Scheiblechner, H. (2003). Linear isotonic models LINISOP
Scheiblechner, H. (1995). Isotonic ordinal probabilistic models (ISOP)
Psychometrika, 1995
Psychometrika, 1995
Psychometrika, 1995
Psychometrika, 1995
Psychometrika, 1995
Psychometrika, 1995
Scheiblechner, H. (1999). Additive conjoint isotonic probabilistic models (ADISOP)
Psychometrika, 1999
Psychometrika, 1999
Psychometrika, 1999
Psychometrika, 1999
Psychometrika, 1999
Psychometrika, 1999
Psychometrika, 1999
Psychometrika, 2003
0 1 ... y ... mj
0
1 + _
...
x n(x,y)
...
mi _ +
Response to Item j
Response to Item i
Table 1.
Contingency table for responses to two items. The entries n(x,y) are the frequencies of the subjects with response vectors (x, y).
Psychometrika, 2003
Psychometrika, 2003
Psychometrika, 2003
Verallgemeinerung der isotonen Ordnung (similar order) auf Vektoren
Psychometrika, 2003
Verallgemeinerung auf 2 Mengen
Psychometrika, 2003
Geltung von W1 für jedes item: W1i
Conservativism (Christodoulides, P., 1993)
Geltung von W2 für jede Vp: W2
€
riV( ) x( )=
Fi x−1( )−Gi x+1( )
€
ρ∧
iV( ) x( )
0 I II
0 I II
0 I II
13 2
13 2
13 2
13 2
33 2 12
item1item2item3
categIIcategIcateg0
0 0 0 I I1
I IIII II
Scheiblechner, H. (2003). Nonparametric IRT: multivariate unidimensional isotonic probabilistic
models (d-ISOP)
Figure 1 2-dimensional partial order
Figure 2 Isotonic rank orders (parameters) 4 Restrictions of 1 common rank order
Scheiblechner, H., Lutz, R. (2004). MR-SOC