graded_info {lazy.irt} | R Documentation |
Calculation of the Information Function associated with the Graded Observed Score.
graded_info(out_obscore, ncat = 5, method = 1, brk = NULL, scorey = NULL, print = 1, plot = 0)
out_obscore |
Output from obscore function |
ncat |
# of categories to be used |
method |
= 1 to equal interval on X |
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 |
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.
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
# 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 )