flatten_SEM {lazy.irt}R Documentation

Find a Transformation g of the Observed Score X such that Y=g(X) has a Flat Standard Error of Measurement.

Description

Find a Transformation g of the Observed Score X such that Y=g(X) has a Flat Standard Error of Measurement.

Usage

flatten_SEM(out_obscore = NULL, sigma = 1, by_s = 0.1, param = NULL,
  weight = NULL, npoints = 131, thmin = -4, thmax = 4, thdist = 1,
  alpha = 0.1, compress = 0, print = 1, plot = 0, debug = 0)

Arguments

out_obscore

The result of obscore function
This has the priority over the set of the arguments of obscore function.

sigma

The standard error of the transformed score

by_s

The interval for continuous S.

param

Item Parameter Data Frame for obscore

weight

Weight data frame for obscore

npoints

# of discrete points for theta for obscore

thmin

Minimum value of discrete thata value for obscore

thmax

Maximum value of discrete thata value for obscore

thdist

Type of theta distribution for obscore
= 0 to use uniform, = 1 to use N(0,1)

alpha

small prob for quantile and confidence interval for obscore

compress

= 1 to remove zero-probability weighted total observed scores for obscore

print

> 1 to print result

plot

> 1 to plot result

debug

= 1 to print intemediate result

Details

Let stdx(t) be the standard error of measurement of X at t.
This can be calculated as stdx_t by the obscore function.
The standard deviation of Y=g(X) at t can be approximated by
g-dash(t)*stdx(t)
and we want it to be a constant (sigma).
Therefore,
g-dash(t) = sigma / stdx(t))
and the g function can be recovered by integrating the above g-dash.
This g is the vaiance-stabilizing transformation.

Notes:
Recommended to use npoints=151, thmin=-4, thmax=4 or larger for obscore function.

Value

A list of the following:
t: The value of the true score
stdx_t: SEM of X at T
s: The transformed true score: Y=g(X) and s=g(t)
gdash: The derivative of g
stdy_s: SEM of Y at s
lengtht: length of t
sigma: New SEM value specified
brk_x2u: Break points of X to create S.
brk_x2uc: Break points of X to create almost condinuous S.

out_obscore: The output from the obscore function.

Examples


# tiny set of binary items
param=paramB1
maxscore=sum(param$ncat-1)
param$p1=1
out_obscore <- obscore( param )
res=flatten_SEM( out_obscore, sigma=1, plot=1, print=1 )

# binary and polytomous items
res2=flatten_SEM( param=paramS1, sigma=1, plot=1, print=1 )



[Package lazy.irt version 0.1.3 Index]