Posts Tagged ‘stochastic resonance’

Feminist Diffractions, Stochastic Resonance, and Education, Revisited

May 25, 2015

Lehrer (2015) offers an insightful commentary on Saxe et al’s (2015) recent article in Human Development that prompts some observations.

Two areas for questions and comments come to mind. The first has to do with construing the development and revision of new ways of understanding as contested, which implicitly aligns with Latour’s (1987, pp. 89, 93) sense of the way new constructs are subjected to tests of strength. Haraway (1996) makes an important point in her critique of what she sees as the overly masculinist metaphors of heroic competition and (perhaps not so) sublimated violence in these contests. Her sense of “feminist diffractions” stops short of what I have in mind, but opens the door to an alternative approach to what Lehrer calls the “close coupling of definitions with the development and revision of new concepts and ways of understanding.”

Galison (1997, pp. 843-844), for instance, seeks a metaphor capable of expressing what happens in the conceptual, practical, and argumentative contests between different communities of scientists (instrumentalist technicians, theoreticians, and experimentalists). He wants a metaphor that does justice to the disunified chaos and disorder one finds in the relationships between these different groups, which paradoxically results in such productive and coherent innovations. He recalls Peirce’s and Wittgenstein’s metaphors of cables and threads that take their strength from being intertwined from smaller wires and bits of fiber but finds these images too mechanical for his purposes. He wants something more akin to amorphous semiconductors or laminated materials that can fail microscopically but hold macroscopically better than more structurally homogenous materials.

Berg and Timmermans (2000, pp. 55-56) make a similar observation in their study of the constitution of universalities in medical fields:

“In order for a statistical logistics to enhance precise decision making, it has to incorporate imprecision; in order to be universal, it has to carefully select its locales. … Paradoxically, then, the increased stability and reach of this network was not due to more (precise) instructions: the protocol’s logistics could thrive only by parasitically drawing upon its own disorder.”

The general problem is taken up by Ricoeur (1992, p. 289), who raises the notion of “universals in context or of potential or inchoate universals” that embody the paradox in which

“on the one hand, one must maintain the universal claim attached to a few values where the universal and the historical intersect, and on the other hand, one must submit this claim to discussion, not on a formal level, but on the level of the convictions incorporated in concrete forms of life.”

To repeat another theme that comes up again and again in this blog, this kind of noise-induced order sounds like the phenomenon of stochastic resonance (Fisher, 1992, 2011). The importance of stochastic resonance is that it opens up a way to connect the phenomena of emergent understanding with measurement, both at the local individual and general systemic levels.

This is the crux of some very important issues in the philosophy of science and in philosophy generally. Haraway (1996, pp. 439-440), for instance, points out that “embedded relationality is the prophylaxis for both relativism and transcendence.” And Golinski (2012, p. 35) similarly says, “Practices of translation, replication, and metrology have taken the place of the universality that used to be assumed as an attribute of singular science.”

A start in the direction of embedded relationality, translation, replication, and metrology in education is apparent, for instance, in work that enables teachers to usefully relate individual student performances to general learning progressions, connecting instructional applications with accountability (Fisher & Wilson, 2015; Lehrer, 2013; Lehrer & Jones, 2014; Wilson, 2004). As Lehrer (2015, p. 49) says about the Saxe et al. work, “Recurrent forms of mathematical practice enabled the authors to create compelling trajectories of collective activity and learning over time while preserving the contributions of individual development.”

The second of the two topics I’d like to address comes up here in the closing paragraph of his short commentary, where Lehrer says a “hoped-for future innovation would make it possible to visualize individual and collective trajectories simultaneously.” Though future improvements can certainlty be expected, visualizations of individual and collective trajectories for growth in reading are already being recognized in both educational and metrological contexts (Stenner, Swartz, Hanlon, & Emerson, 2012; Stenner & Fisher, 2013, p. 4) for their potential to serve as the media of an embedded relationality capable of undercutting both the relativism of uncontrolled local variation and the universalist pretensions often built into accountability programs.

