Construct Deficiency?

Is your construct in trouble? While developing a new version of a widely used achievement test, we noticed several flags that could signal a poorly implemented construct.

                    Achievement Test
   Examinees          Logits  Level      Items
-------------------------------------------------------------
     High Achievement   5.0            Difficult Items
X
XX
XXX                     4.0
XXXX
XXXXX
XXXX                    3.0         5-A
XXXXXX                         5    5-B
XXXXXXX                             5-C 5-D
XXXXXXXXX               2.0  -----  5-E 4-A
XXXXXXX                             4-B 4-C
XXXXXXXXX                           4-D          gap in
XXXXXXXXXXX             1.0    4              <= construct
XXXXXXXXXXX                         5-F 3-A      realization
XXXXXXX                             4-E
XXXXX                   0.0  -----  3-B
XXX                                 4-F 3-C
X                              3    3-C 3-D 2-A
XX                     -1.0  -----  3-E 3-F 2-B 1-A
                                    2-C 2-D
X                              2    2-E 2-F
                       -2.0  -----  1-B 1-C
X                                   1-D 1-E
                               1    1-F
     Low Achievement   -3.0                   Easy Items
-------------------------------------------------------------

Look at the simplified person and item map. We analyzed the responses of a sample of convenience, whose performance happened to cover 7 logits (+5.0 to -2.0). The test is intended to place each examinee into one of 5 achievement levels (1-5), with 5 indicating the highest performance. These levels have been defined by contents experts. The test contains 30 items with 6 items intended to be at each level. The items are shown by level number (1-5) and empirical difficulty ranking within level (A-F). The most difficult item, 5-A, is a level 5 item as expected. Item 1-A is about a logit harder than the other level 1 items. Perhaps this was because it is the first item on the test, where examinees could experience start-up problems.

Scanning down the item map, items written to be at higher levels are usually more difficult than items at lower levels. Around levels 3 and 4, however, there are contradictions. The construct is in trouble!

Notice the item disordering between +1.0 and -1.0 logits. The use of levels to define the construct is uncertain in this area. Examination of the experts' definitions of each level provides clues. Each definition is about 100 words long. Level 1 definitions include words like "simple, uncomplicated"; Level 2, "important details"; Level 3, "more details, greater complexity"; Level 4, "advanced, generalized"; Level 5, "more difficult, general principles". Even though levels 3 and 4 have the longest definitions, the item writers have failed to operationalize these levels as strata of difficulty. Now that the test developers have the benefit of empirical item difficulties, they can write more precise, more discriminating and shorter level definitions. This would enable item reclassification and rewriting that would produce a clearer level hierarchy.

This examinee sample happens to contain higher achievers with a mode of about 1.0 logit, i.e., at level 4. Yet there is a gap in the item map exactly at this point. Gaps not only reduce the effectiveness of a test, they also show points at which the construct is poorly defined. The test could be improved by rewriting item 4-F to have difficulty 1.0 logits. This could be accomplished by asking the item writers to write pilot items with predicted difficulties between 4-D and 4-E, a task which will be easier with improved level definitions.

Construct deficiency? Schulz EM. … Rasch Measurement Transactions, 1995, 9:3 p.447

Rasch Books and Publications
Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, 2nd Edn. George Engelhard, Jr. & Jue Wang	Applying the Rasch Model (Winsteps, Facets) 4th Ed., Bond, Yan, Heene	Advances in Rasch Analyses in the Human Sciences (Winsteps, Facets) 1st Ed., Boone, Staver	Advances in Applications of Rasch Measurement in Science Education, X. Liu & W. J. Boone	Rasch Analysis in the Human Sciences (Winsteps) Boone, Staver, Yale
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes	Statistical Analyses for Language Testers (Facets), Rita Green	Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments (Facets), George Engelhard, Jr. & Stefanie Wind	Aplicação do Modelo de Rasch (Português), de Bond, Trevor G., Fox, Christine M	Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
Exploring Rating Scale Functioning for Survey Research (R, Facets), Stefanie Wind	Rasch Measurement: Applications, Khine	Winsteps Tutorials - free Facets Tutorials - free	Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre	Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan
Other Rasch-Related Resources: Rasch Measurement YouTube Channel
Rasch Measurement Transactions & Rasch Measurement research papers - free	An Introduction to the Rasch Model with Examples in R (eRm, etc.), Debelak, Strobl, Zeigenfuse	Rasch Measurement Theory Analysis in R, Wind, Hua	Applying the Rasch Model in Social Sciences Using R, Lamprianou	El modelo métrico de Rasch: Fundamentación, implementación e interpretación de la medida en ciencias sociales (Spanish Edition), Manuel González-Montesinos M.
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar	Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch	Rasch Models for Measurement, David Andrich	Constructing Measures, Mark Wilson	Best Test Design - free, Wright & Stone Rating Scale Analysis - free, Wright & Masters
Virtual Standard Setting: Setting Cut Scores, Charalambos Kollias	Diseño de Mejores Pruebas - free, Spanish Best Test Design	A Course in Rasch Measurement Theory, Andrich, Marais	Rasch Models in Health, Christensen, Kreiner, Mesba	Multivariate and Mixture Distribution Rasch Models, von Davier, Carstensen

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