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.
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 )
out_obscore |
The result 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 |
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 |
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.
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.
# 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 )