With emerging recognition of the potential Rasch’s stochastic approaches to construct mapping (Bond & Fox, 2007; Wilson, 2005) offer in the way of metrological translation networks (Mari & Wilson, 2013; Pendrill, 2014; Pendrill & Fisher, 2015; Fisher & Wilson, 2015; Stenner & Fisher, 2013; Wilson, 2013; Wilson, Mari, Maul, & Torres Irribarra 2015), there are good reasons to expect significant new kinds of progress in fields that rely on assessments and surveys for outcome measurement and management.

References

Berg, M.,& Timmermans, S. (2000). Order and their others: On the constitution of universalities in medical work. Configurations, 8(1), 31-61.

Bond, T., & Fox, C. (2007). Applying the Rasch model: Fundamental measurement in the human sciences, 2d edition. Mahwah, New Jersey: Lawrence Erlbaum Associates.

Fisher, W. P., Jr. (1992). Stochastic resonance and Rasch measurement. Rasch Measurement Transactions, 5(4), 186-187 [http://www.rasch.org/rmt/rmt54k.htm].

Fisher, W. P., Jr. (2011). Stochastic and historical resonances of the unit in physics and psychometrics. Measurement: Interdisciplinary Research & Perspectives, 9, 46-50.

Fisher, W. P., Jr., & Stenner, A. J. (2015). The role of metrology in mobilizing and mediating the language and culture of scientific facts. Journal of Physics Conference Series, 588(012043).

Fisher, W. P., Jr., & Wilson, M. (2015). Building a productive trading zone in educational assessment research and practice. Pensamiento Educativo, in review.

Galison, P. (1997). Image and logic: A material culture of microphysics. Chicago: University of Chicago Press.

Golinski, J. (2012). Is it time to forget science? Reflections on singular science and its history. Osiris, 27(1), 19-36.

Haraway, D. J. (1996). Modest witness: Feminist diffractions in science studies. In P. Galison & D. J. Stump (Eds.), The disunity of science: Boundaries, contexts, and power (pp. 428-441). Stanford, California: Stanford University Press.

Latour, B. (1987). Science in action: How to follow scientists and engineers through society. New York: Harvard University Press.

Lehrer, R. (2013, April 29). (Chair). In A learning progression emerges in a trading zone of professional community and identity. American Educational Research Association, Division C on Learning and Instruction, Section 2b on Learning and Motivation in Social and Cultural Contexts, San Francisco, CA.

Lehrer, R., & Jones, S. (2014, 2 April). Construct maps as boundary objects in the trading zone. In W. P. Fisher Jr. (Chair), Session 3-A: Rating Scales and Partial Credit, Theory and Applied. International Objective Measurement Workshop, Philadelphia, PA.

Lehrer, R. (2015). Designing for development: Commentary on Saxe, de Kirby, Kang, Le and Schneider. Human Development, 58(1), 45-49.

Mari, L., & Wilson, M. (2013). A gentle introduction to Rasch measurement models for metrologists. Journal of Physics Conference Series, 459(1), http://iopscience.iop.org/1742-6596/459/1/012002/pdf/1742-6596_459_1_012002.pdf.

Pendrill, L. (2014). Man as a measurement instrument [Special Feature]. NCSLi Measure: The Journal of Measurement Science, 9(4), 22-33.

Pendrill, L., & Fisher, W. P., Jr. (2015). Counting and quantification: Comparing psychometric and metrological perspectives on visual perceptions of number. Measurement, 71, 46-55.

Ricoeur, P. (1992). Oneself as another. Chicago, Illinois: University of Chicago Press.

Saxe, G. B., de Kirby, K., Kang, B., Le, M., & Schneider, A. (2015). Studying cognition through time in a classroom community: The interplay between “everyday” and “scientific” concepts. Human Development, 58(1), 5-44.

Stenner, A. J., & Fisher, W. P., Jr. (2013). Metrological traceability in the social sciences: A model from reading measurement. Journal of Physics: Conference Series, 459(012025), http://iopscience.iop.org/1742-6596/459/1/012025.

