simulatedAnnealing {ShortForm}

An adaptation of the simulated annealing algorithm for psychometric models.

Description

Simulated annealing mimics the physical process of annealing metals together. Kirkpatrick et al. (1983) introduces this analogy and demonstrates its use; the implementation here follows this demonstration closely, with some modifications to make it better suited for psychometric models.

Usage

simulatedAnnealing(
  initialModel,
  originalData,
  maxSteps,
  fitStatistic = "cfi",
  temperature = "linear",
  maximize = TRUE,
  Kirkpatrick = TRUE,
  randomNeighbor = TRUE,
  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),
  maxChanges = 5,
  restartCriteria = "consecutive",
  maximumConsecutive = 25,
  maxItems = NULL,
  items = NULL,
  bifactor = FALSE,
  setChains = 1,
  shortForm = T,
  ...
)

Arguments

initialModel

The initial model as a character vector with lavaan model.syntax.

originalData

The original data.frame with variable names.

maxSteps

The number of iterations for which the algorithm will run.

fitStatistic

Either a single model fit statistic produced by lavaan, or a user-defined fit statistic function.

temperature

Either an acceptable character value, or a user-defined temperature function. The acceptable values are "linear", "quadratic", or "logistic".

maximize

Logical indicating if the goal is to maximize (TRUE) the fitStatistic for model selection.

Kirkpatrick

Either TRUE to use Kirkpatrick et al. (1983) acceptance probability, or a user-defined function for accepting proposed models.

randomNeighbor

Either TRUE to use the included function for randomNeighbor selection, or a user-defined function for creating random models.

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.

maxChanges

An integer value greater than 1 setting the maximum number of parameters to change within randomNeighbor. When creating a short form, should be no greater than the smallest reduction in items loading on one factor; e.g., when reducing a 2-factor scale from 10 items on each factor to 8 items on the first and 6 items on the second, maxChanges should be no greater than 2.

restartCriteria

Either "consecutive" to restart after maxConsecutiveSelection times with the same model chosen in a row, or a user-defined function.

maximumConsecutive

A positive integer value used with restartCriteria.

maxItems

When creating a short form, a vector of the number of items per factor you want the short form to contain. Defaults to NULL.

items

A character vector of item names. Defaults to NULL. Ignored if maxItems==FALSE.

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). Ignored if maxItems==FALSE.

setChains

Numeric. Sets the number of parallel chains to run. Default to 1, which also sets the algorithm to run serially (e.g., on a single processor). Values greater than 1 result in the chains running on parallel processes using the doSNOW and foreach packages.

shortForm

Logical. Are you creating a short form (TRUE) or not (FALSE)? Default is TRUE.

...

Further arguments to be passed to other functions. Not implemented for any of the included functions.

Details

Outline of the Pieces of the Simulated Annealing Algorithm

• initialModel – the initial, full form

• currentModel – the model of the current step

• maxSteps – the maximum number of steps (iterations)

• currentStep – the current step

• currentTemp – the current temperature. A function of the number of steps (such that temp = 0 at maxSteps), and values that control the shape of the overall temperature. A part of the function that determines the acceptance probability of newly – generated models

• randomNeighbor – a function that determines how the form is changed at each step. Should be able to change one or more parameters, and should have a way to control how many are changed.

• goal – a function that determines the "goodness" of the currentModel. Typically in SA goodness is defined as minimization! Sometimes called an energy function

• selectionFunction – a function that determines if a randomNeighbor change is accepted. Uses the goal function that determines the "goodness" of the currentModel and the "goodness" of the randomNeighbor, and the currentTemp to generate a probability of acceptance, then compares this probability to a Uniform(0,1) variable to determine if accepted or not. A standard version of this is: (Kirkpatrick et al., 1983)

• bestModel – the model with the best value of the goal function achieved so far

• bestGoal – the best value of the goal function achieved so far

• restartCriteria – if utilized, this would "restart" the SA process by changing currentModel to bestModel and continuing the process. Could be based on (1) the currentStep value, (2) the difference between goal(currentModel) and goal(bestModel), (3) randomness (i.e., could randomly restart, could randomly restart based on some values, etc), (4) other criteria.

Value

A named list: the 'bestModel' found, the 'bestFit', and 'allFit' values found by the algorithm.

Examples

## Not run: 
data(exampleAntModel)
data(simulated_test_data)
trial1 <- simulatedAnnealing(
  initialModel = lavaan::cfa(
    model = exampleAntModel,
    data = simulated_test_data
  ),
  originalData = simulated_test_data, maxSteps = 3,
  fitStatistic = "rmsea", maximize = FALSE
)
summary(trial1) # shows the resulting model

trial2 <- simulatedAnnealing(
  initialModel = exampleAntModel,
  originalData = simulated_test_data,
  maxSteps = 2, maxItems = 30, items = paste0("Item", 1:56)
)
summary(trial2) # shows the resulting model

## End(Not run)