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 jan mod posted on Thursday, June 18, 2015 - 3:57 pm
Dear Muthen & Muthen,

I'm doing an IRT model with two waves (mathematics, dichotomous variables) (single group design). I want to do a concurrent calibration with 10 common items and unique items for each wave. I want to put both waves on a common scale.
1) is this syntax correct?
2) How can I make an IRT calibrated scale for each wave math (two scores on common scale)?

DATA:
FILE = data.csv;

VARIABLE:
NAMES = math1-math10 math11-math20 math21-math45 ID;
USEVARIABLES = math1-math10 math11-math20 math21-math45;
MISSING = ALL(9);
IDVARIABLE = ID;

ANALYSIS:
ESTIMATOR = ML;

MODEL:
THETA by math1* math11-math20 math21-math45;
THETA@1;
[THETA@0];

PLOT:
TYPE = PLOT1 PLOT2 PLOT3;

SAVEDATA:
SAVE = FSCORES;
FILE = Equated.dat;

OUTPUT:
TECH1 TECH5 TECH8 TECH10;
 Bengt O. Muthen posted on Thursday, June 18, 2015 - 6:21 pm
I would think you use 2 theta variables, one for each time point. And with its own indicators. So something like

theta1 by math1-math10
math111-math120* (a1-a20);
theta2 by math211-math220* (a1-a20);
math21-math45;
theta1-theta2@1;

where you have equalities a1-a20 for those items that are in common and administered at both time points (hence the prefix 1 and 2). The 2 theta variables will be correlated as the default. You ask for factor scores to get the individual theta values.

You also want to impose threshold invariance:

[math11$1-math20$1] (b2-b20);
 jan mod posted on Friday, June 19, 2015 - 4:12 am
Thank you very much!

So this will do it for me: (including the imposition of threshold invariances):

DATA:
FILE = data.csv;

VARIABLE:
NAMES = math1-math10 math11-math20 math21-math45 ID;
USEVARIABLES = math1-math10 math11-math20 math21-math45;
MISSING = ALL(9);
IDVARIABLE = ID;

ANALYSIS:
ESTIMATOR = ML;

MODEL:
theta1 by math1-math10 !unique items wave 1
math111-math120* (a1-a10); !common items
theta2 by math211-math220* (a1-a10); !common items
math21-math45; !unique items wave 2
theta1-theta2@1;

[math111$1-math120$1] (b2-b12);
[math211$1-math220$1] (b12-b22);
 jan mod posted on Friday, June 19, 2015 - 4:35 am
EDIT: Is this correct?
 Bengt O. Muthen posted on Friday, June 19, 2015 - 5:10 pm
Almost. Change to (check details):

MODEL:
theta1 by math1-math10* !unique items wave 1
math111-math120* (a1-a10); !common items
theta2 by math211-math220* (a1-a10)
!common items
math21-math45*; !unique items wave 2
theta1-theta2@1;

[math111$1-math120$1] (b2-b12);
[math211$1-math220$1] (b12-b22);
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