Stenner, A. J., Swartz, C., Hanlon, S., & Emerson, C. (2012, February). Personalized learning platforms. Presented at the Pearson Global Research Conference, Fremantle, Western Australia.

Wilson, M. (Ed.). (2004). National Society for the Study of Education Yearbooks. Vol. 103, Part II: Towards coherence between classroom assessment and accountability. Chicago, Illinois: University of Chicago Press.

Wilson, M. (2005). Constructing measures: An item response modeling approach. Mahwah, New Jersey: Lawrence Erlbaum Associates.

Wilson, M. R. (2013). Using the concept of a measurement system to characterize measurement models used in psychometrics. Measurement, 46, 3766-3774.

 

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Revisiting the “Glocal” integration of universals and historical context

April 11, 2014

Integrated considerations of the universal and the local, the pure ideal parameters and the messy concrete observations, seem ever more ubiquitous in my reading lately. For instance, Ricoeur (1992, p. 289) takes up the problem of human rights imperfectly realized as a product of Western Europe’s cultural history that has nonetheless been adopted by nearly every country in the world. Ricoeur raises the notion of “universals in context or of potential or inchoate universals” that embody the paradox in which

“on the one hand, one must maintain the universal claim attached to a few values where the universal and the historical intersect, and on the other hand, one must submit this claim to discussion, not on a formal level, but on the level of the convictions incorporated in concrete forms of life.”

I could hardly come up with a better description of Rasch measurement theory and practice myself. Any given Rasch model data analysis provides many times more individual-level qualitative statistics on the concrete, substantive observations than on the global quantitative measures. The whole point of graphical displays of measurement information in kidmaps (Chien, Wang, Wang, & Lin, 2009; Masters, 1994), Wright maps (Wilson, 2011), construct maps and self-scoring forms (Best, 2008; Linacre, 1997), etc. is precisely to integrate concrete events as they happened with the abstract ideal of a shared measurement dimension.

It is such a shame that there are so few people thinking about these issues aware of the practical value of the state of the art in measurement, and who include all of the various implications of multifaceted, multilevel, and multi-uni-dimensional modeling, fit assessment, equating, construct mapping, standard setting, etc. in their critiques.

The problem falls squarely in the domain of recent work on the coproduction of social, scientific, and economic orders (such as Hutchins 2010, 2012; Nersessian, 2012). Systems of standards, from languages to metric units to dollars, prethink the world for us and simplify a lot of complex work. But then we’re stuck at the level of conceptual, social, economic, and scientific complexity implied by those standards, unless we can create new forms of social organization integrating more domains. Those who don’t know anything about the available tools can’t get any analytic traction, those who know about the tools but don’t connect with the practitioners can’t get any applied traction (see Wilson’s Psychometric Society Presidential Address on this; Wilson, 2013), analysts and practitioners who form alliances but fail to include accountants or administrators may lack financial or organizational traction, etc. etc.

There’s a real need to focus on the formation of alliances across domains of practice, building out the implications of Callon’s (1995, p. 58) observation that “”translation networks weave a socionature.” In other words, standards are translated into the languages of different levels and kinds of practice to the extent that people become so thoroughly habituated to them that they succumb to the illusion that the objects of interest are inherently natural in self-evident ways. (My 2014 IOMW talk took this up, though there wasn’t a lot of time for details.)

Those who are studying these networks have come to important insights that set the stage for better measurement and metrology for human, social, and natural capital. For instance, in a study of universalities in medicine, Berg and Timmermans (2000, pp. 55, 56) note:

“In order for a statistical logistics to enhance precise decision making, it has to incorporate imprecision; in order to be universal, it has to carefully select its locales. The parasite cannot be killed off slowly by gradually increasing the scope of the Order. Rather, an Order can thrive only when it nourishes its parasite—so that it can be nourished by it.”

“Paradoxically, then, the increased stability and reach of this network was not due to more (precise) instructions: the protocol’s logistics could thrive only by parasitically drawing upon its own disorder.”

