Митина Ольга Валентиновна Факультет психологии МГУ им. М.В.Ломоносова

1. MATHEMATICAL METHODS IN PSYCHOSEMANTICS МАТЕМАТИЧЕСКИЕ МЕТОДЫ В ПСИХОСЕМАНТИКЕ Митина Ольга Валентиновна Факультет психологии МГУ им. М.В.Ломоносова Mitina Olga Moscow State University Department of Psychology

2. Main ideas and conceptions about psychosemantics 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 fabricand personal senses and mediates the processes of perception, thinking, memory, decision-making, etc.

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. • 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.

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). • 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

6. The Place of Psychosemanticsin Cognitive Science

7. Charles E. Osgood (1916-1991) Alexander R. Luria (1902-1977) Alexei N. Leontiev (1904-1979) George Kelly (1905-1967) Lev S. Vygotsky (1896-1934) Soviet and Russian Psychology American Cognitive Psychology PSYCHOSEMANTICS ElenaYu.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 Philosophy Psychosemantics Linguistics Psychology Artificial Intelligence Anthropology ______ Strong interdisciplinary ideas _ _ _ _ Weak interdisciplinary ideas Neuroscience

10. The percentage of sites concerning the cognitive sciences among all sites

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 A1, …AM and each of them is “scaled" by a “subject" in the experiment. So the researcher has an opportunity to ascribe to each Aj 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 basic method of experimental psychosemantics The reconstruction of subjective semantic spaces that provide a model representation of the categorical structures of individual and social consciousness

13. The semantic space is • 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

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

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

16. Experimental psychosemantics • Fields of application in basic and applied research • 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 • Individual and • social consciousness • Applied research of individual consciousness with the purpose of • Psychodiagnostics • Psychotherapy • Applied research of social consciousness • Cross-cultural psychology • Political psychology • Psychology of advertising • Methods of psychosemantics as projective methods of diagnostics of consciousness

18. Methods of experimental psychosemantics • Osgood’s Semantic Differential • Verbal • Nonverbal • Kelly’s Repertory Grids (personal constructs) • Subjective scaling • Associative experiment • Linguistic methods • Content-analysis • Semantic networks’ construction • Narrative analysis • Discourse analysis • Luria's Semantic Radical • Indirect methods • Miller’s free classification • Petrenko's Multiple identification • 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 resultof empirical study • Subjects’ Interviews • Texts’ Analysis • 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. Arising mathematical problems • Geometrical representations • Dimension’s Decreasing • Classification • Pattern Recognition • Interpolation and Extrapolation • Spatial and time expansion of the SS • Expansion from discrete to continuous model

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

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

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

26. Main problems

27. General problems of multivariate statistics • Ambiguity of the "objective" statistically tested decision • Permissibility of "a subjective arbitrariness " during interpretation of possible decisions • Absence of strict mathematical verifying criteria • 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? • 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) • "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 • 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. • Collapsing Across Modes • Separate Analyses

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

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

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

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

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

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

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

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

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

41. Why we useThree-mode analysis • The importance of preserving a two-mode structure of a questionnaire • 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 • Weight subject analysis • Three-mode factor analysis

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

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

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

48. MTMM Model in SEM Methods Traits A1 A1=a1*A1+mA1 *M1+EA1 (M1, M2)=* A M1 A2 A2=a2*A1+mA2 *M2+EA2 (M1, M3)=* A3=a3*A1+mA3 *M3+EA3 (M2, M3)=* A3 B1 B1=b1*B1+mB1 *M1+EB1 (A, B)=* B M2 B2 B2=b2*B1+mB2 *M2+EB2 (A, C)=* B3=b3*B1+mB3 *M3+EB3 B3 (B, C)=* C1 C1=c1*C1+mC1 *M1+EC1 C2=c2*C1+mC2 *M2+EC2 C M3 C2 C3=c3*C1+mC3 *M3+EC3 C3

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

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