Vertical Scaling in Value-Added Models for Student Learning. Derek Briggs Jonathan Weeks Ed Wiley University of Colorado, Boulder. Presentation at the annual meeting of the National Conference on Value-Added Modeling. April 22-24, 2008. Madison, WI. Overview.
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University of Colorado, Boulder
Presentation at the annual meeting of the National Conference on Value-Added Modeling. April 22-24, 2008. Madison, WI.
Note: No common linking items were available between 2006 and 2007.
Technical Decisions Psychometricians Make
8 Defensible Vertical Scales
The eqn above it the 3 Parameter Logistic (3PL) IRT model for binary test items.
The 1PL model results from imposing the constraints
Reasons for choosing particular IRT model specification: statistical, pragmatic, philosophical.
A and B represent “linking constants”
Each oval represents a the linking of two separate item calibrations using the Stocking & Lord approach.
20 Unique 2003 Items
20 Unique 2004 Items
10 Common Items
50 Total Unique Items
The item parameters from multiple groups of test-takers are estimated simultaneously
In IRT estimation of student-level scale scores happens after item parameters have been estimated. Two key options:
Note: Scale Score Outcome is in Logit Units, Base Year = Grade 3
3PLM/GPCM & Hybrid
Note: Projection lines based solely on fixed effect estimates
r = .96
Switch to Hybrid calibration
r = .88
Switch to Hybrid calibration & 1PLM/GPCM
r = .75
Switch to Hybrid calibration,1PLM/GPCM, MLE
Value-Added Parameters of Interest:
Notes: Model above assumes complete persistence. Bayesian estimation using non-informative priors.