Though Berg and Timmermans show no awareness at all of probabilistic and additive conjoint measurement theory and practice, their description of how a statistical logistics has to work to enhance precise decision making is right on target. This phenomenon of noise-induced order is a kind of social stochastic resonance (Fisher, 1992, 2011b) that provides another direction in which explanations of Rasch measurement’s potential role in establishing new metrological standards (Fisher, 2009, 2011a) have to be taken.

Berg, M., & Timmermans, S. (2000). Order and their others: On the constitution of universalities in medical work. Configurations, 8(1), 31-61.

Best, W. R. (2008). A construct map that Ben Wright would relish. Rasch Measurement Transactions, 22(3), 1169-70 [http://www.rasch.org/rmt/rmt223a.htm].

Callon, M. (1995). Four models for the dynamics of science. In S. Jasanoff, G. E. Markle, J. C. Petersen & T. Pinch (Eds.), Handbook of science and technology studies (pp. 29-63). Thousand Oaks, California: Sage Publications.

Chien, T.-W., Wang, W.-C., Wang, H.-Y., & Lin, H.-J. (2009). Online assessment of patients’ views on hospital performances using Rasch model’s KIDMAP diagram. BMC Health Services Research, 9, 135 [10.1186/1472-6963-9-135 or http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2727503/%5D.

Fisher, W. P., Jr. (1992, Spring). Stochastic resonance and Rasch measurement. Rasch Measurement Transactions, 5(4), 186-187 [http://www.rasch.org/rmt/rmt54k.htm].

Fisher, W. P., Jr. (2009, November). Invariance and traceability for measures of human, social, and natural capital: Theory and application. Measurement, 42(9), 1278-1287.

Fisher, W. P., Jr. (2011a). Bringing human, social, and natural capital to life: Practical consequences and opportunities. In N. Brown, B. Duckor, K. Draney & M. Wilson (Eds.), Advances in Rasch Measurement, Vol. 2 (pp. 1-27). Maple Grove, MN: JAM Press.

Fisher, W. P., Jr. (2011b). Stochastic and historical resonances of the unit in physics and psychometrics. Measurement: Interdisciplinary Research & Perspectives, 9, 46-50.

Hutchins, E. (2010). Cognitive ecology. Topics in Cognitive Science, 2, 705-715.

Hutchins, E. (2012). Concepts in practice as sources of order. Mind, Culture, and Activity, 19, 314-323.

Linacre, J. M. (1997). Instantaneous measurement and diagnosis. Physical Medicine and Rehabilitation State of the Art Reviews, 11(2), 315-324 [http://www.rasch.org/memo60.htm].

Masters, G. N. (1994). KIDMAP – a history. Rasch Measurement Transactions, 8(2), 366 [http://www.rasch.org/rmt/rmt82k.htm].

Nersessian, N. J. (2012). Engineering concepts: The interplay between concept formation and modeling practices in bioengineering sciences. Mind, Culture, and Activity, 19, 222-239.

Wilson, M. R. (2011). Some notes on the term: “Wright Map.” Rasch Measurement Transactions, 25(3), 1331 [http://www.rasch.org/rmt/rmt253.pdf].

Wilson, M. (2013, April). Seeking a balance between the statistical and scientific elements in psychometrics. Psychometrika, 78(2), 211-236.

Convergence, Divergence, and the Continuum of Field-Organizing Activities

March 29, 2014

So what are the possibilities for growing out green shoots from the seeds and roots of an ethical orientation to keeping the dialogue going? What kinds of fruits might be expected from cultivating a common ground for choosing discourse over violence? What are the consequences for practice of planting this seed in this ground?

The same participant in the conversation earlier this week at Convergence XV who spoke of the peace building processes taking place around the world also described a developmental context for these issues of mutual understanding. The work of Theo Dawson and her colleagues (Dawson, 2002a, 2002b, 2004; Dawson, Fischer, and Stein, 2006) is especially pertinent here. Their comparisons of multiple approaches to cognitive and moral development have provided clear and decisive theory, evidence, and instrumentation concerning the conceptual integrations that take place in the evolution of hierarchical complexity.

