- 1. Introduction to Epistemic Network Analysis Vitomir Kovanovic, University of South Australia #vkovanovic Vitomir.Kovanovic@unisa.edu.au 1
- 2. What is Epistemic Network Analysis (ENA) • Epistemic Network Analysis is a network-based method for analysing codified data. • Developed by Professor David Shaffer from the University of Wisconsin Madison (UWM) and his team. • There is a web interface and R package • http://epistemicnetwork.org 2
- 3. The original problem of ENA • Understand how people become professionals • Involves understanding of the ways important concepts –codes– interact together • The applications of ENA expanded far beyond epistemology domain • New term: Quantitative ethnography. • Can be used to understand how different codes co-occur. 3
- 4. What is Epistemology? Epistemology studies the nature of knowledge, justification, and the rationality of belief New term: quantitative ethnography 4
- 6. ENA in Education • Often used for understanding of student conversations and discussion messages. • Also used for analysis of interview data. 6
- 7. Key concepts in ENA • Codes: a set of concepts whose interactions we want to understand • Unit of analysis: objects for which we want to understand interactions between the codes • Stanza(Conversation): Units in which we measure code co- occurrence 7
- 8. How ENA works: Example dataset 8 • Units of analysis: Individual Students • Stanzas: Individual messages
- 9. How ENA works: Example dataset 9 • Codes: • Data • Technical Constraints • Performance Parameters • Client and Consultant Requests • Design Reasoning • Collaboration
- 10. How ENA works: Code co- occurrence matrix 10 • Code co-occurrence in stanzas is used to produce code co-occurrence matrix for each unit of analysis (i.e., person) Data Technical Constraints Performance Parameters Client and Consultant Requests Design Reasoning Collaboration Data / 120 80 323 52 32 Technical Constraints / 23 120 112 32 Performance Parameters / 17 28 152 Client and Consultant Requests / 21 68 Design Reasoning / 12 Collaboration /
- 11. How ENA works: Code co- occurrence matrix 11 • Code co-occurrence in stanzas is used to produce code co-occurrence matrix for each unit of analysis (i.e., person) C1 C2 C3 C4 C5 C6 C1 / 120 80 323 52 32 C2 / 23 120 112 32 C3 / 17 28 152 C4 / 21 68 C5 / 12 C6 /
- 12. How ENA works: Code co- occurrence matrix 12 • Code co-occurrence in stanzas is used to produce code co-occurrence matrix for each unit of analysis (i.e., person) C1 C2 C3 C4 C5 C6 C1 / 120 80 323 52 32 C2 / 23 120 112 32 C3 / 17 28 152 C4 / 21 68 C5 / 12 C6 /
- 13. How ENA works: Matrix to vector 13 • Co-occurrence matrices are “flattened out” into vectors of N(N-1)/2 elements 6*5/2=15 columns (dimensions) C1- C2 C1- C3 C1- C4 C1- C5 C1- C6 C2- C3 C2- C4 C2- C5 C2- C6 C3- C4 C3- C5 C3- C6 C4- C5 C4- C6 C5- C6 U1 120 80 323 52 32 23 120 112 32 17 28 152 21 68 12 C1 C2 C3 C4 C5 C6 C1 / 120 80 323 52 32 C2 / 23 120 112 32 C3 / 17 28 152 C4 / 21 68 C5 / 12 C6 /
- 14. How ENA works: Matrix to vector 14 • Co-occurrence matrices are “flattened out” into vectors of N(N-1)/2 elements 6*5/2=15 columns (dimensions) C1- C2 C1- C3 C1- C4 C1- C5 C1- C6 C2- C3 C2- C4 C2- C5 C2- C6 C3- C4 C3- C5 C3- C6 C4- C5 C4- C6 C5- C6 U1 120 80 323 52 32 23 120 112 32 17 28 152 21 68 12 C1 C2 C3 C4 C5 C6 C1 / 120 80 323 52 32 C2 / 23 120 112 32 C3 / 17 28 152 C4 / 21 68 C5 / 12 C6 /
