Item response modeling of paired comparison and ranking data.
-
Upload
cory-miles -
Category
Documents
-
view
219 -
download
0
Transcript of Item response modeling of paired comparison and ranking data.
paired comparison and ranking data
• paired comparison– n(n-1)/2 pairs
• Ranking– n!– A special case of paired comparison when no
intransitive pattern• Thurstone’s model (1927)– Utility (property of item)
Ranking
• Ypair = 1 if ti – tk > 0• Design matrix:• Utility distribution:– Case 3: – Case 5:
• Separate person parameter out of random error:– Note they think of loading parameter as item
attributes (e.g., male actors versus female athletes)
Pairwise comparison
• Add intransitive error:• Then
• Identification:– Origin and scale: N(0,I) for η– Rotation: -------------------------– Additions due to pairwise design:• Fix loading parameters of a statement to 0.• Fix one mean parameter of a statement to 0.• Fix one unique variance of a statement to 1.
• Identification:– At least n=5, 6, 7 for m = 1, 2, 3 (number of
dimension). Why?– If not, require more constraints! What it is?• Constrain All the covariance matrix (I have tried this!)
Parameter estimation
• MML may be infeasible because ICCs are conditionally dependent for Thurstone IRT model.
• Limited information method is applicable by using Mplus.
• But d.f. should be modified for ranking data:
Latent trait estimation, information functions, and reliability estimation
• Locally independence is violated!• MAP• Information function
• Reliability – 1.– 2.
•
Simulation studies
• To estimate• Sample size: 200, 500, 1000 • Item size: 6, 12• Equal or unequal variance:
•
Vocational interest (pairwise comparison)
• Unrestricted thresholds: p=.046, RMSEA=.016• Equal w: p=.000, RMSEA=.025• Constrained thresholds: p=.000, RMSEA=.025• Reliability: .62 (theoretical); .43 (empirical) due to shrunken MAP
RealisticInvestigativeArtisticConventionalSocialEnterprising