Conceptual integrations occur when previously tacit, unexamined, and assumed principles informing a sphere of operations are brought into conscious awareness and are transformed into explicit objects of new operations. Developmentally, this is the process of discovery that takes place from the earliest stages of life, in utero. Organisms of all kinds mature in a process of interaction with their environments. Young children at the “terrible two” stage, for instance, are realizing that anything they can detach from, whether by throwing or by denying (“No!”), is not part of them. Only a few months earlier, the same children will have been fascinated with their fingers and toes, realizing these are parts of their own bodies, often by putting them in their mouths.

There are as many opportunities for conceptual integrations between the ages of 21 to 99 as there are between birth and 21. Developmental differences in perspectives can make for riotously comic situations, and can also lead to conflicts, even when the participants agree on more than they disagree on. And so here we arrive at a position from which we can get a grip on how to integrate convergence and divergence in a common framework that follows from the prior post’s brief description of the ontological method’s three moments of reduction, application, and deconstruction.

Image

Woolley and colleagues (Woolley, et al., 2010; Woolley and Fuchs, 2011) describe a continuum of five field-organizing activities categorizing the types of information needed for effective collective intelligence (Figure 1). Four of these five activities (defining, bounding, opening, and bridging) vary in the convergent versus divergent processes they bring to bear in collective thinking. Defining and bounding are convergent processes that inform judgment and decision making. These activities are especially important in the emergence of a new field or organization, when the object of interest and the methods of recognizing and producing it are in contention. Opening and bridging activities, in contrast, diverge from accepted definitions and transgress boundaries in the creative process of pushing into new areas. Undergirding the continuum as a whole is the fifth activity, grounding, which serves as a theory- and evidence-informed connection to meaningful and useful results.

There are instances in which defining and bounding activities have progressed to the point that the explanatory power of theory enables the calibration of test items from knowledge of the component parts included in those items. The efficiencies and cost reductions gained from computer-based item generation and administration are significant. Research in this area takes a variety of approaches; for more information, see Daniel and Embretson (2010), DeBoeck and Wilson (2004), Stenner, et al. (2013), and others.

The value of clear definitions and boundaries in this context stems in large part from the capacity to identify exceptions that prove (test) the rules, and that then also provide opportunities for opening and bridging. Kuhn (1961, p. 180; 1977, p. 205) noted that

To the extent that measurement and quantitative technique play an especially significant role in scientific discovery, they do so precisely because, by displaying significant anomaly, they tell scientists when and where to look for a new qualitative phenomenon.

Rasch (1960, p. 124) similarly understood that “Once a law has been established within a certain field then the law itself may serve as a tool for deciding whether or not added stimuli and/or objects belong to the original group.” Rasch gives the example of mechanical force applied to various masses with resulting accelerations, introducing idea that one of the instruments might exert magnetic as well as mechanical force, with noticeable effects on steel masses, but not on wooden masses. Rasch suggests that exploration of these anomalies may result in the discovery of other similar instruments that vary in the extent to which they also exert the new force, with the possible consequence of discovering a law of magnetic attraction.

There has been an intense interest in the assessment of divergent inconsistencies in measurement research and practice following in the wake of Rasch’s early work in psychological and social measurement (examples from a very large literature in this area include Karabatsos and Ulrich, 2002, and Smith and Plackner, 2009). Andrich, for instance, makes explicit reference to Kuhn (1961), saying, “…the function of a model for measurement…is to disclose anomalies, not merely to describe data” (Andrich, 2002, p. 352; also see Andrich, 1996, 2004, 2011). Typical software for applying Rasch models (Andrich, et al., 2013; Linacre, 2011, 2013; Wu, et al., 2007) thus accordingly provides many more qualitative numbers evaluating potential anomalies than quantitative measuring numbers. These qualitative numbers (digits that do not stand for something substantive that adds up in a constant unit) include uncertainty and confidence indicators that vary with sample size; mean square and standardized model fit statistics; and principal components analysis factor loadings and eigenvalues.

