C ognitive Maps

1. CognitiveMaps I would like to acknowledge Emel Aktaş who has greatinfluence on the organization of these slides

2. Introduction • Cognitive mapping is the task of mapping a person’s thinking about a problem or issue (Tolman, 1948). • A cognitive map is the representation of thinking about a problem that follows from the process of mapping. • 'Cognition' can be used to refer to the mental models, or belief systems, that people use to perceive, contextualize, simplify, and make sense of otherwise complex problems. • Cognitive maps have been studied in various fields of science, such as • psychology, planning, geography and management.

3. Definition • Cognitive maps are cause-effect networks, with nodes representing concepts articulated by individuals, and directional linkages capturing causal dependencies (Srinivas and Shekar, 1997). • Cognitive maps provide graphical descriptions of unique ways in which individuals view a particular domain (Axelrod, 1976; Eden, 1990).

4. Usage • Network-based representations of beliefs occupy an important place among the various schemes of knowledge (or human belief) representation. • Some of the popular network-based formalisms that have occupied key roles in representing beliefs and capturing causality are: • Cognitive Maps (Axelrod, 1976) • Belief Networks (Pearl, 1988) • Qualitative Probabilistic Networks (Wellman, 1990)

5. Causal map • The term “cognitive map” has been used to describe several forms of diagrammatic representation of an individual’s cognitions. • Causal map is one such form of cognitive maps which are essentially network representation of beliefs of individuals. • The networks have nodes representing concepts, and arcs representing directional relationships between these nodes.

6. Causal map • The maps are a network of nodes and arrows as links (a particular type of ‘directed graph’ (Harary et al., 1965; Harary, 1972), where the direction of the arrow implies believed causality. • Thus, cognitive maps are also known as ‘cause maps’ or ‘causal maps’. • When they are constructed by a group, they represent the cognition of the group rather than an individual. • The formalisms for cause maps will be the same as those for cognitive maps.

7. Mapping • Cognitive maps are usually derived through interviews, so they represent the subjective world of the interviewee. • Cognitive mapping is a formal modeling technique with rules for its development. • The formal basis for cognitive maps derives from personal construct theory (Kelly, 1955) which proposes an understanding of how humans ‘‘make sense of’’ their world by seeking to manage and control it.

8. Representation • For representational purposes a cognitive map is usually drawn as short pieces of text linked with unidirectional arrows to link them. • In the general case, a statement at the tail of an arrow is taken to cause, or influence, the statement at the arrowhead. • Cognitive maps can be derived by questionnaire survey, documentary coding and/or interviews.

9. Representation • In cognitive mapping concepts (nodes) are connected to the others by incoming or outgoing arrows. • When there is a negative relationship between concepts a minus sign is attached to the arrow. • For positive relationships plus sign may or may not be attached. • This representation is also referredas signed directed graph.

10. Heads and tails • Typically a node which has no implication (outgoing arrows) is referred to as a “head”, and a node which has no in-arrows is referred to as a “tail”. • The node which has the highest total of incoming and outgoing arrows is the most central element of the map.

11. Example(Ulengin, Topcu, Onsel, 2001) head Contribution to social improvement central - Damage on the inhabitants of the surrounding area by crossing Damage to the historical texture of the region - Construction time - Possibility of increasing employment through creating jobs Suitability for the transportation policy Cost of nationalization Facility in constructing (the topographic structure of the crossing area and the surrounding land, etc) Suitability for urban, regional and national progress plans Financial damage in case of accidents during operation tail

12. Heads and tails • Heads will usually be “goal” type statements: expressions of desired or not-desired outcomes, • Tails will be “options”. • When goals are expressed as not-desired outcomes, sometimes indicating disasters to be avoided at all costs, they are referred to as “negative-goals”. • Usually the map will contain more goal statements than those shown by heads, and more options than those shown by tails.

13. Structural properties • When a cognitive map is pictured in graph form it is then relatively easy to see how each of the concepts and causal relationships relate to each other, and to see the overall structure of the whole set of portrayed assertions’’ (Axelrod, 1976).

14. Problem/issue complexity • Both cognitive scientists and organizational scientists have been fond of simple analyses of cognitive maps. • These analyses are supposed to indicate the central features of a directed graph. • The first of these simple analyses explores the total number of nodes and the total number of arrows; • The second is concerned with “cognitive centrality” of particular nodes.

