rel_irt {lazy.irt} R Documentation

## Calculation of Test Reliability and Average SEM under IRT

### Description

Calculation of Test Reliability and Average SEM under IRT

### Usage

```rel_irt(
param,
weight = NULL,
maxscore = 100,
npoints = 51,
thmin = -4,
thmax = 4,
thdist = 1,
print = 1,
plot = 1
)
```

### Arguments

 `param` Item Parameter Data Frame `weight` Weight data frame `maxscore` The maximum score to be used to calculate var(X) etc. `npoints` # of discrete points for theta `thmin` Minimum value of discrete thata value `thmax` Maximum value of discrete thata value `thdist` Type of theta distribution = 0 to use uniform, = 1 to use N(0,1) `print` = 1 to print result `plot` = 1 to plot result

### Details

For observed score: X = TCC(theta) + E:
var(E) = E(var(E|theta)) = E(var(X|theta))
var(X) = E(var(X|theta)) + var(E(X|theta))
= var(E) + var(TCC)
var(T) = var(TCC)

For thetahat based score: Y = theta + error
vae(error) = E(var(error|theta)) = var(thetahat|theta) = 1/info
var(thetahat) = E(var(thetahat|theta)) + var(E(thetahat|theta))
= E(1/info) + var(theta)
var(theta) = 1

Note that the value depends on the range and the shape of the theta distribution.
Try changing npoints, thmin and thmax.

### Value

A list of:

thmin, thmax, npoints, thdist
SigmaX2 Observed Score Variance
SigmaT2 True Score Variance
SigmaT22 Shoulld be the same as above
SigmaE2 Error Score Variance
aSEM Average Standard Error of Measurement
rel The reliability coefficient

SigmaX_theta2 Variance of Thetahat
SigmaT_theta2 Variance of Theta
SigmaE_theta2 Average Variance of Thetahat
aSEM_theta Average Standard Error of Measurement of Thetahat
rel_theta The reliability coefficient of Thetahat based Score

SigmaX_xs2 Variance of X in [0,maxscore]
SigmaT_xs2 Variance of T in [0,maxscore]
SigmaE_xs2 Average Variance of E in [0,maxscore]
aSEM_xs Average Standard Error of Measurement ofX in [0,maxscore]
rel_xs The reliability coefficient

SigmaX_ys2 Variance of Thetahat in [0,maxscore]
SigmaT_ys2 Variance of Theta in [0,maxscore]
SigmaE_ys2 Average Variance of Thetahat given theta in [0,maxscore]
aSEM_ys Average Standard Error of Measurement of Thetahat in [0,maxscore]
rel_ys The reliability coefficient

### Examples

```res <- rel_irt( paramB1, thmin=-3, thmax=3 )

res <- rel_irt( paramB1, thmin=-3, thmax=3, thdist=0 )

```

[Package lazy.irt version 0.1.3 Index]