fitIRT: Fit a binary Item Response Theory (IRT) model

In cdriveraus/bigIRT: Fits item response theory models to big data

Fit a binary Item Response Theory (IRT) model

Description

This function fits a binary Item Response Theory (IRT) model using various parameters and options.

Usage

fitIRT(
  dat,
  score = "score",
  id = "id",
  item = "Item",
  scale = "Scale",
  pl = 1,
  personDat = NA,
  personPreds = character(),
  itemDat = NA,
  AitemPreds = character(),
  BitemPreds = character(),
  CitemPreds = character(),
  DitemPreds = character(),
  itemSpecificBetas = FALSE,
  betaScale = 10,
  invspAMeandat = 0.542,
  invspASD = 2,
  BMeandat = 0,
  BSD = 10,
  logitCMeandat = -4,
  logitCSD = 2,
  logitDMeandat = 4,
  logitDSD = 2,
  AbilityMeandat = array(0, dim = c(length(unique(dat[[scale]])))),
  AbilitySD = array(10, dim = c(length(unique(dat[[scale]])))),
  AbilityCorr = diag(1, c(length(unique(dat[[scale]])))),
  AMeanSD = 1,
  BMeanSD = BSD,
  logitCMeanSD = logitCSD,
  logitDMeanSD = logitDSD,
  AbilityMeanSD = array(1, dim = c(length(unique(dat[[scale]])))),
  iter = 2000,
  cores = 6,
  carefulfit = FALSE,
  ebayes = TRUE,
  ebayesmultiplier = 2,
  ebayesFromFixed = FALSE,
  ebayesiter = 1,
  estMeans = c("ability", "B", "C", "D"),
  priors = TRUE,
  integrateEachAbility = FALSE,
  integrateEachAbilityFixedSE = FALSE,
  mml = FALSE,
  NintegratePoints = 5,
  normalise = FALSE,
  normaliseScale = 1,
  normaliseMean = 0,
  dropPerfectScores = TRUE,
  trainingRows = 1:nrow(dat),
  init = NA,
  tol = 1e-08 * 10^(log(nrow(dat), 10)),
  ...
)