- 15. How ENA works: Matrix to vector 15 • Co-occurrence matrices are “flattened out” into vectors of N(N-1)/2 elements 6*5/2=15 columns (dimensions) C1- C2 C1- C3 C1- C4 C1- C5 C1- C6 C2- C3 C2- C4 C2- C5 C2- C6 C3- C4 C3- C5 C3- C6 C4- C5 C4- C6 C5- C6 U1 120 80 323 52 32 23 120 112 32 17 28 152 21 68 12 C1 C2 C3 C4 C5 C6 C1 / 120 80 323 52 32 C2 / 23 120 112 32 C3 / 17 28 152 C4 / 21 68 C5 / 12 C6 /
- 16. How ENA works: Matrix to vector 16 • Co-occurrence matrices are “flattened out” into vectors of N(N-1)/2 elements 6*5/2=15 columns (dimensions) C1- C2 C1- C3 C1- C4 C1- C5 C1- C6 C2- C3 C2- C4 C2- C5 C2- C6 C3- C4 C3- C5 C3- C6 C4- C5 C4- C6 C5- C6 U1 120 80 323 52 32 23 120 112 32 17 28 152 21 68 12 C1 C2 C3 C4 C5 C6 C1 / 120 80 323 52 32 C2 / 23 120 112 32 C3 / 17 28 152 C4 / 21 68 C5 / 12 C6 /
- 17. How ENA works: Matrix to vector 17 • Co-occurrence matrices are “flattened out” into vectors of N(N-1)/2 elements 6*5/2=15 columns (dimensions) C1- C2 C1- C3 C1- C4 C1- C5 C1- C6 C2- C3 C2- C4 C2- C5 C2- C6 C3- C4 C3- C5 C3- C6 C4- C5 C4- C6 C5- C6 U1 120 80 323 52 32 23 120 112 32 17 28 152 21 68 12 C1 C2 C3 C4 C5 C6 C1 / 120 80 323 52 32 C2 / 23 120 112 32 C3 / 17 28 152 C4 / 21 68 C5 / 12 C6 /
- 18. How ENA works: Matrix to vector 18 • Co-occurrence matrices are “flattened out” into vectors of N(N-1)/2 elements 6*5/2=15 columns (dimensions) C1- C2 C1- C3 C1- C4 C1- C5 C1- C6 C2- C3 C2- C4 C2- C5 C2- C6 C3- C4 C3- C5 C3- C6 C4- C5 C4- C6 C5- C6 U1 120 80 323 52 32 23 120 112 32 17 28 152 21 68 12 C1 C2 C3 C4 C5 C6 C1 / 120 80 323 52 32 C2 / 23 120 112 32 C3 / 17 28 152 C4 / 21 68 C5 / 12 C6 /
- 19. How ENA works: Matrix to vector 19 • Co-occurrence matrices are converted to vectors and joined together to form Analytic space of N*(N-1)/2 elements C1- C2 C1- C3 C1- C4 C1- C5 C1- C6 C2- C3 C2- C4 C2- C5 C2- C6 C3- C4 C3- C5 C3- C6 C4- C5 C4- C6 C5- C6 U1 120 80 323 52 32 23 120 112 32 17 28 152 21 68 12 U2 U3 … … U20 32 125 112 52 32 17 128 211 54 36 63 85 109 276 42 • NOTE: Each vector is a point in a 15-dimensional space • EACH GRAPH IS A POINT
- 20. How ENA works: Matrix to vector 20 • Co-occurrence matrices are converted to vectors and joined together to form Analytic space of N*(N-1)/2 elements 1-2 1-3 1-4 1-5 1-6 2-3 2-4 2-5 2-6 3-4 3-5 3-6 4-5 4-6 5-6 U1 120 80 323 52 32 23 120 112 32 17 28 152 21 68 12 U2 U3 … … U20 32 125 112 52 32 17 128 211 54 36 63 85 109 276 42 • NOTE: Each vector is a point in a 15-dimensional space • EACH GRAPH IS A POINT
- 21. How ENA works: Singular Value Decomposition of Analytic Space 21 • Approximate N columns with a smaller number R of “composite columns” • The whole point is to be able to plot N dimensions on a 2D plot
- 22. How ENA works: Singular Value Decomposition of Analytic Space 22 • Approximate N columns with a smaller number R of “composite columns” • The whole point is to be able to plot N dimensions on a 2D plot m=1,000 students n=100 edges A=100,000 U = 1,000 x 1,000 = 1,000,000 VT= 100 x 100 = 10,000
- 23. How ENA works: Singular Value Decomposition of Analytic Space 23 • Approximate N columns with a smaller number R of “composite columns” • The whole point is to be able to plot N dimensions on a 2D plot m=1,000 students n=100 edges A=100,000
