conv2Bnc {lazy.irt}

R Documentation

Conversion to Two Parameter Normal Ogive Model with Fixed c Parameter

Description

Conversion to 2PNM with fixed c parameter using Weighted Least Squares
Japanese help file: (conv2Bnc_JPH)

Usage

conv2Bnc(
  param,
  theta = NULL,
  init = 1,
  paramBnc = NULL,
  cval = 0.2,
  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", "Bn3"
theta	Vector of theta points
init	= 1 to use fitG2P, else use equally spaced b-parameters
paramBnc	initial parameter data frame. This has priority over init.
cval	fixed c parameter value.
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 2PNMc 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_2PNMc(theta|PARAM)) )^2 )
with respect to the 2PNMc item parameters, PARAM,
where icrf(theta) is the icrf of input items,
icrf_2PNMc(theta|PARAM) is the icrf of fitted 2PNMc 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_2PNMc(theta|PARAM) )^2 )
with respect to the 2PNMc item parameters, PARAM,
where info_i(theta) is the item information function of input items and
info_i_2PNMc(theta|PARAM) is the item information function of the fitted 2PNMc items.

If method = 2, this function minimizes
sum( w*( vec(info_ic(theta)) - vec(info_ic_2PNMc(theta|PARAM)) )^2 )
with respect to the 2PNMc item parameters, PARAM,
where info_ic(theta) is the item category information function of input items and
info_ic_2PNMc(theta|PARAM) is the item category information function of the fitted 2PNMc items.

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 2PNMc item parameter data frame paramP: Input 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 3PNM items to 2PNMc items
res1 <- conv2Bnc( paramA1[c(2,4),], maxiter=20, plot=1, method=1, cval=0.25 )
res2 <- conv2Bnc( paramA1[c(2,4),], maxiter=20, plot=1, method=2, cval=0.25 )
Print(res1$rmse_p, res1$rmse_iic, res1$rmse_ii)
Print(res2$rmse_p, res1$rmse_iic, res1$rmse_ii)

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