# Mathematical psychology

Talk0*34,117*pages on

this wiki

Assessment |
Biopsychology |
Comparative |
Cognitive |
Developmental |
Language |
Individual differences |
Personality |
Philosophy |
Social |

Methods |
Statistics |
Clinical |
Educational |
Industrial |
Professional items |
World psychology |

**Statistics:**
Scientific method ·
Research methods ·
Experimental design ·
Undergraduate statistics courses ·
Statistical tests ·
Game theory ·
Decision theory

**Mathematical Psychology** is an approach to psychological research that is based on mathematical modeling of perceptual, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior. In practice "quantifiable behavior" is often constituted by "task performance".

As quantification of behavior is fundamental in this endeavor, the theory of measurement is a central topic in mathematical psychology. Mathematical psychology is therefore closely related to psychometrics. However, where psychometrics is concerned with individual differences (or population structure) in mostly static variables, mathematical psychology focuses on process models of perceptual, cognitive and motor processes as inferred from the 'average individual'. Furthermore, where psychometrics investigates the stochastic dependence structure between variables as observed in the population, mathematical psychology almost exclusively focuses on the modeling of data obtained from experimental paradigms and is therefore even more closely related to experimental psychology/cognitive psychology/psychonomics. Like computational neuroscience and econometrics, mathematical psychology theory often uses statistical optimality as a guiding principle, apparently assuming that the human brain has evolved to solve problems in an optimized way. Central themes from cognitive psychology—limited vs. unlimited processing capacity, serial vs. parallel processing, etc.—and their implications, are central in rigorous analysis in mathematical psychology.

Mathematical psychologists are active in many fields of psychology, especially in psychophysics, sensation and perception, problem solving, decision-making, learning, memory, and language, collectively known as Cognitive Psychology, but also, e.g., in clinical psychology, social psychology, and psychology of music.

## History

Mathematical modeling has a long tradition in Psychology. Heinrich Weber (1795–1878) and Gustav Fechner (1801–1887) were among the first to apply successful mathematical technique of functional equations from physics to psychological processes, thereby establishing the fields of experimental psychology in general, and within that psychophysics in particular. During that time, in astronomy researchers were mapping distances between stars by denoting the exact time of a star's passing of a cross-hair on a telescope. For lack of the automatic registration instruments of the modern era, these time measurements relied entirely on human response speed. It had been noted that there were small systematic differences in the times measured by different astronomers, and these were first systematically studied by German astronomer Friedrich Bessel (1782-1846). Bessel constructed *personal equations* constructed from measurements of basic response speed that would cancel out individual differences from the astronomical calculations. Independently, physicist Hermann von Helmholtz measured reaction times to determine nerve conduction speed. These two lines of work came together in the research of Dutch physiologist F. C. Donders and his student J. J. de Jaager, who recognized the potential of reaction times for more or less objectively quantifying the amount of time elementary mental operations required. Donders envisioned the employment of his *mental chronometry* to scientifically infer the elements of complex cognitive activity by measurement of *simple reaction time*^{[1]}

The first psychological laboratory was established in Germany by Wundt, who amply used Donders' ideas. However, findings that came from the laboratory were hard to replicate and this was soon attributed to the method of introspection that Wundt introduced. Part of the problems was due to the individual differences in response speed found by astronomers. Although Wundt did not seem to take interest in these individual variations and kept his focus on the study of the *general human mind*, Wundt's American student James McKeen Catell was fascinated by these differences and started to work on them during his stay in England. The failure of Wundt's method of introspection led to the rise of different schools of thought. Wundt's laboratory was directed towards conscious human experience, in line with the work of Fechner and Weber on the intensity of stimuli. In the United Kingdom, under the influence of the anthropometric developments led by Francis Galton, interest focussed on individual differences between humans on psychological variables, in line with the work of Bessel. Catell soon adopted the methods of Galton and helped laying the foundation of psychometrics. In the United States, behaviorism arose in despise of introspectionism and associated reaction time research, and turned the focus of psychological research entirely to learning theory.^{[1]} Behaviorism dominated American psychology until then end of the Second World War. In Europe introspection survived in Gestalt psychology. Behaviorism largely refrained from inference on mental processes, and formal theories were mostly absent (except for vision and audition. During the war, developments in engineering, mathematical logic and computability theory, computer science and mathematics, and the military need to understand human performance and limitations, brought together experimental psychologist, mathematicians, engineers, physicists, and economists. Out of this mix of different disciplines mathematical psychology arose. Especially the developments in signal processing, information theory, linear systems and filter theory, game theory, stochastic processes and mathematical logic gained a large influence on psychological thinking.^{[1]}^{[2]}

Two seminal papers on learning theory in Psychological Review, helped establishing the field in a world that was still dominated by behaviorists: A paper by Bush and Mosteller^{[3]} instigated the linear operator approach to learning, and a paper by Estes^{[4]} that started the stimulus sampling tradition in psychological theorizing. These two papers presented the first detailed formal accounts of data from learning experiments.

The 1950s saw a surge in mathematical theories of psychological processes, including Luce's theory of choice, Tanner and Swets' introduction of Signal detection theory for human stimulus detection, and Miller's approach to information processing.^{[2]} By the end of the 1950s the number of mathematical psychologists had increased from a hand full by more than a tenfold—not counting psychometricians. Most of these were concentrated at the University of Indiana, Michigan, Pennsylvania, and Stanford.^{[5]}^{[2]} Some of these were regularly invited by the U.S. Social Science Research Counsel to teach in summer workshops in mathematics for social scientists at Stanford University, promoting collaboration.

To better define field of mathematical psychology, the mathematical models of the 1950s were brought together in sequence of volumes edited by Luce, Bush, and Galanter: Two readings^{[6]} and three handbooks^{[7]}. This series of volumes turned out to be helpful in the developmen of the field. In the summer of 1963 the need was felt for a journal for theoretical and mathematical studies in all areas in psychology, excluding work that was mainly factor analytical. An initiative led by R. C. Atkinson, R. R. Bush, W. K. Estes, R. D. Luce, and P. Suppes resulted in the appearance of the first issue of the *Journal of Mathematical Psychology* in January, 1964.^{[5]}

Under the influence of developments in computer science, logic, and language theory, in the 1960s modeling became more in terms of computational mechanisms and devices. Examples of the latter constitute so called cognitive architectures (e.g., production rule systems, ACT-R) as well connectionist systems or neural networks.

