fitG2P_ls {lazy.irt}R Documentation

Conversion of Partial Credit Items to Logistic Graded Response Items

Description

Conversion of Partial Credit Items to Logistic Graded Response Items

Usage

fitG2P_ls(paramP, 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

paramP

Item Parameter Data Frame for 2PLM or GPCM Items

theta

Vector of theta points

init

= 1 to use fitP2G, else use equally spaced b-parameters

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


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


Weighted Gauss-Newton method is used for the minimization.

Value

A list of:
paramP: Input GPCM item parameter data frame (subset, type="P")
paramG: GRM Item Parameter Data Frame (type="G")
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(2,5,8),]
theta <- seq(-4,4,length=51)

# maxiter below is too small!!
res0 <- fitG2P_ls( param, theta, maxiter=20, plot=1, wtype=1, method=0 )
res1 <- fitG2P_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]