1. Митина Ольга Валентиновна Факультет психологии МГУ им. М.В.Ломоносова Mitina Olga Moscow State University Department of Psychology

2. PSYCHOSEMANTICS (from Greek semantikos - designating) –the area of psychology studying genesis, structure and functioning of the system of meanings, which forms the individual consciousness of the subject in the unity with sensory fabric and personal senses and mediates the processes of perception, thinking, memory, decision-making, etc. Main ideas and conceptions about psychosemantics

3. Psychosemantics investigates various forms of existence of meanings in individual and social consciousness (images, symbols, colors, symbolical actions, and also sign, verbal forms). It analyzes the influence of motivators and emotional conditions of the individual or collective subject on meanings’ system, which he or she or they have.

4. Psychosemantics studies general, differential and social psychological aspects of the process of categorization. Psychosemantics studies general, differential and social psychological aspects of the process of categorization. It reconstructs individual’s system of representations about the world by reconstructing the system of his individual meanings and personal senses. It reconstructs individual’s system of representations about the world by reconstructing the system of his individual meanings and personal senses. It reconstructs social and psychological systems of representation in groups. It reconstructs social and psychological systems of representation in groups.

5. Psychosemantic methods reconstruct the implicit pictures, the models of the world. They are inherent to the subject who may not realize them, but these pictures and models are actualized in a "a mode of use " (Petrenko). Psychosemantic methods reconstruct the implicit pictures, the models of the world. They are inherent to the subject who may not realize them, but these pictures and models are actualized in a "a mode of use " (Petrenko). In the course of the psychosemantic experiment the subject solves the problem of the explication of the picture of the world with the help of the researcher (a philosophical task!). In the course of the psychosemantic experiment the subject solves the problem of the explication of the picture of the world with the help of the researcher (a philosophical task!). In order to achieve it the researcher should dismember a complex data domain into elementary components, so that the respondent could explicate the representations about these units, and then from separate small pieces collect the whole picture - like a puzzle In order to achieve it the researcher should dismember a complex data domain into elementary components, so that the respondent could explicate the representations about these units, and then from separate small pieces collect the whole picture - like a puzzle

6. The Place of Psychosemantics in Cognitive Science

7. Soviet and Russian Psychology American Cognitive Psychology PSYCHOSEMANTICS Charles E. Osgood (1916-1991) George Kelly (1905-1967) Alexander R. Luria (1902-1977) Alexei N. Leontiev (1904-1979) Lev S. Vygotsky (1896-1934) Elena Yu. Artemieva (1940-1987) Alexander G. Shmelev Victor F. Petrenko

8. «Petrenko borrows American technological tools for the solution of traditional Russian psychological problems originating from L.S.Vygotsky». Michael Cole, 1993

9. Gardner’s Hexagon Connections among Cognitive sciences Psychology Artificial Intelligence Philosophy Linguistics Anthropology Neuroscience ______ Strong interdisciplinary ideas _ _ _ _ Weak interdisciplinary ideas

10. The percentage of sites concerning the cognitive sciences among all sites ConcerningRussianEnglish Personal Constructs Psyshology0.150.29 Semantic Differential0.020.03 Psychosemantics0.370.27

11. The formal scheme of the semantic experiment, which allows to build semantic spaces Let’s suppose that there is some final set of concepts A 1, …A M and each of them is “scaled" by a “subject" in the experiment. So the researcher has an opportunity to ascribe to each A j an n-dimensional vector. Its coordinates are values of the evaluations on n aspects of scaling. Then semantic space (SS) - is the multivariate metric space: vectors of the initial set of concepts are elements ("points") of such a space, and the dimension is equal to the number of the independent vectors, forming the basis of this space Let’s suppose that there is some final set of concepts A 1, …A M and each of them is “scaled" by a “subject" in the experiment. So the researcher has an opportunity to ascribe to each A j an n-dimensional vector. Its coordinates are values of the evaluations on n aspects of scaling. Then semantic space (SS) - is the multivariate metric space: vectors of the initial set of concepts are elements ("points") of such a space, and the dimension is equal to the number of the independent vectors, forming the basis of this space

12. The reconstruction of subjective semantic spaces that provide a model representation of the categorical structures of individual and social consciousness The reconstruction of subjective semantic spaces that provide a model representation of the categorical structures of individual and social consciousness The basic method of experimental psychosemantics

13. The semantic space is Geometrical representation of an image of the world Geometrical representation of an image of the world In the ideal!, it allows to formalize, study and model the formation and functioning of consciousness in its various forms and at various levels In the ideal!, it allows to formalize, study and model the formation and functioning of consciousness in its various forms and at various levels