Important mathematical expressions for relations between physical characteristics of stimuli and subjective perception are Weber's law (which is now sometimes called Weber-Fechner Law), Ekman's Law, Stevens' Power Law, Thurstone's Law of Comparative Judgement, the Theory of Signal Detection (borrowed from radar engineering), the Matching Law, and Rescorla-Wagner rule for classical conditioning. While the first three laws are all deterministic in nature, later established relations are more fundamentally stochastic. This has been a general theme in the evolution in mathematical modeling of psychological processes: From deterministic relations as found in classical physics to inherently stochastic models.

## Influential Mathematical Psychologists

## Important theories and models^{[8]}

### Sensation, Perception, and Psychophysics

### Simple detection

### Stimulus identification

- Accumulator models
- Random Walk models
- Diffusion models
- Renewal models
- Race models
- Neural network/connectionist models

### Simple decision

- Recruitment model
- Cascade model
- Level and Change Race model
- SPRT

### Memory scanning, visual search

- Serial exhaustive search (SES) model
- Push-Down Stack

### Error response times

- Fast Guess model

### Sequential Effects

- Linear Operator model

### Learning

- Linear operator model
- Stochastic Learning theory

## Journals and Organizations

Central journals are the *Journal of Mathematical Psychology* and the *British Journal of Mathematical and Statistical Psychology*. There are two annual conferences in the field, the annual meeting of the *Society for Mathematical Psychology* in the U.S, and the annual *European Mathematical Psychology Group* (EMPG) meeting.

## See also

## Areas covered

- Decision theory
- Game theory
- Log-linear analysis
- Mathematical ability
- Multidimensional scaling
- Numeracy, innumeracy
- Numbers (numerals)
- Numerical cognition
- Numerical intuition
- Numerosity perception
- Numerosity adaptation effect

## Societies

## Journals

- British Journal of Mathematical and Statistical Psychology
- Journal of Mathematical Psychology
- Journal of the Society for Mathematical Psychology [3]
- Mathematical Cognition

## References

- ↑
^{1.0}^{1.1}^{1.2}T. H. Leahey (1987)*A History of Psychology*, Englewood Cliffs, NJ: Prentice Hall. - ↑
^{2.0}^{2.1}^{2.2}W. H. Batchelder (2002). Mathematical Psychology. In A.E. Kazdin (Ed.)*Encyclopedia of Psychology*, Washington, DC: APA and New York: Oxford University Press. - ↑ R. R. Bush & F. Mosteller (1951). A mathematical model for simple learning.
*Psychological Review, 58*, p. 313-323. - ↑ W. K. Estes (1950). Towards a statistical theory of learning.
*Psychological Review, 57*, p. 94-107. - ↑
^{5.0}^{5.1}W. K. Estes (2002). History of the Society, [1] - ↑ R. D. Luce, R. R. Bush, & Galanter, E. (Eds.) (1963).
*Readings in mathematical psychology. Volumes I & II.*New York: Wiley. - ↑ R. D. Luce, R. R. Bush, & Galanter, E. (Eds.) (1963). Handbook of mathematical psychology. Volumes I-III
*, New York: Wiley. Volume II from Internet Archive* - ↑ Luce, R. D. (1986)
*Response Times (Their Role in Inferring Elementary Mental Organization)*. New York: Oxford University Press.

