Validity from the Perspective of Model-Based Reasoning

1. Validity from the Perspective of Model-Based Reasoning Robert J. Mislevy Measurement, Statistics and Evaluation University of Maryland, College Park Presented at the conference “The Concept of Validity: Revisions, New Directions and Applications,” University of Maryland, College Park, MD October 9-10, 2008. Supported by a grant from the Spencer Foundation.

2. Overview of the Talk • Sources of unease • Cognition in terms of patterns • Model-based reasoning • Measurement models as model-based reasoning • Implications for validity • Feeling better now

3. Sources of Unease (1) Different models fit the same data • Tatsuoka (1983) mixed number subtraction

4. Container metaphor Person B Person D Measurement metaphor Person A Person B Person D Item 1 Item 4 Item 5 Item 3 Item 6 Item 2 Sources of Unease (1) Cognitive diagnosis model for instruction • Student characterized by vector of 0/1 variables, say h, for which operations she had mastered • Task characterized by which ones the task needed • Probability of correct response via latent class model 2PL IRT model for overall proficiency • Student characterized by univariate, continuous q, for proficiency in the domain • Tasks modeled by difficulty & discrimination • Probability of correct response via IRT model

5. Sources of Unease (2) Summary test scores, and factors based on them, have often been though of as “signs” indicating the presence of underlying, latent traits. … An alternative interpretation of test scores as samples of cognitive processes and contents … is equally justifiable and could be theoretically more useful. Snow & Lohman, 1989, p. 317

6. Sources of Unease (2) The evidence from cognitive psychology suggests that test performances are comprised of complex assemblies of component information-processing actions that are adapted to task requirements during performance. Snow & Lohman, 1989, p. 317

7. Sources of Unease (2) The implication is that sign-trait interpretations of test scores and their intercorrelations are superficial summaries at best. At worst, they have misled scientists, and the public, into thinking of fundamental, fixed entities, measured in amounts. Snow & Lohman, 1989, p. 317

8. Sources of Unease (2) Whatever their practical value as summaries, for selection, classification, certification, or program evaluation, the cognitive psychological view is that such interpretations no longer suffice as scientific explanations of aptitude and achievement constructs. Snow & Lohman, 1989, p. 317

9. Sources of Unease (3) • What is the nature of parameters like q and h? Where are they? • What is the interpretation of the probabilities that arise from IRT, latent class / cognitive diagnosis models, and the like? • What does this mean about validity of the data / the models / the uses of them?

10. Cognition in Terms of Patterns • The sociocognitive paradigm • Metaphors as foundation • Formal model-based reasoning

11. The sociocognitive paradigm • Converging ideas from cog psych, neurology, anthropology, linguistics, science ed, etc. • Knowledge as patterns, at many levels… • Assembled to understand, to interact with, and to create particular situations in the world • Developed, strengthened, modified by use • Associations of all kinds, including applicability, affordances, procedures, strategies, affect

12. Text base Context LTM Situation Model Context1 Walter Kintsch’s CI Theory of Reading Comprehension Text More focused research areas within cognitive psychology today differ as to their foci, methods, and levels of explanation. They include perception and attention, language and communication, development of expertise, situated and sociocultural psychology, and neurological bases of cognition. Kintsch is focusing here on “experiential” cognition – not conscious, occurring at the scale of milliseconds. We’ll talk about reflective cognition in a couple minutes.

13. Walter Kintsch’s CI Theory of Reading Comprehension Text Text base Context LTM Situation Model Action Context1 More focused research areas within cognitive psychology today differ as to their foci, methods, and levels of explanation. They include perception and attention, language and communication, development of expertise, situated and sociocultural psychology, and neurological bases of cognition. Context2

14. Walter Kintsch’s CI Theory of Reading Comprehension Text Text base Context LTM Situation Model Action Context1 More focused research areas within cognitive psychology today differ as to their foci, methods, and levels of explanation. They include perception and attention, language and communication, development of expertise, situated and sociocultural psychology, and neurological bases of cognition. Context2

15. Walter Kintsch’s CI Theory of Reading Comprehension Text Text base Context LTM Situation Model Action More focused research areas within cognitive psychology today differ as to their foci, methods, and levels of explanation. They include perception and attention, language and communication, development of expertise, situated and sociocultural psychology, and neurological bases of cognition. Context2 Context3

16. Metaphors as foundation Lakoff & Johnson • Metaphors we live by (1980); Philosophy in the flesh (1999) Key idea: • Cognitive machinery builds from capabilities for interacting with the real physical and social world. • We extend and creatively recombine basic patterns and relationships to think about everything from … everyday things to extremely complicated and abstract social, conceptual, philosophical realms True of both experiential and reflective cognition.

