simAnneal: Main function that performs simulated annealing (SA)

In falkcarl/mpirt: Semi- and non-parametric item response theory

Main function that performs simulated annealing (SA)

Description

Main function that performs simulated annealing (SA)

Usage

simAnneal(
  dat,
  k.mat,
  itermax = 1000,
  inittemp = 10,
  type = "aic",
  random = FALSE,
  startimat = NULL,
  step = 1,
  items = 1,
  temptype = "straight",
  ...
)

Arguments

dat	The data, typically in a format prepared by mxFactor.
k.mat	Starting matrix that represents k for each item (e.g., as generated by newkmat).
itermax	Number of iterations for SA algorithm.
inittemp	Staring temperature for SA algorithm.
type	Which information criterion to use as the objective function to minimize. Anything supported by getIC is currently possible and "aic" or "bic" are typical choices.
random	Logical value indicating whether to just automatically accept neighboring models (meaning not actually do SA).
startimat	Starting item parameter matrix, if any. Used only for the first iteration.
step	Maximum allowed change in k for candidate models. e.g., step 1 -> k=0 to k=1 allowed, but not k=0 to k=2. Smaller steps less likely to have estimation problems.
items	How many items' k should be perturbed for computing a neighboring model?
temptype	Method for temperature schedule decreases (see newTemp function).
...	Additional arguments to be passed to fitMP.

Details

In monotonic polynomial (MP) models, each item may have a different polynomial order. This function performs simulated annealing to select polynomial order. Details of the exact implementation are given in Falk (2019). In brief, at a given iteration of the algorithm, a candidate model is generated by perturbing the polynomial order for a certain number of items. The candidate model is fit to the data and model fit is compared to the current model. If fit improves, the candidate model is accepted and will be the current model in the next iteration. If the candidate model's fit is worse, it may still be accepted with some non-zero probability that depends on the discrepancy in fit and the current "temperature" of the algorithm. High temperatures will result in a higher probability of accepting a poorer candidate model. In the algorithm, temperature declines towards zero over time, yet depends on the temperature schedule and number of iterations(see newTemp).

This function assumes that all items on the test are candidates for higher order polynomials; functionality to restrict the search space is possible, but not yet implemented. The only functionality for search space restriction is the highest k to consider for each item, as determined by the size of the matrix in k.mat. Note also that the starting polynomial order is also determined by this matrix.

Value

A list with the following elements

Slots

k.mat

A matrix of the same type as its input that encodes the polynomial order for each item.

beste

A recording of the best objective function encountered from the best fitting model.

bestk

A vector encoding the values of k for the best model.

bestmod

The best fitted mxModel. This is what may be most useful to pass to other functions or to extract information from as it is a fitted MP model.

bestimat

The item parameter matrix from the best fitted model (useful if one wants to do more iterations or re-fit the same model).

Examples

# For now, just load something from mirt
#library(mirt)
data(Science)

dat <- mxFactor(Science,levels=1:4)
safit <- simAnneal(dat, k.mat=newkmat(0,2,4),
                   itermax = 4*6,
                   inittemp = 5,
                   type = "aic",
                   step = 1,
                   items = 1,
                   temptype = "logarithmic",
                   itemtype=rep("grmp",4))


samod <- safit$bestmod

getIC(samod, "aic") # extract AIC from best model
getkrec(samod, 4) # value of k for each item from best model

falkcarl/mpirt documentation built on July 11, 2024, 12:09 a.m.