The opportunities for divergent openings onto new qualitative phenomena provided by data consistency evaluations are complemented in Rasch measurement by a variety of bridging activities. Different instruments intended to measure the same or closely related constructs may often be equated or co-calibrated, so they measure in a common unit (among many publications in this area, see Dawson, 2002a, 2004; Fisher, 1997; Fisher, et al., 1995; Massof and Ahmadian, 2007; Smith and Taylor, 2004). Similarly, the same instrument calibrated on different samples from the same population may exhibit consistent properties across those samples, offering further evidence of a potential for defining a common unit (Fisher, 1999).

Other opening and bridging activities include capacities (a) to drop items or questions from a test or survey, or to add them; (b) to adaptively administer subsets of custom-selected items from a large bank; and (c) to adjust measures for the leniency or severity of judges assigning ratings, all of which can be done, within the limits of the relevant definitions and boundaries, without compromising the unit of comparison. For methodological overviews, see Bond and Fox (2007), Wilson (2005), and others.

The various field-organizing activities spanning the range from convergence to divergence are implicated not only in research on collective thinking, but also in the history and philosophy of science. Galison and colleagues (Galison, 1997, 1999; Galison and Stump, 1996) closely examine positivist and antipositivist perspectives on the unity of science, finding their conclusions inconsistent with the evidence of history. A postpositivist perspective (Galison, 1999, p. 138), in contrast, finds “distinct communities and incommensurable beliefs” between and often within the areas of theory, experiment, and instrument-making. But instead of finding these communities “utterly condemned to passing one another without any possibility of significant interaction,” Galison (1999, p. 138) observes that “two groups can agree on rules of exchange even if they ascribe utterly different significance to the objects being exchanged; they may even disagree on the meaning of the exchange process itself.” In practice, “trading partners can hammer out a local coordination despite vast global differences.”

In accord with Woolley and colleagues’ work on convergent and divergent field-organizing activities, Galison (1999, p. 137) concludes, then, that “science is disunified, and—against our first intuitions—it is precisely the disunification of science that underpins its strength and stability.” Galison (1997, pp. 843-844) concludes with a section entitled “Cables, Bricks, and Metaphysics” in which the postpositivist disunity of science is seen to provide its unexpected coherence from the simultaneously convergent and divergent ways theories, experiments, and instruments interact.

But as Galison recognizes, a metaphor based on the intertwined strands in a cable is too mechanical to support the dynamic processes by which order arises from particular kinds of noise and chaos. Not cited by Galison is a burgeoning literature on the phenomenon of noise-induced order termed stochastic resonance (Andò  and Graziani 2000, Benzi, et al., 1981; Dykman and McClintock, 1998; Fisher, 1992, 2011; Hess and Albano, 1998; Repperger and Farris, 2010). Where the metaphor of a cable’s strands breaks down, stochastic resonance provides multiple ways of illustrating how the disorder of finite and partially independent processes can give rise to an otherwise inaccessible order and structure.

Stochastic resonance involves small noisy signals that can be amplified to have very large effects. The noise has to be of a particular kind, and too much of it will drown out rather than amplify the effect. Examples include the interaction of neuronal ensembles in the brain (Chialvo, Lontin, and Müller-Gerking, 1996), speech recognition (Moskowitz and Dickinson, 2002), and perceptual interpretation (Rianni and Simonotto, 1994). Given that Rasch’s models for measurement are stochastic versions of Guttman’s deterministic models (Andrich, 1985), the question has been raised as to how Rasch’s seemingly weaker assumptions could lead to a measurement model that is stronger than Guttman’s (Duncan, 1984, p. 220). Stochastic resonance may provide an essential clue to this puzzle (Fisher, 1992, 2011).

Another description of what might be a manifestation of stochastic resonance akin to that brought up by Galison arises in Berg and Timmermans’ (2000, p. 56) study of the constitution of universalities in a medical network. They note that, “Paradoxically, then, the increased stability and reach of this network was not due to more (precise) instructions: the protocol’s logistics could thrive only by parasitically drawing upon its own disorder.” Much the same has been said about the behaviors of markets (Mandelbrot, 2004), bringing us back to the topic of the day at Convergence XV earlier this week. I’ll have more to say on this issue of universalities constituted via noise-induced order in due course.