- Abraham, R. H. (1995). Erodynamics and the dischaotic personality. Westport, CT: Praeger Publishers/Greenwood Publishing Group.
- Adams, E. W. (1997). Bias-independent constructions from biased bisection and adjacency judgements: Journal of Mathematical Psychology Vol 41(4) Dec 1997, 311-318.
- Adams-Webber, J. R. (1990). A model of reflexion from the perspective of personal construct theory. New York, NY: Peter Lang Publishing.
- al-Nowaihi, A., & Dhami, S. (2006). A simple derivation of Prelec's probability weighting function: Journal of Mathematical Psychology Vol 50(6) Dec 2006, 521-524.
- Alper, T. M. (1987). A classification of all order-preserving homeomorphism groups of the reals that satisfy finite uniqueness: Journal of Mathematical Psychology Vol 31(2) Jun 1987, 135-154.
- Azrieli, Y., & Lehrer, E. (2007). Categorization generated by extended prototypes--An axiomatic approach: Journal of Mathematical Psychology Vol 51(1) Feb 2007, 14-28.
- Baker, F. B. (1998). An investigation of the item parameter recovery characteristics of a Gibbs sampling procedure: Applied Psychological Measurement Vol 22(2) Jun 1998, 153-169.
- Ballard, D. H., Zhang, Z., & Rao, R. P. N. (2002). Distributed synchrony: A probabilistic model of neural signaling. Cambridge, MA: The MIT Press.
- Baroody, A. J., & Dowker, A. (2003). The development of arithmetic concepts and skills: Constructing adaptive expertise. Mahwah, NJ: Lawrence Erlbaum Associates Publishers.
- Batchelder, W. H. (1971). What's (nu) in Math Psych? : PsycCRITIQUES Vol 16 (10), Oct, 1971.
- Batchelder, W. H. (1986). European Mathematical Psychology: PsycCRITIQUES Vol 31 (7), Jul, 1986.
- Batchelder, W. H. (1990). Some critical issues in Lefebvre's framework for ethical cognition and reflexion. New York, NY: Peter Lang Publishing.
- Batchelder, W. H. (2000). Mathematical psychology: Kazdin, Alan E (Ed).
- Batchelder, W. H., & Crowther, C. S. (1997). Multinomial processing tree models of factorial categorization: Journal of Mathematical Psychology Vol 41(1) Mar 1997, 45-55.
- Baum, W. M. (1989). Quantitative prediction and molar description of the environment: Behavior Analyst Vol 12(2) Fal 1989, 167-176.
- Baumunk, K., & Dowling, C. E. (1997). Validity of spaces for assessing knowledge about fractions: Journal of Mathematical Psychology Vol 41(1) Mar 1997, 99-105.
- Beghi, L., Xausa, E., Tomat, L., & Zanforlin, M. (1997). The depth effect of an oscillating tilted bar: Journal of Mathematical Psychology Vol 41(1) Mar 1997, 11-18.
- Bell, D. E., & Fishburn, P. C. (2003). Probability weights in rank-dependent utility with binary even-chance independence: Journal of Mathematical Psychology Vol 47(3) Jun 2003, 244-258.
- Bennett, B. M., & Lehman, R. C. (2001). Directed convergence in stable percept acquisition: Journal of Mathematical Psychology Vol 45(5) Oct 2001, 732-779.
- Berlyne, D. E. (1971). Effects of auditory prechoice stimulation on visual exploratory choice: Psychonomic Science Vol 25(4) Nov 1971, 193-194.
- Billot, A., & Thisse, J.-F. (1999). A discrete choice model when context matters: Journal of Mathematical Psychology Vol 43(4) Dec 1999, 518-538.
- Birnbaum, M. H. (2004). Causes of Allais common consequence paradoxes: An experimental dissection: Journal of Mathematical Psychology Vol 48(2) Apr 2004, 87-106.
- Bockenholt, U. (1994). The 20th Meeting of the European Mathematical Psychology Group: PsycCRITIQUES Vol 39 (2), Feb, 1994.
- Bogatyrew, K. K. (1990). A marginal note to Vladimir Lefebvre's theory of moral cognition. New York, NY: Peter Lang Publishing.
- Bogin, B. (1988). Patterns of human growth. New York, NY: Cambridge University Press.
- Bolt, D., & Stout, W. (1996). Differential item functioning: Its multidimensional model and resulting SIBTEST detection procedure: Behaviormetrika Vol 23(1) Jan 1996, 67-95.
- Boudewijnse, G.-J. A., Murray, D. J., & Bandomir, C. A. (1999). Herbart's mathematical psychology: History of Psychology Vol 2(3) Aug 1999, 163-193.
- Boudewijnse, G.-J. A., Murray, D. J., & Bandomir, C. A. (2001). The fate of Herbart's mathematical psychology: History of Psychology Vol 4(2) May 2001, 107-132.
- Bresson, F. (1973). Some aspects of mathematization in psychology: Social Science Information/sur les sciences sociales Vol 12(4) Aug 1973, 51-65.
- Brichacek, V. (1973). Mathematical psychology: 1972: Activitas Nervosa Superior Vol 15(4) 1973, 278-286.
- Brown, D. R., & Smith, J. E. K. (1991). Frontiers of mathematical psychology: Essays in honor of Clyde Coombs. New York, NY: Springer-Verlag Publishing.
- Burros, R. H. (1975). Complementary properties of binary relations: Theory and Decision Vol 6(2) May 1975, 177-183.
- Candeal, J. C., De Miguel, J. R., & Indurain, E. (1996). Extensive measurement: Continuous additive utility functions on semigroups: Journal of Mathematical Psychology Vol 40(4) Dec 1996, 281-286.
- Candeal, J. C., Indurain, E., & Oloriz, E. (1998). Weak extensive measurement without translation-invariance axioms: Journal of Mathematical Psychology Vol 42(1) Mar 1998, 48-62.
- Carlton, E. H., & Shepard, R. N. (1990). Psychologically simple motions as geodesic paths: I. Asymmetric objects: Journal of Mathematical Psychology Vol 34(2) Jun 1990, 127-188.
- Carlton, E. H., & Shepard, R. N. (1990). Psychologically simple motions as geodesic paths: II. Symmetric objects: Journal of Mathematical Psychology Vol 34(2) Jun 1990, 189-228.
- Cartwright, D. (1997). Formalization and Progress in Psychology (1940). Washington, DC: American Psychological Association.
- Chater, N., & Vitanyi, P. (2003). Simplicity: A unifying principle in cognitive science? : Trends in Cognitive Sciences Vol 7(1) Jan 2003, 19-22.
- Chechile, R. A. (2003). Journal of Mathematical Psychology: Telegraphic reviews: Journal of Mathematical Psychology Vol 47(1) Feb 2003, 106-107.
- Chechile, R. A. (2003). Telegraphic reviews: Journal of Mathematical Psychology Vol 47(4) Aug 2003, 472-474.
- Chechile, R. A. (2005). Telegraphic reviews: Journal of Mathematical Psychology Vol 49(3) Jun 2005, 255-256.
- Chechile, R. A. (2006). Telegraphic reviews: Journal of Mathematical Psychology Vol 50(4) Aug 2006, 437-438.