- 24. How ENA works: Singular Value Decomposition of Analytic Space 24 • Approximate N columns with a smaller number R of “composite columns” • The whole point is to be able to plot N dimensions on a 2D plot m=1,000 students n=100 edges A=100,000 r=2 (keep top two singular values) U=1,000 x 2 = 2,000 VT=2 x 100 = 200 Total=2,200
- 25. How ENA works: Singular Value Decomposition of Analytic Space 25 • Approximate N columns with a smaller number R of “composite columns” • The whole point is to be able to plot N dimensions on a 2D plot m=1,000 students n=100 edges A=100,000 r=2 (singular values) U=1,000 x 2 = 2,000 VT=2 x 100 = 200 Total=2,200 Latent factor scores (student 2D coordinates) Latent factor coefficients (code pair 2D coordinates)
- 26. Visualising SVD’ed Analytic Space: Projection space 26
- 27. Visualising individual graphs: ENA network models 27
- 28. Visualising individual graphs: ENA network models 28
- 29. Visualising individual graphs: ENA network models 29
- 30. Remarks on coding • Code values can be Boolean: 0 if code does not occurs, 1 if it does Integer: 0 if code does not occur, N if it does N times Fractional number: Value indicating “strength” or “association” of the code to the text • In case of binary values, co-occurrence is 1 if both codes occur • In case or integer or fractional numbers, co-occurrence score is the product if the individual scores. • Fractions useful for: LDA topic modelling: Each topic is a code, code value are topic associations to individual texts • Integers useful for: Word count analysis: Each word (category) is a code, co-occurrence value is the product of code scores. 30
- 31. Moving stanza • Stanza can be moving, specially useful for conversations where individual messages are too short 31
- 32. ENA Example 1: CoI + LDA E Ferreira, R., Kovanovic, V., Gasevic, D., & Rolim, V. (2018). Towards Combined Network and Text Analytics of Student Discourse in Online Discussions. In The 19th International Conference on Artificial Intelligence in Education. London, UK. • Understand the development of cognitive presence with respect to different course topics CoI process model, does not pay attention to course content • Examine the role of instructional intervention of role assignment 32
- 33. ENA Example 1: CoI + LDA • 1,747 messages from 6 course offers • Each message coded for the level of cognitive presence: Triggering Event Exploration Integration Resolution Other • Applied topic modelling to pick course topics Extracted topics were corresponding to course topics + one topic regarding logistics 33
- 34. Results: Projection graph all students 34
- 35. Results: Projection graph (intervention + control groups) 35 Control Intervention
- 36. Results: ENA network model for all students 36All students
- 37. Results: ENA network model for two student groups 37Control Intervention
- 39. ENA clusters
- 40. Topics per cluster Cluster 1 Cluster 2 Cluster 3 Cluster 4
- 41. Social centrality per ENA cluster
- 42. Recap • ENA works on codified data • We need to define Codes Units Stanzas • Unit’s co-occurrence matrices are converted to vectors • All unit’s merged to form Analytic space matrix • Analytic space is reduced to 2D with SVD • Plot units on the 2D plot • Plot codes on the 2D plot 42
- 43. Practical example • Data: download from http://bit.ly/enanie • Go to http://epistemicnetwork.org and create account 43