Table 31.1 Differential person functioning DPF pairwise

Table 31 supports person bias, Differential Person Functioning (DPF), i.e., interactions between individual persons and classifications of items. This is useful for estimating sub-test, domain and strand measures for individuals in the context of an overall measure.



31.2 DPF report (measure list: item class within person)

31.3 DPF report (measure list: person within item class)

31.4 DPF report (person by item-class chi-squares)

31.5 Within-class fit report (item class within person)

31.6 Within-class fit report person class within item)

31.7 Person measure profiles for classes of items

DPF plots


Table 31.1 reports a probability and a size for DPF statistics. Usually we want:

1. probability so small that it is unlikely that the DPF effect is merely a random accident

2. size so large that the DPF effect has a substantive impact on scores/measures on the test


Specify DPF= for classifying indicators in item labels. Use difficulty stratification to look for non-uniform DPF using the selection rules.


From the Output Tables menu, the DPF dialog is displayed.


Table 30 supports the investigation of item bias, Differential Item Functioning (DIF), i.e., interactions between individual items and types of persons.


Table 33 reports bias or interactions between classifications of items and classifications of persons.


In these analyses, persons and items with extreme scores are excluded, because they do not exhibit differential ability across items. For background discussion, see DIF and DPF concepts.


Example output:


Table 31.1


DPF class specification is: DPF=$S1W1


| TAP   Obs-Exp   DPF   DPF   TAP   Obs-Exp   DPF   DPF      DPF    JOINT  Rasch-Welch      KID           |

| CLASS Average MEASURE S.E.  CLASS Average MEASURE S.E.  CONTRAST  S.E.   t  d.f. Prob. Number  Name     |


| 1        -.05  -3.52  1.05  2         .04  -2.80  1.65      -.73  1.95  -.37   2 .7459      1 Adam    M1|

| 1        -.05  -3.52  1.05  3         .39  -2.78> 2.07      -.74  2.32  -.32   0 .0000      1 Adam    M1|

| 1        -.05  -3.52  1.05  4         .00  -2.94E  .00      -.58   .00   .00   0 1.000      1 Adam    M1|


DPF Specification defines the columns used to identify Differential Person Function classifications, using the selection rules.


TAP CLASS is the item class

Obs-Exp Average is the average difference between the observed and expected responses for the Class by the person. When this is positive, the Class is easier than expected or the person has higher ability than expected.

DPF MEASURE is the ability of the person for this item class, with all else held constant. This is output in the Excel file for the DPF plots.

DPF S.E. is the standard error of the measure

DPF CONTRAST is the difference in the person ability measures, i.e., size of the DPF, for the two classifications of items.

JOINT S.E. is the standard error of the DPF CONTRAST


DPF estimates with the  the iterative-logit (Rasch-Welch) method:

t gives the DPF significance as a Student's t-statistic test. The t-test is a two-sided test for the difference between two means (i.e., the estimates) based on the standard error of the means (i.e., the standard error of the estimates). The null hypothesis is that the two estimates are the same, except for measurement error.

d.f. is the joint degrees of freedom. This is shown as the sum of the counts (see Table 31.2) of two classifications - 2 for the two measure estimates, but this estimate of d.f. is somewhat high, so interpret the t-test conservatively. When the d.f. are large, the t statistic can be interpreted as a unit-normal deviate, i.e., z-score.

Prob. is the two-sided probability of Student's t. See t-statistics.


-5.24> reports that this measure corresponds to an extreme maximum score. EXTRSCORE= controls extreme score estimate.

5.30< reports that this measure corresponds to an extreme minimum score. EXTRSCORE= controls extreme score estimate.

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Rasch Publications
Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments, George Engelhard, Jr. & Stefanie Wind Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
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Jan. 5 - Feb. 2, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps),
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