14. Geometrical models, which are used Metric spaces Metric spaces Graphs Graphs Trees Trees

15. Arising problems: Problem of the model’s construction Problem of the model’s construction –Relevancy of parameterization –Choice of the metrics –Dimension’s Decreasing Problem of the model’s verification Problem of the model’s verification –Uniqueness of the solution –Reliability and stability, etc. Problems of visual representation Problems of visual representation

16. Experimental psychosemantics Fields of application in basic and applied research Fields of application in basic and applied research Methods Methods

17. Fields of application of psychosemantics in basic and applied research Theoretical problems from General psychology, connected with the research in the field of Theoretical problems from General psychology, connected with the research in the field of –Individual and –social consciousness Applied research of individual consciousness with the purpose of Applied research of individual consciousness with the purpose of –Psychodiagnostics – Psychotherapy Applied research of social consciousness Applied research of social consciousness –Cross-cultural psychology –Political psychology –Psychology of advertising Methods of psychosemantics as projective methods of diagnostics of consciousness Methods of psychosemantics as projective methods of diagnostics of consciousness

18. Methods of experimental psychosemantics Osgood’s Semantic Differential Osgood’s Semantic Differential –Verbal –Nonverbal Kelly’s Repertory Grids (personal constructs) Kelly’s Repertory Grids (personal constructs) Subjective scaling Subjective scaling Associative experiment Associative experiment Linguistic methods Linguistic methods –Content-analysis –Semantic networks’ construction –Narrative analysis –Discourse analysis Luria's Semantic Radical Luria's Semantic Radical Indirect methods Indirect methods Miller’s free classification Miller’s free classification Petrenko's Multiple identification Petrenko's Multiple identification Petrenko's motivation and attribution Petrenko's motivation and attribution

19. Mathematical (Quantitative) methods of data analysis, used in experimental psychosemantics

20. Objects of the analysis - multivariate multidimensional files of the numerical data received as a result of empirical study Subjects’ Interviews Subjects’ Interviews Texts’ Analysis Texts’ Analysis Other sources of meanings Other sources of meanings Attribution, estimation, scaling, reconstruction of meanings, explication of emotional attitudes

21. Scheme of three-mode data Scales X Concepts X Subjects

22. Geometrical representations Geometrical representations Dimension’s Decreasing Dimension’s Decreasing Classification Classification Pattern Recognition Pattern Recognition Interpolation and Extrapolation Interpolation and Extrapolation –Spatial and time expansion of the SS –Expansion from discrete to continuous model Arising mathematical problems

23. One-dimensional statistics One-dimensional statistics Two-dimensional (multivariate) statistics Two-dimensional (multivariate) statistics Mathematical methods of texts’ analysis Mathematical methods of texts’ analysis Three-dimensional statistics Three-dimensional statistics Methods of nonlinear dynamic systems Methods of nonlinear dynamic systems Neural networks Neural networks Mathematical (Quantitative) methods of analysis data, used in experimental psychosemantics Traditional New

24. Descriptive Descriptive –Calculation of measures of central tendency and data scattering in estimations of the various stimulus given by various subjects in various situations Inductive Inductive Hypotheses’ testing about uniformity of various samples, interrelations of various features, influence of additional factors on estimations Hypotheses’ testing about uniformity of various samples, interrelations of various features, influence of additional factors on estimations Analysis of Semantic codes (E.J.Artemieva) Analysis of Semantic codes (E.J.Artemieva) One-dimensional statistics Raw (non compression) data analysis

25. Factor analysis Factor analysis Cluster analysis Cluster analysis Multivariate scaling Multivariate scaling Discriminate analysis Discriminate analysis Determinancy analysis Determinancy analysis Structural Equation Modeling Structural Equation Modeling Two-dimensional (multivariate) statistics Data compressing

26. Main problems

27. General problems of multivariate statistics Ambiguity of the "objective" statistically tested decision Ambiguity of the "objective" statistically tested decision Permissibility of "a subjective arbitrariness " during interpretation of possible decisions Permissibility of "a subjective arbitrariness " during interpretation of possible decisions Absence of strict mathematical verifying criteria Absence of strict mathematical verifying criteria Problem of adequacy of the empirical data (stability of interpretation) Problem of adequacy of the empirical data (stability of interpretation)

28. Specific problems of multivariate statistics in psychosemantics What is the nature of axes in semantic space? What is the nature of axes in semantic space? Does metric exist in semantic space? Does metric exist in semantic space? "Attempt of coordinate-metric modeling can lead to the unpredictable distortions and give no psychologically interpretive coordinates" (Shmelev, 1983, p. 18) "Attempt of coordinate-metric modeling can lead to the unpredictable distortions and give no psychologically interpretive coordinates" (Shmelev, 1983, p. 18) "The technique of SD application with the subsequent factorization in order to construct SS could not remain the only technique of structuring attributive attitudes to stimulus." (Artemieva, 1999, p. 35). "The technique of SD application with the subsequent factorization in order to construct SS could not remain the only technique of structuring attributive attitudes to stimulus." (Artemieva, 1999, p. 35).

