fitP2G_ls {lazy.irt}R Documentation

Conversion of Graded Response Items to Partial Credit Items

Description

Conversion of Graded Response Items to Partial Credit Items

Usage

fitP2G_ls(paramG, theta = NULL, init = 1, method = 0, wtype = 1,
  wmean = 0, wsd = 1, DinP = 1, npoints = 21, thmin = -3, thmax = 3,
  maxiter = 500, eps = 1e-06, print = 1, plot = 0)

Arguments

paramG

Item Parameter Data Frame for Graded Response Items

theta

Vector of theta points

init

= 1 to use fitP2G, else use equally spaced b-parameters
Setting this equal to 0 may result in better solution, especially in fitP2G_ls.

method

= 0 to use icrf to calculate rmse (default)
= 1 to use item info to calculate rmse,
= 2 to use item category info* to calculate rmse

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 thata value

thmax

Maximum value of discrete thata value

maxiter

Maximum # of GN iterations

eps

Convergence criterion for the relative improvement of rmse

print

>= 1 to print result

plot

>= 1 to plot result

Details

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

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

If method = 1, this function minimizes
sum( w*( vec(info_i(theta)) - vec(info_i_GRM(theta)) )^2 )
with respect to the GPCM item parameters,
where info_i(theta) is the item infomation function of input GRM items and
info_i_GRM(theta) is the item infomation function of fitted GPCM items.
If method = 2, this function minimizes
sum( w*( vec(info_ic(theta)) - vec(info_ic_GRM(theta)) )^2 )
with respect to the GPCM item parameters,
where info_ic(theta) is the item category infomation function of input GRM items and
info_ic_GRM(theta) is the item category infomation function* of fitted GPCM items.


When 3PLM items are included, 2PLM will be fitted.


Weighted Gauss-Newton method is used for the minimization.

Value

A list of:
paramG: Input GRM item parameter data frame (subset, type="G" or "Gn)
paramP: GPCM Item Parameter Data Frame (type="P")
grad: Gradient matrix
wtype, wmean, wsd, method, init
rmse_p: rmse in terms of icrf (method=0)
rmse_ii: rmse in terms of item infomation (method=1)
rmse_iic: rmse in terms of item category infomation* (method=2)
icrfP, infoP, iteminfoP
icrfG, infoG, iteminfoG

Examples

paramP1 <- fitP2G_ls( paramS2, plot=1, print=1 )$paramP
paramG1 <- fitG2P_ls( paramP1, plot=1, print=1 )

# convert 3PLM and GPCM items
param <- paramA1[c(2,6,9),]
theta <- seq(-4,4,length=51)

# maxiter below is too small!!
res0 <- fitP2G_ls( param, theta, maxiter=20, plot=1, wtype=1, method=0 )
res1 <- fitP2G_ls( param, theta, maxiter=20, plot=1, wtype=1, method=1 )

Print(res0$rmse_p, res0$rmse_iic, res0$rmse_ii)
Print(res1$rmse_p, res1$rmse_iic, res1$rmse_ii)



[Package lazy.irt version 0.1.3 Index]