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Roche, Wainer, and Thissen (1975) calibrated
34 "indicators" (items) of skeletal maturity using
Samejima's (1969) graded model; a description of the model
and methods used is in Chapter V of that volume. The parameters
of the data for the males are used here to "score"
(estimate  =
skeletal age) using the following data in the file knee.dat:
40 1 0.5 2112111111112111111111111111111111
33 1 1.0 3113211111112122111111111111111111
33 1 2.0 4333211111113122111111111111111111
29 1 3.0 4543211111113122111111011111111111
8 1 5.0 5553211211114222112111111111323111
10 1 6.0 5553211211115322121111121111323011
23 1 7.0 5553211311115322111001111111323011
26 1 8.0 5553212221115322221001221111423211
35 1 9.0 5553211321115422222111211111423111
10 1 12.0
5553212321115522222111222111523021
23 1 14.0
5553210320115522022100220011523121
24 1 16.0 5553222323105522222222222221523222
46 1 18.0
5553222323025522222202222202523224
The parameters for the
34 indicators are in a file called knee.par.
This file was produced by MULTILOG as a consequence of the
inclusion of >SAVE among the commands in a (previous) calibration
run. Note that the parameters in Roche et al. (1975)
table (in which the thresholds are called  and the slopes are called d)
are in years, instead of the usual standard units, so the
results appear in years.
The MULTILOG syntax file
includes instructions to SCORE INDIVIDUAL data on the >PROBLEM
command, as well as to use NO population distribution, because
RWT skeletal ages are not normally computed using a population
distribution. We also use CRITERION, which instructs MULTILOG
to read the chronological age of each individual to use as
a starting value for the iterative modal estimation procedure.
The first ten characters (NCHARS=10) on each record are read
as an identification field; using T-format, the age in that
field is also read later as the CRITERION. The "test"
has varying numbers of response categories for the 34 indicators,
which are entered in the NC list on the >TEST command.
The syntax file knee.mlg
is shown below.
ESTIMATION OF SKELETAL MATURITY BY THE RWT (1975) METHOD
NEW COMMAND FORMAT
>PROBLEM SCORE, INDIVIDUAL, CRITERION, NEXAMINEES=13, NITEMS=34, NCHARS=10,
DATA='KNEE.DAT';
>TEST ALL, GRADED, NC=(5,5,5,3,2,2,2,3,2,3,3,3,5,5,2(0)12,3,3,5,2,3,2,2,4);
>START ALL, FORMAT, PARAM='KNEE.PAR';
>SAVE;
>END;
6
123450
1111111111111111111111111111111111
2222222222222222222222222222222222
3333333333333333333333333333333333
4444444444444444444444444444444444
5555555555555555555555555555555555
0000000000000000000000000000000000
(10A1,1X,34A1,T7,F4.0)
The RWT estimates of skeletal
age are modal estimates of , labeled THETAHAT on
the last page of the MULTILOG output. Their estimated standard
errors, the number of iterations required to compute each, and the contents of the ID field are also
printed there. When using MULTILOG, modal estimates of
are
always computed in this way, in a subsequent run after the
item parameters have been estimated. Frequently, several item
analysis runs are required with a set of item-response data
before a satisfactory?set of item parameters are obtained;
only then is it useful to score the individuals. Selected
output for this run follows. Only items 1, 4, and 5 are shown.
ESTIMATION OF SKELETAL MATURITY BY THE RWT (1975) METHOD
DATA PARAMETERS:
NUMBER OF COMMANDS IN THE DATA
FILE: 13
NUMBER OF CATEGORICAL-RESPONSE
ITEMS: 34
NUMBER OF CONTINUOUS-RESPONSE ITEMS,
AND/OR GROUPS: 0
TOTAL NUMBER OF "ITEMS"
(INCLUDING GROUPS): 34
NUMBER OF CHARACTERS IN ID FIELDS: 10
MAXIMUM NUMBER OF RESPONSE-CODES FOR
ANY ITEM: 6
THE MISSING VALUE CODE FOR CONTINUOUS
DATA: 9.0000
EXTERNAL CRITERION VALUES WILL BE READ
THE DATA WILL BE
STORED IN MEMORY
ESTIMATION
PARAMETERS:
MODAL THETAS WILL BE ESTIMATED
OUTPUT-CONTROL
PARAMETERS
THE MODAL THETAS WILL BE SAVED ON FILE
<jobname>.SCO
ESTIMATION OF
SKELETAL MATURITY BY THE RWT (1975) METHOD
READING DATA...
KEY-
CODE CATEGORY
1 1111111111111111111111111111111111
2 2222222222222222222222222222222222
3 3333333333333333333333333333333333
4 4444444444444444444444444444444444
5 5555555555555555555555555555555555
0 0000000000000000000000000000000000
FORMAT FOR DATA-
(10A1,1X,34A1,T7,F4.0)
FIRST OBSERVATION
AS READ-
ID 40 1 0.5
ITEMS 2112111111112111111111111111111111
WT/CR 0.50
SCORING DATA...
THETAHAT S.E. ITER ID
FIELD
-2.306 0.432 5 40
1 0.5
-1.730 0.386 3 33
1 1.0
-1.352 0.361 4 33
1 2.0
-1.243 0.367 4 29
1 3.0
-0.507 0.328 4 8
1 5.0
-0.276 0.331 4 10
1 6.0
-0.340 0.346 4 23
1 7.0
0.376 0.337 3 26
1 8.0
0.155 0.330 4 35
1 9.0
0.814 0.358 3 10
1 12.0
1.012 0.397 3 23
1 14.0
1.963 0.422
4 24
1 16.0
2.383 0.465 6 46
1 18.0
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