29. Mathematical methods of text’s analysis Measurement of contextual relations between concepts, their lexical or functional compatibility Measurement of contextual relations between concepts, their lexical or functional compatibility Allocation of statistical units of semantic fields and elements that form their periphery Allocation of statistical units of semantic fields and elements that form their periphery

30. ANALYSIS OF THREE- DIMENSIONAL DATA

31. Analyzing Three Modes with Two-Mode Procedures One may wish to analyze three modes with two-mode procedures. If so, there are several options available to the investigator. One may wish to analyze three modes with two-mode procedures. If so, there are several options available to the investigator. Collapsing Across Modes Collapsing Across Modes Separate Analyses Separate Analyses

32. Collapsing Across Modes Subjects by Scales (R and Q techniques) Subjects by Scales (R and Q techniques) Concepts by Scales (R and Q techniques) Concepts by Scales (R and Q techniques)

33. Subjects by Scales Subject 1 Subject 2 Subject K Concept 1 Concept 2 Concept I Scale 1 Scale J

34. Subject 1 Subject 2 Subject K Scale 1 Scale J Concept 1Concept 2 Concept I Concepts by Scales

35. Separate Analyses Subjects by Scales – Separate Concepts Subjects by Scales – Separate Concepts Concepts by Scales – Separate Subjects Concepts by Scales – Separate Subjects “Stringing Out” “Stringing Out”

36. Subjects by Scales – Separate Concepts Subject 1 Subject 2 Subject K Scale 1 Scale J Concept 1 Concept 2 Concept I Comparison

37. Subject 1 Subject 2 Subject K Comparison Scale 1 Scale J Concepts by Scales – Separate Subjects Concept 1 Concept 2 Concept I

38. Data Averaging Averaging of raw data Averaging of raw data Averaging of correlation matrices Averaging of correlation matrices

39. “Stringing Out” Subject 1 Subject 2 Subject K Concept 1 Concept 2 Concept I Scale 1 Concept 1 Concept 2 Concept I Scale 2 Concept 1 Concept 2 Concept I Scale J IxJ variables

40. “Stringing Out” K cases (= Subjects) by K cases (= Subjects) by IxJ variables (Concepts x Scales) IxJ variables (Concepts x Scales) KxI cases (= Subjects x Concepts) by KxI cases (= Subjects x Concepts) by J variables (Scales) J variables (Scales)

41. Why we use Three-mode analysis The importance of preserving a two- mode structure of a questionnaire The importance of preserving a two- mode structure of a questionnaire To avoid the loss of information To avoid the loss of information Capability to make multivariate analysis using the information from all Concepts, Scales and Subjects simultaneously

42. Three-mode analysis Structural Equation Modeling Structural Equation Modeling Weight subject analysis Weight subject analysis Three-mode factor analysis Three-mode factor analysis

43. Structural Equation Modeling Multi-trait Multi Method (MTMM) Multi-trait Multi Method (MTMM) Repeated Measures techniques Repeated Measures techniques Multilevel analysis Multilevel analysis

44. Multitrait-Multimethod Matrix It was developed by Campbell and Fiske (1959) for assessing the construct validity of a set of measures in a study

45. Scheme of an individual MTMM matrix Methods Traits АВС Method 1 A1 A1 B1 B1 C1 C1 Method 2 A2 A2 B2 B2 C2 C2 Method 3 A3 A3 B3 B3 C3 C3

46. MTMM  SD Traits  Scales Traits  Scales Methods  Concepts Methods  Concepts

47. Structure of General MTMM Matrix (from William Trochim)

48. MTMM Model in SEM A1A1 A2A2 A3A3 A B1B1 B2B2 B3B3 B C1C1 C2C2 C3C3 C A 1 =a 1 *A 1 +m A1 *M 1 +E A1 (M 1, M 2 )=* (M 1, M 3 )=* (M 2, M 3 )=* M1M1 M2M2 M3M3 TraitsMethods A 2 =a 2 *A 1 +m A2 *M 2 +E A2 A 3 =a 3 *A 1 +m A3 *M 3 +E A3 B 1 =b 1 *B 1 +m B1 *M 1 +E B1 B 2 =b 2 *B 1 +m B2 *M 2 +E B2 B 3 =b 3 *B 1 +m B3 *M 3 +E B3 C 1 =c 1 *C 1 +m C1 *M 1 +E C1 C 2 =c 2 *C 1 +m C2 *M 2 +E C2 C 3 =c 3 *C 1 +m C3 *M 3 +E C3 (A, B)=* (A, C)=* (B, C)=*