References

Andò, B., & Graziani, S. (2000). Stochastic resonance theory and applications. New York: Kluwer Academic Publishers.

Andrich, D. (1985). An elaboration of Guttman scaling with Rasch models for measurement. In N. B. Tuma (Ed.), Sociological methodology 1985 (pp. 33-80). San Francisco, California: Jossey-Bass.

Andrich, D. (1996). Measurement criteria for choosing among models with graded responses. In A. von Eye & C. Clogg (Eds.), Categorical variables in developmental research: Methods of analysis (pp. 3-35). New York: Academic Press, Inc.

Andrich, D. (2002). Understanding resistance to the data-model relationship in Rasch’s paradigm: A reflection for the next generation. Journal of Applied Measurement, 3(3), 325-359.

Andrich, D. (2004, January). Controversy and the Rasch model: A characteristic of incompatible paradigms? Medical Care, 42(1), I-7–I-16.

Andrich, D. (2011). Rating scales and Rasch measurement. Expert Reviews in Pharmacoeconomics Outcome Research, 11(5), 571-585.

Andrich, D., Lyne, A., Sheridan, B., & Luo, G. (2013). RUMM 2030: Rasch unidimensional models for measurement. Perth, Australia: RUMM Laboratory Pty Ltd [www.rummlab.com.au].

Benzi, R., Sutera, A., & Vulpiani, A. (1981). The mechanism of stochastic resonance. Journal of Physics. A. Mathematical and General, 14, L453-L457.

Berg, M., & Timmermans, S. (2000). Order and their others: On the constitution of universalities in medical work. Configurations, 8(1), 31-61.

Bond, T., & Fox, C. (2007). Applying the Rasch model: Fundamental measurement in the human sciences, 2d edition. Mahwah, New Jersey: Lawrence Erlbaum Associates.

Chialvo, D., Longtin, A., & Müller-Gerking, J. (1996). Stochastic resonance in models of neuronal ensembles revisited [Electronic version].

Daniel, R. C., & Embretson, S. E. (2010). Designing cognitive complexity in mathematical problem-solving items. Applied Psychological Measurement, 34(5), 348-364.

Dawson, T. L. (2002a, Summer). A comparison of three developmental stage scoring systems. Journal of Applied Measurement, 3(2), 146-89.

Dawson, T. L. (2002b, March). New tools, new insights: Kohlberg’s moral reasoning stages revisited. International Journal of Behavioral Development, 26(2), 154-66.

Dawson, T. L. (2004, April). Assessing intellectual development: Three approaches, one sequence. Journal of Adult Development, 11(2), 71-85.

Dawson, T. L., Fischer, K. W., & Stein, Z. (2006). Reconsidering qualitative and quantitative research approaches: A cognitive developmental perspective. New Ideas in Psychology, 24, 229-239.

De Boeck, P., & Wilson, M. (Eds.). (2004). Explanatory item response models: A generalized linear and nonlinear approach. Statistics for Social and Behavioral Sciences). New York: Springer-Verlag.

Duncan, O. D. (1984). Notes on social measurement: Historical and critical. New York: Russell Sage Foundation.

Dykman, M. I., & McClintock, P. V. E. (1998, January 22). What can stochastic resonance do? Nature, 391(6665), 344.

Fisher, W. P., Jr. (1992, Spring). Stochastic resonance and Rasch measurement. Rasch Measurement Transactions, 5(4), 186-187 [http://www.rasch.org/rmt/rmt54k.htm].

Fisher, W. P., Jr. (1997). Physical disability construct convergence across instruments: Towards a universal metric. Journal of Outcome Measurement, 1(2), 87-113.

Fisher, W. P., Jr. (1999). Foundations for health status metrology: The stability of MOS SF-36 PF-10 calibrations across samples. Journal of the Louisiana State Medical Society, 151(11), 566-578.

