conv2Gn {lazy.irt}

R Documentation

Conversion to Normal Graded Response Model

Description

Conversion to Normal Graded Response Model using Weighted Least Squares
Japanese help file: (conv2Gn_JPH)

Usage

conv2Gn(
  param,
  theta = NULL,
  init = 1,
  paramG = NULL,
  method = 1,
  wtype = 1,
  wmean = 0,
  wsd = 1,
  DinP = 1,
  npoints = 21,
  thmin = -3,
  thmax = 3,
  printGN = 0,
  maxiter = 500,
  eps = 1e-06,
  epsg = 1e-06,
  epsx = 1e-09,
  print = 1,
  plot = 0
)

Arguments

param	Item Parameter Data Frame with item types "B3","Bn","Bn3","P", "G"
theta	Vector of theta points
init	= 1 to use fitG2P, else use equally spaced b-parameters
paramG	initial parameter data frame. This has priority over init.
method	= 1 to use item category response function (icrf) to calculate rmse (default) = 2 to use item category information function (icif) to calculate rmse = 3 to use item response function (irf) to calculate rmse (not yet available), = 4 to use item information function (iif) to calculate rmse, (not yet available),
wtype	= 0 not to use dnorm(theta) as the weight
wmean	The mean of normal distribution to be used as the weight
wsd	The sd of normal distribution to be used as the weight
DinP	= 1 to include D=1.7 in logistic function
npoints	# of discrete points for theta
thmin	Minimum value of discrete theta value
thmax	Maximum value of discrete theta value
printGN	print level for lazy.mat::GN function
maxiter	Maximum # of GN iterations
eps	Convergence criterion for the relative improvement of rmse
epsg	Convergence crit for the maximum absolute value of the gradient
epsx	Convergence crit for the maximum absolute change of the parameter value
print	>= 1 to print result
plot	>= 1 to plot result

Details

This function finds the set of Normal GRM item parameters which best fit the given icrfs or item info functions of the items in the input parameter data frame.

If method = 0, this function minimizes
sum( w*( vec(icrf(theta)) - vec(icrf_GRM(theta|PARAM)) )^2 )
with respect to the GRM item parameters, PARAM,
where icrf(theta) is the icrf of input items,
icrf_GRM(theta|PARAM) is the icrf of fitted GRM items,
and w is the weight vector ( N(wmean,wsd^2) or 1 ).

If method = 1, this function minimizes
sum( w*( (info_i(theta) - info_i_GRM(theta|PARAM) )^2 )
with respect to the GRM item parameters, PARAM,
where info_i(theta) is the item information function of input items and
info_i_GRM(theta|PARAM) is the item information function of the fitted GRM items.

If method = 2, this function minimizes
sum( w*( vec(info_ic(theta)) - vec(info_ic_GRM(theta|PARAM)) )^2 )
with respect to the GRM item parameters, PARAM,
where info_ic(theta) is the item category information function of input items and
info_ic_GRM(theta|PARAM) is the item category information function of the fitted GRM items.

When three parameter binary items are included, two parameter normal ogive model will be fitted.
Weighted Gauss-Newton method (lazy.mat::GN) is used for the minimization with the numerical Jacobian matrix calculated by lazy.mat::JacobianMat.

Value

A list of:
paramNew: Fitted normal GRM item parameter data frame
2PLM or 2PNM items remain unchaged.
paramP: Input GPCM Item Parameter Data Frame
grad: Gradient matrix
wtype, wmean, wsd, method, init
rmse_p: rmse in terms of icrf (minimized with method=1)
rmse_irf: rmse in terms of irf
rmse_ii: rmse in terms of item information
rmse_iic: rmse in terms of item category information (minimized with method=2)
icrfNew, icifNew, iifNew, irfNew
icrfOld, icifOld, iifOld, irfOld

Examples

# convert 3PLM and GPCM items to normal GRM items
param <- paramA1[c(2,5,8),]
theta <- seq(-4,4,length=51)#'
# maxiter for method=2 is too small.
res1 <- conv2Gn( param, theta, maxiter=20, plot=1, wtype=1, method=1 )
res2 <- conv2Gn( param, theta, maxiter=2, plot=1, wtype=1, method=2 )

Print(res1$rmse_p, res1$rmse_iic, res1$rmse_ii)
Print(res2$rmse_p, res1$rmse_iic, res1$rmse_ii)

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