifications that take the same number of lines
per short form.
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 userselected model fit index thresholds.
4. Define how many short forms should be evaluated before the bestsofar 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 items' weights.
Step 3. Fit latent variable model to the n short forms.
Step 4. Calculate the pheronome levels for the n short forms. Define the bestsofar pheronome level (if iteration 1) or compare the current best pheronome from the set of n short forms to the bestsofar pheronome.
Step 5. If the pheronome level of the best short form from step 4 exceeds the bestsofar pheronome level, update the bestsofar 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.
A named matrix containing final model's best RMSEA, CFI, and TLI values, the final pheromone level (the mean of the standardized regression coefficients (gammas)), and a series of 0/1 values indicating the items selected in the final solution.
Walter Leite; Anthony W Raborn, [email protected]
https://doi.org/10.1080/00273170802285743
Other Ant Colony Algorithms: antcolony.lavaan
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59  ## Not run:
# use MplusAutomation to find a 15item short form of a simulated 56item unidimensional test
# first, 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'))
# then, load the data
data(simulated_test_data)
# Create the mplusObject with MplusAutomation
# notice the explicit call of each item, instead of the shorthand "Item1Item56"
initial.MplusAutomation.model < MplusAutomation::mplusObject(
TITLE = "Trial ACO MpluAutomation with FERA 2016 Data;",
MODEL = "Ability BY 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;",
ANALYSIS = "ESTIMATOR = WLSMV;",
VARIABLE = "CATEGORICAL = 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;",
OUTPUT = "stdyx;",
rdata = simulated_test_data
)
# finally, call the function with some minor changes to the default values.
abilityShortForm = antcolony.mplus(ants = 3, evaporation = 0.7,
mplus = initial.MplusAutomation.model,list.items = list.items, full = 56,
i.per.f = 15, factors = 'Ability', steps = 3, max.run = 50, resultfile = NULL,
summaryfile = 'C:/Users/lordmaxwell/Desktop/summary.txt',
min.CFI = 0.95, min.TLI = 0.95, max.RMSEA = 0.06,
feedbackfile = 'C:/Users/lordmaxwell/Desktop/iteration.html', Mplus.Automation=TRUE,
dataOut = 'exampleModel.dat',
modelOut = 'exampleModel.inp')
## End(Not run)

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