Fisher, W. P., Jr. (2011). Stochastic and historical resonances of the unit in physics and psychometrics. Measurement: Interdisciplinary Research & Perspectives, 9, 46-50.

Fisher, W. P., Jr., Harvey, R. F., Taylor, P., Kilgore, K. M., & Kelly, C. K. (1995, February). Rehabits: A common language of functional assessment. Archives of Physical Medicine and Rehabilitation, 76(2), 113-122.

Galison, P. (1997). Image and logic: A material culture of microphysics. Chicago: University of Chicago Press.

Galison, P. (1999). Trading zone: Coordinating action and belief. In M. Biagioli (Ed.), The science studies reader (pp. 137-160). New York: Routledge.

Galison, P., & Stump, D. J. (1996). The disunity of science: Boundaries, contexts, and power. Palo Alto, California: Stanford University Press.

Hess, S. M., & Albano, A. M. (1998, February). Minimum requirements for stochastic resonance in threshold systems. International Journal of Bifurcation and Chaos, 8(2), 395-400.

Karabatsos, G., & Ullrich, J. R. (2002). Enumerating and testing conjoint measurement models. Mathematical Social Sciences, 43, 487-505.

Kuhn, T. S. (1961). The function of measurement in modern physical science. Isis, 52(168), 161-193. (Rpt. in T. S. Kuhn, (Ed.). (1977). The essential tension: Selected studies in scientific tradition and change (pp. 178-224). Chicago: University of Chicago Press.)

Linacre, J. M. (2011). A user’s guide to WINSTEPS Rasch-Model computer program, v. 3.72.0. Chicago, Illinois: Winsteps.com.

Linacre, J. M. (2013). A user’s guide to FACETS Rasch-Model computer program, v. 3.71.0. Chicago, Illinois: Winsteps.com.

Mandelbrot, B. (2004). The misbehavior of markets. New York: Basic Books.

Massof, R. W., & Ahmadian, L. (2007, July). What do different visual function questionnaires measure? Ophthalmic Epidemiology, 14(4), 198-204.

Moskowitz, M. T., & Dickinson, B. W. (2002). Stochastic resonance in speech recognition: Differentiating between /b/ and /v/. Proceedings of the IEEE International Symposium on Circuits and Systems, 3, 855-858.

Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests (Reprint, with Foreword and Afterword by B. D. Wright, Chicago: University of Chicago Press, 1980). Copenhagen, Denmark: Danmarks Paedogogiske Institut.

Repperger, D. W., & Farris, K. A. (2010, July). Stochastic resonance –a nonlinear control theory interpretation. International Journal of Systems Science, 41(7), 897-907.

Riani, M., & Simonotto, E. (1994). Stochastic resonance in the perceptual interpretation of ambiguous figures: A neural network model. Physical Review Letters, 72(19), 3120-3123.

Smith, R. M., & Plackner, C. (2009). The family approach to assessing fit in Rasch measurement. Journal of Applied Measurement, 10(4), 424-437.

Smith, R. M., & Taylor, P. (2004). Equating rehabilitation outcome scales: Developing common metrics. Journal of Applied Measurement, 5(3), 229-42.

Stenner, A. J., Fisher, W. P., Jr., Stone, M. H., & Burdick, D. S. (2013, August). Causal Rasch models. Frontiers in Psychology: Quantitative Psychology and Measurement, 4(536), 1-14 [doi: 10.3389/fpsyg.2013.00536].

Wilson, M. (2005). Constructing measures: An item response modeling approach. Mahwah, New Jersey: Lawrence Erlbaum Associates.

Woolley, A. W., Chabris, C. F., Pentland, A., Hashmi, N., & Malone, T. W. (2010, 29 October). Evidence for a collective intelligence factor in the performance of human groups. Science, 330, 686-688.

Woolley, A. W., & Fuchs, E. (2011, September-October). Collective intelligence in the organization of science. Organization Science, 22(5), 1359-1367.

Wu, M. L., Adams, R. J., Wilson, M. R., Haldane, S.A. (2007). ACER ConQuest Version 2: Generalised item response modelling software. Camberwell: Australian Council for Educational Research.