- Chechile, R. A. (2007). Telegraphic reviews: Journal of Mathematical Psychology Vol 51(1) Feb 2007, 53-54.
- Chen, S. (2006). The relationship between mathematical beliefs and performance: A study of students and their teachers in Beijing and New York (China). Dissertation Abstracts International Section A: Humanities and Social Sciences.
- Chubb, C. (1999). Texture-based methods for analyzing elementary visual substances: Journal of Mathematical Psychology Vol 43(4) Dec 1999, 539-567.
- Cohen, M. A. (1980). Random utility systems: The infinite case: Journal of Mathematical Psychology Vol 22(1) Aug 1980, 1-23.
- Colonius, H. (1991). Progress in European Mathematical Psychology: PsycCRITIQUES Vol 36 (7), Jul, 1991.
- Colonius, H., & Ellermeier, W. (1997). Distribution inequalities for parallel models of reaction time with an application to auditory profile analysis: Journal of Mathematical Psychology Vol 41(1) Mar 1997, 19-27.
- Confrey, J., & Kazak, S. (2006). A Thirty-Year Reflection on Constructivism in Mathematics Education in PME. Rotterdam, Netherlands: Sense Publishers.
- Coombs, C. H. (1974). What is mathematical psychology? : Pakistan Journal of Psychology Vol 7(3-4) Dec 1974, 3-6.
- Cosyn, E. (2002). Coarsening a knowledge structure: Journal of Mathematical Psychology Vol 46(2) Apr 2002, 123-139.
- Crassini, B. (1998). Editorial: Australian Journal of Psychology Vol 50(3) Dec 1998, ii.
- Creelman, C. D. (1998). Detecting, discriminating, and proselytizing: PsycCRITIQUES Vol 43 (12), Dec, 1998.
- Cuijpers, R. H., Kappers, A. M. L., & Koenderink, J. J. (2003). The metrics of visual and haptic space based on parallelity judgements: Journal of Mathematical Psychology Vol 47(3) Jun 2003, 278-291.
- Davies, G. B., & Satchell, S. E. (2007). The behavioural components of risk aversion: Journal of Mathematical Psychology Vol 51(1) Feb 2007, 1-13.
- Dawson, W. E., & Miller, M. E. (1978). A reply to the critique by Marks: Perception & Psychophysics Vol 24(6) Dec 1978, 571.
- Degreef, E., Doignon, J.-P., Ducamp, A., & Falmagne, J.-C. (1986). Languages for the assessment of knowledge: Journal of Mathematical Psychology Vol 30(3) Sep 1986, 243-256.
- Diderich, A., & Busemeyer, J. R. (2003). Simple matrix methods for analyzing diffusion models of choice probability, choice response time, and simple response time: Journal of Mathematical Psychology Vol 47(3) Jun 2003, 304-322.
- Doignon, J.-P., & Falmagne, J.-C. (1991). Mathematical psychology: Current developments. New York, NY: Springer-Verlag Publishing.
- Doignon, J.-P., Fiorini, S., & Joret, G. (2006). Facets of the linear ordering polytope: A unification for the fence family through weighted graphs: Journal of Mathematical Psychology Vol 50(3) Jun 2006, 251-262.
- Doignon, J.-P., Fiorini, S., & Joret, G. (2007). Erratum to "Facets of the linear ordering polytope: A unification for the fence family through weighted graphs": Journal of Mathematical Psychology Vol 51(5) Oct 2007, 341.
- Doignon, J.-P., & Regenwetter, M. (2005). Editor's foreword: Journal of Mathematical Psychology Vol 49(6) Dec 2005, 429.
- Dorans, N. J., & MacCallum, R. C. (2005). Ledyard R. Tucker (1910-2004): Psychometrika Vol 70(1) Mar 2005, 1-2.
- Dorfman, D. D. (1992). Man Proposes, God Disposes--Thomas a Kempis: PsycCRITIQUES Vol 37 (3), Mar, 1992.
- Dowling, C. E., Roberts, F. S., & Theuns, P. (1998). Recent progress in mathematical psychology: Psychophysics, knowledge, representation, cognition, and measurement. Mahwah, NJ: Lawrence Erlbaum Associates Publishers.
- Drosler, J. (2000). An n-dimensional Weber law and the corresponding Fechner law: Journal of Mathematical Psychology Vol 44(2) Jun 2000, 330-335.
- Droste, M. (1987). Classification and transformation of ordinal scales in the theory of measurement. New York, NY: Elsevier Science.
- Dunn, J. C., & James, R. N. (2003). Signed difference analysis: Theory and application: Journal of Mathematical Psychology Vol 47(4) Aug 2003, 389-416.
- Duntsch, I., & Gediga, G. (1996). On query procedures to build knowledge structures: Journal of Mathematical Psychology Vol 40(2) Jun 1996, 160-168.
- Dyer, J. S., & Sarin, R. K. (1978). On the relationship between additive conjoint and difference measurement: Journal of Mathematical Psychology Vol 18(3) Dec 1978, 270-272.
- Dzhafarov, E. N. (1999). Double skew-dual scaling: A conjoint scaling of two sets of objects related by a dominance matrix: Journal of Mathematical Psychology Vol 43(4) Dec 1999, 483-517.
- Dzhafarov, E. N. (2001). Unconditionally selective dependence of random variables on external factors: Journal of Mathematical Psychology Vol 45(3) Jun 2001, 421-451.
- Dzhafarov, E. N. (2003). Selective influence through conditional independence: Psychometrika Vol 68(1) Mar 2003, 7-25.
- Dzhafarov, E. N., & Colonius, H. (2001). Multidimensional Fechnerian Scaling: Basics: Journal of Mathematical Psychology Vol 45(5) Oct 2001, 670-719.
- Edwards, D. C., & Metz, C. E. (2006). Analysis of proposed three-class classification decision rules in terms of the ideal observer decision rule: Journal of Mathematical Psychology Vol 50(5) Oct 2006, 478-487.
- Estes, W. K. (1969). The Magic of Words Plus Numbers: PsycCRITIQUES Vol 14 (11), Nov, 1969.
- Estes, W. K. (1975). Some targets for mathematical psychology: Journal of Mathematical Psychology Vol 12(3) Aug 1975, 263-282.
- Evans, J. S. B. T., & Over, D. E. (1997). Editorial: The contribution of Amos Tversky: Thinking & Reasoning Vol 3(1) 1997, 1-8.
- Falmagne, J.-C. (2000). Suppes, Patrick: Kazdin, Alan E (Ed).
- Falmagne, J.-C. (2005). Mathematical psychology--A perspective: Journal of Mathematical Psychology Vol 49(6) Dec 2005, 436-439.
- Falmagne, J.-C. (2007). A set-theoretical outlook on the philosophy of science: Journal of Mathematical Psychology Vol 51(1) Feb 2007, 45-52.
- Falmagne, J.-C., & Doignon, J.-P. (1998). Meshing knowledge structures. Mahwah, NJ: Lawrence Erlbaum Associates Publishers.
- Feldman, C. F. (1997). Boden's middle way: Viable or not? New York, NY: Oxford University Press.
- Feldman, J. (2003). A catalog of Boolean concepts: Journal of Mathematical Psychology Vol 47(1) Feb 2003, 75-89.
