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