Arguments

dat	A data frame containing the data to be analyzed.
score	Character. The name of the column in dat representing the response. Default is 'score'.
id	Character. The name of the column in dat representing the individual. Default is 'id'.
item	Character. The name of the column in dat representing the item. Default is 'Item'.
scale	Character. The name of the column in dat representing the scale of each item. Default is 'Scale'.
pl	Integer. The number of parameters for the logistic model (1PL, 2PL, 3PL, or 4PL). Default is 1.
personDat	Data frame. Any fixed ability data for persons. Default is NA.
personPreds	Character vector. Names of predictors for person parameters found in data. Default is an empty character vector.
itemDat	Data frame. Any fixed item data. Default is NA.
AitemPreds	Character vector. Names of predictors for item discrimination parameters. Default is an empty character vector.
BitemPreds	Character vector. Names of predictors for item difficulty parameters. Default is an empty character vector.
CitemPreds	Character vector. Names of predictors for item guessing parameters. Default is an empty character vector.
DitemPreds	Character vector. Names of predictors for item upper asymptote (slipping) parameters. Default is an empty character vector.
itemSpecificBetas	Logical. Whether to allow item-specific betas for covariate effects, or simply estimate one effect per covariate. Default is FALSE.
betaScale	Numeric. Scale of the prior for beta parameters. Default is 10.
invspAMeandat	Numeric. Mean for the prior distribution of the raw discrimination parameters, which subsequently have a 'softplus' log(1+exp(x)) applied. Default is 0.542, giving a mean for A pars of ~ 1.
invspASD	Numeric. Standard deviation for the prior distribution of the raw discrimination parameters. Default is 2.
BMeandat	Numeric. Mean for the prior distribution of the item difficulty parameters. Default is 0.
BSD	Numeric. Standard deviation for the prior distribution of the item difficulty parameters. Default is 10.
logitCMeandat	Numeric. Mean for the prior distribution of the item guessing parameters (on logit scale). Default is -4.
logitCSD	Numeric. Standard deviation for the prior distribution of the item guessing parameters (on logit scale). Default is 2.
logitDMeandat	Numeric. Mean for the prior distribution of the item upper asymptote parameters (on logit scale). Default is 4.
logitDSD	Numeric. Standard deviation for the prior distribution of the item upper asymptote parameters (on logit scale). Default is 2.
AbilityMeandat	Numeric array. Mean for the prior distribution of the ability parameters. Default is 0 for each scale.
AbilitySD	Numeric array. Standard deviation for the prior distribution of the ability parameters. Default is 10 for each scale.
AbilityCorr	Matrix. Correlation matrix for the ability parameters. Default is an identity matrix.
AMeanSD	Numeric. Standard deviation for the prior distribution of the discrimination parameters. Default is 1.
BMeanSD	Numeric. Standard deviation for the prior distribution of the difficulty parameters. Default is BSD.
logitCMeanSD	Numeric. Standard deviation for the prior distribution of the guessing parameters (on logit scale). Default is logitCSD.
logitDMeanSD	Numeric. Standard deviation for the prior distribution of the upper asymptote parameters (on logit scale). Default is logitDSD.
AbilityMeanSD	Numeric array. Standard deviation for the prior distribution of the ability parameters. Default is 1 for each scale.
iter	Integer. Maximum number of iterations for the fitting algorithm. Default is 2000.
cores	Integer. Number of cores to use for parallel computation. Default is 6.
carefulfit	Logical. Whether to use a slower, careful fitting procedure. Default is FALSE. Experimental.
ebayes	Logical. Whether to use empirical Bayes estimation. Default is TRUE. With ebayes, the priors are adapted based on a first pass estimate.
ebayesmultiplier	Numeric. Multiplier for the widths of the empirical Bayes priors. Default is 2, as this appears to work better in practice.
ebayesFromFixed	Logical. Whether to initialize empirical Bayes from any specifed fixed values Default is FALSE.
ebayesiter	Integer. Number of iterations for empirical Bayes estimation. Default is 1.
estMeans	Character vector. Which means to estimate from 'ability', 'A', 'B', 'C', 'D'. Default is c('ability', 'B', 'C', 'D'), with discrimination means fixed.
priors	Logical. Whether to use prior distributions. Default is TRUE.
integrateEachAbility	Logical. Whether to integrate across each ability. Default is FALSE.
integrateEachAbilityFixedSE	Logical. Whether to integrate each ability with fixed standard error. Default is FALSE.
mml	Logical. Experimental and not working well. Whether to use marginal maximum likelihood estimation. Default is FALSE.
NintegratePoints	Integer. Number of integration points for numerical integration. Default is 5.
normalise	Logical. Whether to normalize the output estimates. Default is FALSE.
normaliseScale	Numeric. Scale for normalization. Default is 1.
normaliseMean	Numeric. Mean for normalization. Default is 0.
dropPerfectScores	Logical. Whether to drop perfect scores from each subject and item before estimation. Default is TRUE.
trainingRows	Integer vector. Rows of data to use for estimation of parameters. Default is all rows in dat.
init	Initial values for the fitting algorithm. Default is NA.
tol	Numeric. Tolerance for convergence. Default attempts to sensibly adjust for amount of data.
...	Additional arguments passed to the fitting function.

Value

A list containing the fitted IRT model parameters and additional information about the fit.

Examples

#Generate some data (here 2pl model
require(data.table)
dat <- simIRT(Nsubs = 50,Nitems = 100,Nscales = 1,
  logitCMean = -10,logitCSD = 0,AMean = 1,ASD = .3,
  BMean=0,BSD = .5,
  AbilityMean = 0,AbilitySD = 1)

#fit using bigIRT
fit <- fitIRT(dat$dat,cores=2,score = 'score',id = 'id',
  scale = 'Scale',item = 'Item', pl=2)

  print(fit$personPars)
  print(fit$itemPars)

cdriveraus/bigIRT documentation built on Sept. 14, 2024, 5:42 a.m.