- Feldt, L. S., & Ankenmann, R. D. (1998). Appropriate sample size for comparing alpha reliabilities: Applied Psychological Measurement Vol 22(2) Jun 1998, 170-178.
- Fishburn, P. (1998). Utility of wealth in nonlinear utility theory. Mahwah, NJ: Lawrence Erlbaum Associates Publishers.
- Fisher, D. L., Wisher, R. A., & Ranney, T. A. (1996). Optimal static and dynamic training schedules: State models of skill acquisition: Journal of Mathematical Psychology Vol 40(1) Mar 1996, 30-47.
- Fridman, L. M. (1974). Some methodological problems of modeling and mathematization in psychology: Voprosy Psychologii No 5 Sep-Oct 1974, 3-12.
- Fries, S. (1997). Empirical validation of a Markovian learning model for knowledge structures: Journal of Mathematical Psychology Vol 41(1) Mar 1997, 65-70.
- Garson, J. W. (1996). Is Logic the Core of Cognition? : PsycCRITIQUES Vol 41 (9), Sep, 1996.
- Gates, P. (2006). The Place of Equity and Social Justice in the History of PME. Rotterdam, Netherlands: Sense Publishers.
- Geissler, H. G. (1975). Towards a new reconciliation of Stevens' and Helson's approaches to psychophysics: A tentative solution of the Stevens-Greenbaum puzzle: Acta Psychologica Vol 39(6) Dec 1975, 417-426.
- Gentry, T. A. (1995). Fractal geometry and human understanding. Westport, CT: Praeger Publishers/Greenwood Publishing Group.
- George, R. (2005). Review of The development of arithmetic concepts and skills: Constructing adaptive expertise: British Journal of Educational Psychology Vol 75(1) Mar 2005, 142-143.
- Ghahramani, Z. (1996). Computation and psychophysics of sensorimotor integration. Dissertation Abstracts International: Section B: The Sciences and Engineering.
- Gnepp, E. H. (1975). A mathematical reformulation of the persistence of the phobic response: Psychology: A Journal of Human Behavior Vol 12(2) May 1975, 51-52.
- Golden, R. R. (1991). Is a latent trait a matter of degree or a matter of kind? : PsycCRITIQUES Vol 36 (2), Feb, 1991.
- Gonzales, C. (1996). Additive utilities when some components are solvable and others are not: Journal of Mathematical Psychology Vol 40(2) Jun 1996, 141-151.
- Gormezano, I. (2002). Donald D. Dorfman (1933-2001): Obituary: American Psychologist Vol 57(12) Dec 2002, 1124.
- Greeno, J. G. (1972). Mathematics in psychology: Dodwell, P C (Ed) (1972) New horizons in psychology Oxford, England: Penguin.
- Gregson, R. A. M. (1998). Confusing rotation-like operations in space, mind and brain: British Journal of Mathematical and Statistical Psychology Vol 51(1) May 1998, 135-162.
- Griesinger, D. W. (1978). The physics of motivation and choice: IEEE Transactions on Systems, Man, & Cybernetics Vol 8(12) Dec 1978, 902-907.
- Groen, G. (1972). A Limited Introduction: PsycCRITIQUES Vol 17 (12), Dec, 1972.
- Gutierrez, A., & Boero, P. (2006). Handbook of research on the psychology of mathematics education: Past, present and future. Rotterdam, Netherlands: Sense Publishers.
- Hand, I., & Henning, P. A. (2004). Gambling at the stock exchange: A psychological-mathematical analysis: Sucht: Zeitschrift fur Wissenschaft und Praxis Vol 50(3) Jun 2004, 172-186.
- Harel, G., Selden, A., & Selden, J. (2006). Advanced Mathematical Thinking: Some PME Perspectives. Rotterdam, Netherlands: Sense Publishers.
- Harris, R. J. (1976). Handling negative inputs: On the plausible equity formulae: Journal of Experimental Social Psychology Vol 12(2) Mar 1976, 194-209.
- Healy, A. F. (2000). Estes, William Kaye: Kazdin, Alan E (Ed).
- Healy, A. F., Kosslyn, S. M., & Shiffrin, R. M. (1992). Essays in honor of William K. Estes, Vol. 1: From learning theory to connectionist theory; Vol. 2: From learning processes to cognitive processes. Hillsdale, NJ, England: Lawrence Erlbaum Associates, Inc.
- Heller, J. (2006). Illumination-invariance of Plateau's midgray: Journal of Mathematical Psychology Vol 50(3) Jun 2006, 263-270.
- Herden, G. (1995). On some equivalent approaches to Mathematical Utility Theory: Mathematical Social Sciences Vol 29(1) Feb 1995, 19-31.
- Hirst, W. (1988). The making of cognitive science: Essays in honor of George A. Miller. New York, NY: Cambridge University Press.
- Hoffman, W. C., & Dodwell, P. C. (1985). Geometric psychology generates the visual Gestalt: Canadian Journal of Psychology/Revue Canadienne de Psychologie Vol 39(4) Dec 1985, 491-528.
- Iberall, A. S. (1997). Nonlinear dynamics from a physical point of view: Ecological Psychology Vol 9(3) 1997, 223-244.
- Indow, T. (1997). Hyperbolic representation of global structure of visual space: Journal of Mathematical Psychology Vol 41(1) Mar 1997, 89-98.
- Irtel, H. (1987). On specific objectivity as a concept in measurement. New York, NY: Elsevier Science.
- Iverson, G. J. (2006). Analytical methods in the theory of psychophysical discrimination I: Inequalities, convexity and integration of just noticeable differences: Journal of Mathematical Psychology Vol 50(3) Jun 2006, 271-282.
- Iverson, G. J. (2006). Analytical methods in the theory of psychophysical discrimination II: The Near-miss to Weber's Law, Falmagne's Law, the Psychophysical Power Law and the Law of Similarity: Journal of Mathematical Psychology Vol 50(3) Jun 2006, 283-289.
- Iverson, G. J. (2006). An essay on inequalities and order-restricted inference: Journal of Mathematical Psychology Vol 50(3) Jun 2006, 215-219.
- Janssens, R. (1998). Structuring complex concepts. Mahwah, NJ: Lawrence Erlbaum Associates Publishers.
- Johnston, B., & Yasukawa, K. (2001). Numeracy: Negotiating the world through mathematics. Mahwah, NJ: Lawrence Erlbaum Associates Publishers.
- Karni, E., & Safra, Z. (1998). The hexagon condition and additive representation for two dimensions: An algebraic approach: Journal of Mathematical Psychology Vol 42(4) Dec 1998, 393-399.
- Katsikopoulos, K. V., & Martignon, L. (2006). Naive heuristics for paired comparisons: Some results on their relative accuracy: Journal of Mathematical Psychology Vol 50(5) Oct 2006, 488-494.
- Kauffman, L. H. (1990). Self and mathematics. New York, NY: Peter Lang Publishing.