17. Metaphors as foundation Example: Containers Free Clip Art Provided by Artclips.com

18. Metaphors as foundation Example: Containers Example: Containers • Everyday experience  Set theory • Very good, mostly. • Knowledge as collection of discrete things inside our heads • Usually good and useful, in communication • Sometimes inapt, as sole basis of instructional practice and assessment design (the Jeopardy model of cognition—Rosie Perez in White men can’t jump)

19. Metaphors as foundation Example: Cause & Effect

20. Metaphors as foundation Example: Cause & Effect Newton’s laws; kinematics; quantitative models of force and motion, esp. F=MA

21. Metaphors as foundation Example: Cause & Effect q xj IRT & SEM models; quantitative models for response probabilities, esp. Rasch’s P=qd.

22. Metaphors as foundation Example: Cause & Effect • Everyday experience  F=MA • Very good, mostly. • Teleological theories of history, a la Hegel • Not so good, mostly. Example: Cause & Effect • Everyday experience  F=MA • Very good, mostly. Example: Cause & Effect

23. Representational Form A Representational Form B y=ax+b (y-b)/a=x Mappings among representational systems Entities and relationships Real-WorldSituation Reconceived Real-World Situation Model-Based Reasoning Mainly syntactic Mainly semantic

24. Properties of Models (1) • Human way to think about complex unique situations • Abstract structure of entities, relationships, processes • What’s included, what’s omitted • Levels of analysis and grainsize • Newtonian and quantum mechanics • Transmission genetics at level of species, individuals, cells, or molecules

25. Properties of Models (2) • Can apply different models to same situation • Can view selling car to brother-in-law in terms of economic transaction model vs family relationships model • Models tuned to uses / problems / purposes • Mixed number subtraction

26. Properties of Models (2) The modeling cycle: Revise Observe Evaluate Model • Fit? • Does it work? • What’s left out? • Adequacy of rationale? Predict/Use

27. Models with probabilistic layers • Probability from analogy with physical games of chance (Shafer) • Probability connects to model representation • Key in model criticism • Model posits space for patterns; parameter values characterize them; probability models can characterize … • Variation in patterns • Modeler’s uncertainty about patterns & parameters

28. Psychometric / Measurement Models • E.g., IRT, CTT, FA, SEM, CDM • Model posits space for patterns, parameter values characterize them • Semantic layer is cause & effect metaphor • Q: In what sense does q “cause” X? • A: The C&E metaphor grounds productive connection between observations and inferences • Modeling patterns across people, not explaining item responses (Snow & Lohman) • Could model within-person processes at finer grainsize

29. Some answers • What is the nature of parameters like q and h? Where are they? • These are characterizations of patterns we observe in real-world situations (ones we in part construct for target uses) through the lens of a simplified model we are (provisionally) using to think about those situations and the use situations in which the patterns are apt to be relevant. • So they are in our heads, but they aren’t worth much unless they reflect patterns in examinees’ actions in the world.

30. Some answers • What is the interpretation of the probabilities that arise from IRT, latent class / cognitive diagnosis models, and the like? • These are characterizations of patterns we observe in situations and our degree of knowledge about them, again through the lens of a simplified model we are (provisionally) using to think about those situations. • In addition to guiding inference through the model, they provide tools for seeing where the model may be misleading, inadequate.

31. Some answers • What does this mean about validity of the data / the models / the uses of them?

32. Representational Form B Mappings among representational systems Entities and relationships Real-WorldSituation Reconceived Real-World Situation Validity Evidence Representational Form A y=ax+b (y-b)/a=x Theory and experience supporting the narrative/scientific frame Theoretical and empirical grounding of task-scoring procedures Empirical evaluation of predictions / outcomes Theoretical and empirical grounding of task design

33. Validity Implications, Sense 1 • The currently dominant view: Validity is an integrated evaluative judgement of the degree to which empirical evidence and theoretical rationales support the adequacy and appropriateness of inferences and actions based on test scores or other modes of assessment. (Messick, 1989) • Focus on situated use of data from test • Consistent with MBR perspective; i.e., reasoning through psychometric model in particular situations & inferences.

34. Validity Implications, Sense 2 • Alternative (e.g., Wiley, Borsboom, Lissitz): [A] test is valid for measuring an attribute if and only if (a) the attribute exists and (b) variations in the attribute causally produce variations in the outcomes of the measurement procedure. (Borsboom et al, 2004) • MBR view can omit specific uses, but • must consider range of situations and uses that are apt to be thought about effectively via the model. • Broader range consistent with scientific program, in opposition to Snow & Lohman quote. • Is realist but strong correspondence to existence of traits qua traits in individuals is not required.

35. I am Feeling Better Now Model-based reasoning provides a way of thinking about validity that … • is consistent with the practical methods that have developed to assure quality of inferences from assessments • is realist, in L&J’s “embodied realism” sense • is consistent with developments in cognitive psychology, including the nature of scientific reasoning, and the meaning of probability.