15. The extent of the map • The more nodes (or concepts) are there in a map, the more complex is the map and the issue. • The map, as model, acts as a device for establishing a mutual understanding of the issue. • The number of concepts elicited during an interview is dependent upon the length of the interview and the skills of the interviewer.

16. The complexity of the map as a network • An alternative analysis of issue complexity is to determine the ratio of arrows to concepts. A higher ratio indicates a densely connected map and supposedly a higher level of complexity. • Ratios of 1.15 to 1.20 is fine for maps elicited from interviews.

17. Representation • Graph • Helps to see the causal relationships between variables better • Matrix • Allows mathematical analysis in en effective way.

18. Example: How can we motivate employees? • Variables • Motivation • Salaries • Problems in the work environment • Good attitude of the employer • Good attitude of the colleagues • Carreer possibilities

19. Causal relationships between the variables • positive (+) salary motivation • negative (-) problemsin the work environment motivation • no relationship attitude of colleagues salary –

20. Determination of the causal relationships • Construction of a square matrix including all concepts • Determination of the causal relationships by pairwise comparisons

21. mtv. sal. env. emp. col. car. mtv. 0 0 0 0 0 0 sal. + 0 0 0 0 0 env. - 0 0 0 0 0 emp. + 0 - 0 0 + col. + 0 0 0 0 0 car. + 0 0 0 0 0 How can we motivate employees?

22. How can we motivate employees? sal. + emp. + mtv. - env. + + + car. col.

23. Construction of the Group Cognitive Map • Gathering a list of related concepts about the issue on hand from different persons • Preparing a collective list of concepts • Persons’ pairwise comparisons to reveal the relationships between the concepts • Construction of personal cognitive maps • Aggregating personal cognitive maps • Single number of experts • Taking experts’ opinions again about the doubtful relations

24. Size • Usually cognitive maps of problem situations are reasonably large–over 100 nodes on the map.

25. MatrixAlgebra • ValencyMatrix • Centrality • ReachabilityMatrix

26. ValencyMatrix • The adjacency matrix • V isa square matrix of n*n, where n is the total number of concept variables • Entry displays the directeffect ofthe column variable onthe row variable • The valency matrix indicates only direct relations between concept variables, that is, concept linkage paths of length 1 poc Immigr’ntothecity Population of thecity + ic +1

27. Centrality • Therowsum of theabsolutevalues of theelements of V forrowigivestheoutdegree (od) of variablei. • Thecolumnsum of theabsolutevalues of theelements of V forcolumnigivestheindegree (id) of variablei. • Thesum of odiand idigivesthetotal degree of i (tdi) which is a usefuloperationalmeasureof thatvariable’scognitivecentrality in theopinionstructure of theexperts

28. Şehirdeki insan sayısı Şehire göç Modernizasyon Sağlık faaliyetleri – Hastalık sayısı Çöp miktarı yoğunluğu – Bakteri yoğunluğu – Indirecteffect Vijn: forthepath of lengthn, indirect effect of variablei on variablej Vsis,sis3=1 (loopexists) Vsis,hs3=0 (twoalternativepaths)

29. Indirecteffect Reachability of variable i on variable j j i Vi,j2 = +3 (Three paths +) For the path of length 2, the cumulative indirect effects of variable i on variable j Vi,j2 = +1 (Two paths +, one path -) Vi,j2 = -1 (Two paths -, one path +) Vi,j2 = -3 (Three paths -)

30. ReachabilityMatrix • R reflectstheexistence of indirectrelations • Iftheadjacencymatrixcontains no feedbackloops, thecumulativeindirecteffects(R) arecalculated as: R = V + V2 ... + Vn-1 • Thesumof theabsolutevaluesforrowi of R showsthe total number of variablesreachablefromvariablei • Thesum of theabsolutevaluesforcolumni of R showsthe total number of variablesreachingvariablei

31. Satış fiyatını arttırma Pazar payı – Satış hacmi + Reklam yapma + + Kar + – Kaliteli ürün üretme Üretim maliyeti Talep + – Fabrika verimliliği İşçi tatmini Ücret artışı + + Example

32. – – – Example Şehirdeki insan sayısı Şehire göç Modernizasyon Sağlık faaliyetleri Hastalık sayısı Çöp miktarı yoğunluğu Bakteri yoğunluğu