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 )

[Package lazy.irt version 0.1.3 Index]