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]