flatten_SEM_theta {lazy.irt}

R Documentation

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

Description

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

Usage

flatten_SEM_theta(
  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:
theta: The value of theta
stdx_theta: SEM of X at theta
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_theta( out_obscore, sigma=1, plot=1, print=1 )

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

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