- Khromov, A. G. (2001). Logical self-reference as a model for conscious experience: Journal of Mathematical Psychology Vol 45(5) Oct 2001, 720-731.
- Ki, H. K., & Roush, F. W. (1978). Ultrametrics and matrix theory: Journal of Mathematical Psychology Vol 18(2) Oct 1978, 195-203.
- Kiener, S. (1997). On the relationship between two types of effects caused by color adaptation: Changes in color appearance and color discriminability: Journal of Mathematical Psychology Vol 41(1) Mar 1997, 107-121.
- Kim, C. (1998). Modeling individual differences in mathematical psychology. Dissertation Abstracts International: Section B: The Sciences and Engineering.
- Knapp, T. (2000). Shepard, Roger N: Kazdin, Alan E (Ed).
- Kobberling, V. (2003). Comments on: Edi Karni and Zvi Safra (1998), the hexagon condition and additive representations for two dimensions: An algebraic approach: Journal of Mathematical Psychology Vol 47(3) Jun 2003, 370.
- Kondo, K. (1968). RAAG memoirs of the unifying study of basic problems in engineering and physical sciences by means of geometry: IV. Oxford, England: Gakujutsu Bunken Fukyu-Kai.
- Kondo, K., Shimbo, M., Sato, K., & Date, T. (1968). Mathematical foundations of psychophysical recognitions: Kondo, K (Ed) (1968) RAAG memoirs of the unifying study of basic problems in engineering and physical sciences by means of geometry.
- Koppen, M. G. (1987). On finding the bidimension of a relation: Journal of Mathematical Psychology Vol 31(2) Jun 1987, 155-178.
- Krantz, D. H., Atkinson, R. C., Luce, R. D., & Suppes, P. (1974). Contemporary developments in mathematical psychology: I. Learning, memory and thinking. Oxford, England: W H Freeman.
- Krantz, D. H., Atkinson, R. C., Luce, R. D., & Suppes, P. (1974). Contemporary developments in mathematical psychology: II. Measurement, psychophysics, and neural information processing. Oxford, England: W H Freeman.
- Krause, B., & Raykov, T. (1987). On models for measuring changes: Zeitschrift fur Psychologie mit Zeitschrift fur angewandte Psychologie Vol 195(2) 1987, 163-170.
- Krylov, V. Y. (1992). Urgent problems of mathematical psychology: Psikhologicheskiy Zhurnal Vol 13(6) Nov-Dec 1992, 13-24.
- Kyngdon, A. (2006). An Introduction to the Theory of Unidimensional Unfolding: Journal of Applied Measurement Vol 7(3) 2006, 260-277.
- Lakshminarayan, K., & Gilson, F. (1998). An application of a stochastic knowledge structure model. Mahwah, NJ: Lawrence Erlbaum Associates Publishers.
- Laming, D. (1975). Ten Years Progress in Mathematical Psychology: PsycCRITIQUES Vol 20 (9), Sep, 1975.
- Leary, D. E. (2000). Herbert, Johann Friedrich: Kazdin, Alan E (Ed).
- Leder, G. C., & Forgasz, H. J. (2006). Affect and Mathematics Education: PME Perspectives. Rotterdam, Netherlands: Sense Publishers.
- Lefebvre, V. A. (1990). From psychophysics to the modeling of the soul. New York, NY: Peter Lang Publishing.
- Lefebvre, V. A. (1990). The fundamental structures of human reflexion. New York, NY: Peter Lang Publishing.
- Lefebvre, V. A., & Batchelder, W. H. (1981). The nature of Soviet mathematical psychology: Journal of Mathematical Psychology Vol 23(2) Apr 1981, 153-183.
- Lerman, S. (2006). Socio-Cultural Research in PME. Rotterdam, Netherlands: Sense Publishers.
- Levin, D. N. (2000). A differential geometric description of the relationships among perceptions: Journal of Mathematical Psychology Vol 44(2) Jun 2000, 241-284.
- Lewandowsky, S., Kalish, M., & Dunn, J. C. (1998). Guest editorial: Australian Journal of Psychology Vol 50(3) Dec 1998, iii.
- Lewin, G. W. (1997). Constructs in Field Theory (1944). Washington, DC: American Psychological Association.
- Lovie, S. (2003). Review of Theories of meaningfulness: British Journal of Mathematical and Statistical Psychology Vol 56(1) May 2003, 183-184.
- Lovie, S., & Lovie, P. (2004). A Privileged and Exemplar Resource: Traumatic Avoidance Learning and the Early Triumph of Mathematical Psychology: History of Psychology Vol 7(3) Aug 2004, 248-264.
- Luce, D. (2005). Editorial: Journal of Mathematical Psychology Vol 49(6) Dec 2005, 430-431.
- Luce, R. D. (1989). Mathematical psychology and the computer revolution. Oxford, England: North-Holland.
- Luce, R. D. (1992). A path taken: Aspects of modern measurement theory. Hillsdale, NJ, England: Lawrence Erlbaum Associates, Inc.
- Luce, R. D. (1995). Four tensions concerning mathematical modeling in psychology: Annual Review of Psychology Vol 46 1995, 1-26.
- Luce, R. D. (1996). The ongoing dialog between empirical science and measurement theory: Journal of Mathematical Psychology Vol 40(1) Mar 1996, 78-98.
- Luce, R. D. (1996). When four distinct ways to measure utility are the same: Journal of Mathematical Psychology Vol 40(4) Dec 1996, 297-317.
- Luce, R. D. (1997). Several unresolved conceptual problems of mathematical psychology: Journal of Mathematical Psychology Vol 41(1) Mar 1997, 79-87.
- Kuce, R. D. (1999). Where is mathematical modeling in psychology headed?
*Theory & Psychology, 9,*723-737. Full text - Luce, R. D., & Suppes, P. (2002). Representational measurement theory. Hoboken, NJ: John Wiley & Sons Inc.
- Marek, T., & Noworol, C. (1985). The sequential testing of the difference between means: Z-sub(mn ) test: Przeglad Psychologiczny Vol 28(2) 1985, 547-553.
- Margineanu, N. (1997). Logical and mathematical psychology: Dialectical interpretation of their relations. Cluj-Napoca, Romania: Editura Presa Universitara Clujeana.
- Maris, G., & Maris, E. (2002). A MCMC-method for models with continuous latent responses: Psychometrika Vol 67(3) Sep 2002, 335-350.
- Marks, L. E. (1978). A critique of Dawson and Miller's "Inverse attribute functions and the proposed modifications of the power law." Perception & Psychophysics Vol 24(6) Dec 1978, 569-570.
- Marr, M. J. (1989). Some remarks on the quantitative analysis of behavior: Behavior Analyst Vol 12(2) Fal 1989, 143-151.
- Mayekawa, S.-i. (1996). Maximum likelihood estimation of the cell probabilities under linear constraints: Behaviormetrika Vol 23(1) Jan 1996, 111-128.
- Mayer, R. E. (1989). Explorations in Mathematical Cognition: PsycCRITIQUES Vol 34 (3), Mar, 1989.
