## Calculation of the Information Function associated with the Graded Observed Score.

### Description

Calculation of the Information Function associated with the Graded Observed Score.

### Usage

```graded_info(
out_obscore,
ncat = 5,
method = 1,
brk = NULL,
scorey = NULL,
print = 1,
plot = 0
)
```

### Arguments

 `out_obscore` Output from obscore function `ncat` # of categories to be used `method` = 1 to equal interval on X = 2 to equal interval on percent `brk` Break points to be used or NULL. This has priority over ncat. `scorey` The value of Y or 0 to length(brk)-1. `print` = 1 to print result `plot` = 1 to plot information functions = 2 to plot posterior distribution of theta given Y.

### Details

The graded score, Y, 0 <= Y <= ncat-1, will be calculated on the basis of the (weighted) observed score X as:
` Y=scorey[ unclass( cut( scorex, brk, include.lowest=TRUE ) ) ]`
That is:
` if brk[q] < X <= brk[q+1] then Y = scorey[q] `

Then, the probability distribution of Y given theta will be calculated by summing the probability distribution of X given theta.
Finally, the information function associated with the graded score Y will be calculated as the ratio of the slope of TRF of Y squared to the conditional variance of Y given theta.
The slope of TRF will be calculated numerically.

### Value

A list of:
theta Discrete theta points defined in obscore function.

info Information function (LO) defined in obscore function.

infoX Information function associated with X defined in obscore function.
infoY Information function associated with Y

TRFy_t_t stdy_t

Py_t Distribution of Y given theta

Pt_y Distribution of theta given Y

meant_y Posterior mean of theta given Y

stdt_y Posterior std of theta given Y

### Examples

```# Define the observed score X using the category and the item weights given
# in weightsS21, and calculate the score distribution etc.
out_obscore <- obscore( paramS2, weight=weightS21, npoints=21, print=0 )
# On the basis of the observed score X calculated above using weightS21,
# categorize X into ncat categories to create new score Y.
res <- graded_info( out_obscore, ncat=5, method=1, plot=1 )
res <- graded_info( out_obscore, ncat=9, method=1, plot=1 )

```

[Package lazy.irt version 0.1.3 Index]