49. Repeated Measures techniques Autoregressive modeling Autoregressive modeling Latent curve modeling (LCM) Latent curve modeling (LCM) Concepts represent time periods (e.g. years of life, dates of the history of the country) Concepts represent time periods (e.g. years of life, dates of the history of the country) Or Concepts can be ordered by another parameter Or Concepts can be ordered by another parameter

50. Multilevel analysis Concepts x Scales – the first level; Subjects – the second level Concepts x Scales – the first level; Subjects – the second level Subjects x Scales – the first level; Concepts – the second level Subjects x Scales – the first level; Concepts – the second level

51. Weight subject analysis “Stringing out” Subjects by “Stringing out” Subjects by Concepts x Scales Concepts x Scales Q-technique Q-technique

52. Subjects’ cluster 1 Subjects’ cluster 2 Subjects’ cluster R Comparison Scale 1 Scale J Concepts by Scales – Separate Subjects’ clusters Concept 1 Concept 2 Concept I

53. Three mode factor analysis Parallel factor analysis (PARAFAC) /Canonical decomposition (CANDECOMP) – CP- model Parallel factor analysis (PARAFAC) /Canonical decomposition (CANDECOMP) – CP- model Tucker model Tucker model Three-mode company Three-mode company –Pieter Kroonenberg –3WAYPACK Software –Related literature and references –http://three-mode.leidenuniv.nl

54. CP-model R.A. Harshman, Foundations of the PARAFAC procedure: Model and conditions for an 'explanatory' multi-mode factor analysis. UCLA Working Papers in phonetics, 1970. R.A. Harshman, Foundations of the PARAFAC procedure: Model and conditions for an 'explanatory' multi-mode factor analysis. UCLA Working Papers in phonetics, 1970. J.D. Carroll and J. Chang, Analysis of individual differences in multidimensional scaling via an N- way generalization of "Eckart-Young" decomposition. Psychometrika, 35 (1970) 283. J.D. Carroll and J. Chang, Analysis of individual differences in multidimensional scaling via an N- way generalization of "Eckart-Young" decomposition. Psychometrika, 35 (1970) 283. R. Bro, PARAFAC. Tutorial & applications. Chemometrics Group, Food Technology. Royal Veterinary & Agricultural University. 1996. R. Bro, PARAFAC. Tutorial & applications. Chemometrics Group, Food Technology. Royal Veterinary & Agricultural University. 1996.

55. Tucker model Tucker, L. R. (1964). The extension of factor analysis to three-dimensional matrices. In H. Gulliksen & N. Frederiksen (Eds.), Contributions to mathematical psychology. Tucker, L. R. (1964). The extension of factor analysis to three-dimensional matrices. In H. Gulliksen & N. Frederiksen (Eds.), Contributions to mathematical psychology. Tucker, L. R. (1966). Some mathematical notes on three-mode factor analysis. Psychometrika, 31, 279-311. Tucker, L. R. (1966). Some mathematical notes on three-mode factor analysis. Psychometrika, 31, 279-311.

56. Natural extensions of two-way models Standard Principal component analysis (PCA) - bilinear mode Standard Principal component analysis (PCA) - bilinear mode CP-model: CP-model: Tucker-model: Tucker-model:  Each mode has the same number of components  Each mode can have different number of components G – core matrix

57. Graphical representation CP-model CP-model Tucker-model Tucker-model =

58. For studying processes, development, changes, transformations For studying processes, development, changes, transformations Nonlinear Dynamic Systems Methods

59. Two Lines Of Development of Mathematical Modeling In Psychosemantics «Rigorous» modeling, «Rigorous» modeling, leads to mathematical improving and developing of the procedures of constructing SP, search of formal ways to verify and testify models. «Mild» modeling, «Mild» modeling, Postulates existence of meanings’ structures with final exactness; models are testified during experiments.

60. Problems Low level of mathematical knowledge among psychologists Low level of mathematical knowledge among psychologists Absence of quantitative laws (as it is in physics, chemistry) Absence of quantitative laws (as it is in physics, chemistry) Necessity of multidimensional generalization of Freshener's task (application of tensor analysis) Necessity of multidimensional generalization of Freshener's task (application of tensor analysis) Necessity to go from “pictures” (cuts of SP) toward “movies” (dynamic processes of SP functioning) Necessity to go from “pictures” (cuts of SP) toward “movies” (dynamic processes of SP functioning)

61. Conclusions It is impossible to reduce psychosemantics to one or even to several mathematical methods used for psychosemantic data analysis. It is impossible to reduce psychosemantics to one or even to several mathematical methods used for psychosemantic data analysis. There are no specific mathematical methods which can be used only for analyzing psychosemantic data. There are no specific mathematical methods which can be used only for analyzing psychosemantic data. There are no specific restrictions which could come from psychosemantic theory on using these or those mathematical methods. There are no specific restrictions which could come from psychosemantic theory on using these or those mathematical methods. Try! Try!