View source: R/simulated_annealing.R

simulatedAnnealing | R Documentation |

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.

```
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,
...
)
```

`initialModel` |
The initial model as a |

`originalData` |
The original |

`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 |

`maximize` |
Logical indicating if the goal is to maximize ( |

`Kirkpatrick` |
Either |

`randomNeighbor` |
Either |

`lavaan.model.specs` |
A |

`maxChanges` |
An |

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

`maximumConsecutive` |
A positive |

`maxItems` |
When creating a short form, a |

`items` |
A |

`bifactor` |
Logical. Indicates if the latent model is a bifactor model. If |

`setChains` |
Numeric. Sets the number of parallel chains to run. Default to |

`shortForm` |
Logical. Are you creating a short form ( |

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

**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.

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

```
## 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)
```

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