- Mazur, J. E. (1975). The matching law and quantifications related to Premack's principle: Journal of Experimental Psychology: Animal Behavior Processes Vol 1(4) Oct 1975, 374-386.
- McClain, E. G. (1990). Tonal automata. New York, NY: Peter Lang Publishing.
- McDowell, J. J. (1989). Two modern developments in matching theory: Behavior Analyst Vol 12(2) Fal 1989, 153-166.
- McGill, W. J. (1988). George A. Miller and the origins of mathematical psychology. New York, NY: Cambridge University Press.
- McGill, W. J., & Gibbon, J. (1965). The general-gamma distribution and reaction times: Journal of Mathematical Psychology 2(1) 1965, 1-18.
- McNemar, Q. (1968). Review of Basic Mathematical and Statistical Tables for Psychology and Education: PsycCRITIQUES Vol 13 (2), Feb, 1968.
- Meda, G., Martinez, G., & Morgante, E. (1997). Numerical taxonomy applied to Leonhard's classification of endogenous psychoses: Psychopathology Vol 30(5) Sep-Oct 1997, 291-297.
- Meenes, M. (1921). Manhood of humanity: The science and art of human engineering: Journal of Applied Psychology Vol 5(2) Jun 1921, 189-190.
- Menai, M. E. B., & Batouche, M. (2006). An effective heuristic algorithm for the maximum satisfiability problem: Applied Intelligence Vol 24(3) Jun 2006, 227-239.
- Molenaar, P. C. M. (1994). On the viability of nonlinear dynamics in psychology. Lisse, Netherlands: Swets & Zeitlinger Publishers.
- Myung, I. J., & Shepard, R. N. (1996). Maximum entropy inference and stimulus generalization: Journal of Mathematical Psychology Vol 40(4) Dec 1996, 342-347.
- Nandakumar, R., Yu, F., Li, H.-H., & Stout, W. (1998). Assessing unidimensionality of polytomous data: Applied Psychological Measurement Vol 22(2) Jun 1998, 99-115.
- Narens, L. (1980). A note on Weber's Law for Conjoint Structures: Journal of Mathematical Psychology Vol 21(1) Feb 1980, 88-91.
- Narens, L. (2003). A theory of belief: Journal of Mathematical Psychology Vol 47(1) Feb 2003, 1-31.
- Narens, L. (2006). Symmetry, direct measurement, and Torgerson's conjecture: Journal of Mathematical Psychology Vol 50(3) Jun 2006, 290-301.
- Niederee, R. (1987). On the reference to real numbers in fundamental measurement: A model-theoretic approach. New York, NY: Elsevier Science.
- No authorship, i. (1986). Review of Australian Psychology: Review of Research: PsycCRITIQUES Vol 31 (9), Sep, 1986.
- No authorship, i. (1989). Review of Progress in Mathematical Psychology-1: PsycCRITIQUES Vol 34 (1), Jan, 1989.
- No authorship, i. (2005). 37th Annual Meeting of the Society for Mathematical Psychology: Journal of Mathematical Psychology Vol 49(1) Feb 2005, 87-113.
- Norman, M. F. (1981). Lectures on linear systems theory: Journal of Mathematical Psychology Vol 23(1) Feb 1981, 1-89.
- Norman, M. F., & Gallistel, C. R. (1978). What can one learn from a strength-duration experiment? : Journal of Mathematical Psychology Vol 18(1) Aug 1978, 1-24.
- Orth, B. (1987). Applications of the theory of meaningfulness to attitude models. New York, NY: Elsevier Science.
- Ovchinnikov, S. (2005). Hyperplane arrangements in preference modeling: Journal of Mathematical Psychology Vol 49(6) Dec 2005, 481-488.
- Plaud, J. J., & O'Donohue, W. (1991). Mathematical statements in the experimental analysis of behavior: Psychological Record Vol 41(3) Sum 1991, 385-400.
- Ponson, B. (1984). Vote by consensus: Mathematiques et Sciences Humaines Vol 22(87) Fal 1984, 5-32.
- Poon, W.-Y., & Chan, W. (2002). Influence analysis of ranking data: Psychometrika Vol 67(3) Sep 2002, 421-436.
- Presmeg, N. (2006). Research on Visualization in Learning and Teaching Mathematics: Emergence from Psychology. Rotterdam, Netherlands: Sense Publishers.
- Rapoport, A. (1990). Reflexion, modeling and ethics. New York, NY: Peter Lang Publishing.
- Ratcliff, R. (1998). The role of mathematical psychology in experimental psychology: Australian Journal of Psychology Vol 50(3) Dec 1998, 129-130.
- Roberts, F. S. (1984). Review of Mathematical Models in the Social and Behavioral Sciences: PsycCRITIQUES Vol 29 (12), Dec, 1984.
- Rocci, R., & ten Berge, J. M. F. (2002). Transforming three-way arrays to maximal simplicity: Psychometrika Vol 67(3) Sep 2002, 351-365.
- Roskam, E. E. (1973). Mathematical psychology as theory and method: Nederlands Tijdschrift voor de Psychologie en haar Grensgebieden Vol 27(11) Apr 1973, 701-730.
- Roskam, E. E. (1989). Mathematical psychology in progress. New York, NY: Springer-Verlag Publishing.
- Roskam, E. E., & Suck, R. (1987). Progress in mathematical psychology, 1. New York, NY: Elsevier Science.
- Rouder, J. N. (1996). Premature sampling in random walks: Journal of Mathematical Psychology Vol 40(4) Dec 1996, 287-296.
- Samejima, F. (1996). Evaluation of mathematical models for ordered polychotomous responses: Behaviormetrika Vol 23(1) Jan 1996, 17-35.
- Schiffman, H., & Schiffman, E. (2000). Gulliksen, Harold: Kazdin, Alan E (Ed).
- Schmidt, U., & Zimper, A. (2007). Security and potential level preferences with thresholds: Journal of Mathematical Psychology Vol 51(5) Oct 2007, 279-289.
- Schonemann, P. H. (1980). On possible psychophysical maps: II. Projective transformations: Bulletin of the Psychonomic Society Vol 15(2) Feb 1980, 65-68.
- Schonemann, P. H., Cafferty, T., & Rotton, J. (1973). A note on additive functional measurement: Psychological Review Vol 80(1) Jan 1973, 85-87.
- Schonemann, P. H., Cafferty, T., & Rotton, J. (1973). "A note on additive functional measurement": Erratum: Psychological Review Vol 80(2) Mar 1973, 138.
- Schwager, K. W. (1991). The representational theory of measurement: An assessment: Psychological Bulletin Vol 110(3) Nov 1991, 618-626.
- Schwarz, W. (1990). Stochastic accumulation of information in discrete time: Comparing exact results and Wald approximations: Journal of Mathematical Psychology Vol 34(2) Jun 1990, 229-236.
- Shafir, E. (2004). Preference, belief, and similarity: Selected writings by Amos Tversky. Cambridge, MA: MIT Press.
- Sheldon, W. H. (1898). Review of The Mathematical Psychology of Gratry and Boole: Psychological Review Vol 5(4) Jul 1898, 426-428.
- Shepard, R. N. (1988). George Miller's data and the development of methods for representing cognitive structures. New York, NY: Cambridge University Press.
- Sheu, C.-F. (2006). Triadic judgment models and Weber's law: Journal of Mathematical Psychology Vol 50(3) Jun 2006, 302-308.
- Shigemasu, K., & Nakamura, T. (1996). A Bayesian marginal inference in estimating item parameters using the Gibbs Sampler: Behaviormetrika Vol 23(1) Jan 1996, 97-110.
- Smolenaars, A. J. (1987). Likelihood considerations within a deterministic setting. New York, NY: Elsevier Science.
- Sommer, R., & Suppes, P. (1997). Dispensing with the continuum: Journal of Mathematical Psychology Vol 41(1) Mar 1997, 3-10.
- Spellman, B. A. (1996). Conditionalizing causality. San Diego, CA: Academic Press.
- Stefanutti, L., & Koppen, M. (2003). A procedure for the incremental construction of a knowledge space: Journal of Mathematical Psychology Vol 47(3) Jun 2003, 265-277.
- Sternberg, R. J. (1993). How Do You Size Up the Contributions of a Giant? : PsycCRITIQUES Vol 38 (9), Sep, 1993.
- Stout, W., Nandakumar, R., & Habing, B. (1996). Analysis of latent dimensionality of dichotomously and polytomously scored test data: Behaviormetrika Vol 23(1) Jan 1996, 37-65.
- Sturm, T. (2006). Is there a problem with mathematical psychology in the eighteenth century? A fresh look at Kant's old argument: Journal of the History of the Behavioral Sciences Vol 42(4) Fal 2006, 353-377.
- Suck, R. (1987). Approximation theorems for conjoint measurement models. New York, NY: Elsevier Science.
- Suck, R. (1997). Probabilistic biclassification and random variable representations: Journal of Mathematical Psychology Vol 41(1) Mar 1997, 57-64.
- Suck, R. (2004). Set representations of orders and a structural equivalent of saturation: Journal of Mathematical Psychology Vol 48(3) Jun 2004, 159-166.
- Suppes, P. (2006). All you ever wanted to know about meaningfulness: Journal of Mathematical Psychology Vol 50(4) Aug 2006, 421-425.
- Tanaka, Y., & England, G. W. (1972). Psychology in Japan: Annual Review of Psychology 1972, 695-732.
- Taylor, D. A. (1975). Mathematical Psychology: What Have We Accomplished? : PsycCRITIQUES Vol 20 (6), Jun, 1975.
- Thomas, R. D. (1996). Separability and independence of dimensions within the same-different judgment task: Journal of Mathematical Psychology Vol 40(4) Dec 1996, 318-341.
- Thumin, F. J., & Barclay, A. G. (2002). Philip Hunter DuBois (1903-1998): Obituary: American Psychologist Vol 57(5) May 2002, 368.
- Tinker, M. A. (1944). Review of Lewin's Topological and Vector Psychology: Journal of Educational Psychology Vol 35(2) Feb 1944, 125-126.
- Townsend, J. T. (1990). Lefebvre's human reflexion and its scientific acceptance in psychology. New York, NY: Peter Lang Publishing.
- Townsend, J. T., & Nozawa, G. (1995). Spatio-temporal properties of elementary perception: An investigation of parallel, serial, and coactive theories: Journal of Mathematical Psychology Vol 39(4) Dec 1995, 321-359.
- Van Geert, P. (1993). Metabletics of the fig tree: Psychology and nonlinear dynamics: Nederlands Tijdschrift voor de Psychologie en haar Grensgebieden Vol 48(6) Dec 1993, 267-276.
- Varela, J. A. (1990). A general law for psychology: Revista Interamericana de Psicologia Vol 24(2) 1990, 121-137.
- Vigo, R. (2006). A note on the complexity of Boolean concepts: Journal of Mathematical Psychology Vol 50(5) Oct 2006, 501-510.
- Vigo, R. (2009a). Categorical invariance and structural complexity in human concept learning: Journal of Mathematical Psychology Vol 53(4) Aug 2009, 203-221.
- Vigo, R. (2009b). Modal Similarity. Journal of Experimental and Theoretical Artificial Intelligence. DOI: 10.1080/09528130802113422
- Wackermann, J. (2006). On additivity of duration reproduction functions: Journal of Mathematical Psychology Vol 50(5) Oct 2006, 495-500.
- Wakker, P. (1991). Additive representations on rank-ordered sets: I. The algebraic approach: Journal of Mathematical Psychology Vol 35(4) Dec 1991, 501-531.
- Wang, T. (1998). Weights that maximize reliability under a congeneric model: Applied Psychological Measurement Vol 22(2) Jun 1998, 179-187.
- Wheeler, H. (1990). A reflexional model of the mind's hermeneutic processes. New York, NY: Peter Lang Publishing.
- Wheeler, H. (1990). The structure of human reflexion: The reflexional psychology of Vladimir Lefebvre. New York, NY: Peter Lang Publishing.
- Wille, U. (1997). The role of synthetic geometry in representational measurement theory: Journal of Mathematical Psychology Vol 41(1) Mar 1997, 71-78.
- Woltz, D. J., & Shute, V. J. (1995). Time course of forgetting exhibited in repetition priming of semantic comparisons: American Journal of Psychology 108(4) Win 1995, 499-525.
- Yellott, J. I., Jr. (1971). What's (nu) in Math Psych? : PsycCRITIQUES Vol 16 (10), Oct, 1971.
- Yoshino, R. (1989). On some history and the future development of axiomatic measurement theory: Japanese Psychological Review Vol 32(2) 1989, 119-135.
- Zajonc, R. B. (1990). Interpersonal affiliation and the golden section. New York, NY: Peter Lang Publishing.
- Zaus, M. (1987). Hybrid adaptive methods. New York, NY: Elsevier Science.
- Zbrodoff, N. J., & Logan, G. D. (2005). What everyone finds: The problem-size effect. New York, NY: Psychology Press.
- Zhang, J. (2004). Binary choice, subset choice, random utility, and ranking: A unified perspective using the permutahedron: Journal of Mathematical Psychology Vol 48(2) Apr 2004, 107-134.
- Zhang, J. (2004). Dual scaling of comparison and reference stimuli in multi-dimensional psychological space: Journal of Mathematical Psychology Vol 48(6) Dec 2004, 409-412.
- Zhuravlev, G. E. (1976). Towards the definition of mathematical psychology: Voprosy Psychologii No 2 Mar-Apr 1976, 22-31.

## External links

- Journal of Mathematical Psychology
- British Journal of Mathematical and Statistical Psychology
- Society for Mathematical Psychology
- European Mathematical Psychology Group
- Online tutorials on Mathematical Psychology from the Open Distance Learning initiative of the University of Bonn.

This page uses Creative Commons Licensed content from Wikipedia (view authors). |