Network Analysis: Lecture 1. Sacha Epskamp

Transcription

1 : Lecture 1 University of Amsterdam Department of Psychological Methods

2 Who are you? What is your specialization? Why are you here? Are you familiar with the network perspective? How familiar are you with?

3 Denny Borsboom Claudia van Borkulo Jolanda Kossakowski

4 Date Subject Lecturer Start Due Tu 02/09 Introduction Th 04/09 Intro to Assignment 1 Tu 09/09 Correlational structures Th 11/09 qgraph workshop Assignment 2 Assignment 1 Tu 16/09 Network descriptives Th 18/09 Centrality in qgraph Assignment 3 Assignment 2 Tu 23/09 Causal networks Denny Borsboom Th 25/09 Practical Denny Borsboom Assignment 4 Assignment 3 Tu 30/09 Directed networks Claudia van Borkulo Th 02/10 Practical Claudia van Borkulo Assignment 5 Assignment 4 Tu 07/10 Undirected networks Th 09/10 Practical Assignment 6 & Final Project Assignment 5 Tu 14/10 Final project Th 16/10 Final project Assignment 6 Tu 21/10 Th 23/10 Fr 24/10 Final project presentations Final project presentations Final project report Assignments are due on 11:00, the final project report on 24:00

5 Assignments Assignments are made available during the practicals on Thursday The deadline for every assignment is the start of the next practical Assignments should be handed in on blackboard Most assignments contain an essay question These should be written as proper scientific reports Include reference list, correct APA formatting, etcetera These will be graded on writing quality in addition to content Assignments have to be written in English Assignment 6 will be significantly smaller than other assignments

6 Final Project Groups of 2 Choose a dataset Apply the methodology discussed in this course Apply the methods of week 5 and 6 to estimate network structures Apply the methodology discussed in week 3 Substantively interpret the results Conceptually interpret the meaning of network analysis on your dataset Write a 1500 word scientific report on your findings 10 minute presentations in the last week Creativity is rewarded! Detailed info to follow

7 Grading 50% Assignments 50% Final project Both must be at least 5.5

8 Network Models (2015) This course is not the same course as the Network Models course given by Lourens Waldorp Generally NM is a followup course to NA (NA is not required for NM) You are allowed to do both! NA teaches you to apply the network methodology to psychological data and NM teaches you a deeper understanding of graph theory More equations in NM and more pretty pictures in NA Some overlap, but not that much

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10 is the statistical programming language used throughout the esearch master programme: Multivariate Analysis Programming Skills: SEM and other statistical courses You could very well use it during research projects as well This course requires a basic understanding of ead data into Work with vectors, matrices and data frames Creating Indexing Use functions in, and consult their help pages Correlate data ead data into

11 If you don t already know : Install from Install Studio from this Thursday during practical ead the very short introduction to on blackboard A nice introduction to is also given at

12 Euler s problem

13 Euler s problem

14 Worry Insomnia MD Concentration Fatigue

21 Worry Insomnia Concentration Fatigue

22 Worry Insomnia Concentration Fatigue

23 Mutualism Van der Maas et al. (2006)

24 Psychology as a Disorders usually first diagnosed in infancy, childhood or adolescence Delirium, dementia, and amnesia and other cognitive disorders Mental disorders due to a general medical condition Substance related disorders Schizophrenia and other psychotic disorders Mood disorders Anxiety disorders Somatoform disorders Factitious disorders Dissociative disorders Sexual and gender identity disorders Eating disorders Sleep disorders Impulse control disorders not elsewhere classified Adjustment disorders Personality disorders Symptom is featured equally in multiple chapters Disorders usually first diagnosed in infancy, childhood or adolescence Delirium, dementia, and amnesia and other cognitive disorders Mental disorders due to a general medical condition Substance related disorders Schizophrenia and other psychotic disorders Mood disorders Anxiety disorders Somatoform disorders Factitious disorders Dissociative disorders Sexual and gender identity disorders Eating disorders Sleep disorders Impulse control disorders not elsewhere classified Adjustment disorders Personality disorders Symptom is featured equally in multiple chapters

25 What is a network? A network is a set of nodes connected by a set of edges Nodes are also called vertices Edges are also called links Networks are also called graphs

26 Node 1 Edge Node 2

27 What is a network? A network is a set of nodes connected by a set of edges A node represents an entity, this can be anything: People Cities Symptoms Psychological constructs An edge represents some connection between two nodes. Again, this can be anything: Friendship / contact Distance Causality Interaction

28 Anne is friends with Laura: Anne Friendship Laura

29 Anne is friends with Laura and oger, but Laura is not friends with oger: Anne oger Laura

30 Networks can be weighted Anne is better friends with met oger than Laura: Anne oger Laura

31 Weights can be signed Anne is friends with oger and Laura, but oger and Laura don t like each other at all! Anne oger Laura

32 Edge weights Weights can be positive or negative, and indicates the strength of an edge, with zero indicating no strength (identical to the absence of an edge) Nodes that are connected by a strong edge can be seen as close by or easily reachable from one to the other Sometimes an edge has a length rather than a weight This is a positive value indicating the distance between two nodes A length of indicates no edge A weight is often recoded to a length by taking the inverse of the absolute value of the weight

33 Networks can be directed Anne likes Laura, but Laura doesn t like Anne: Anne Laura

34 Edges can be weighted or unweighted A network with weighted edges is called a weighted graph Otherwise it is called an unweighted graph Edges can be directed or undirected If all edges are directed the network is called a directed graph If all edges are not directed the network is called an undirected graph Otherwise it is called a mixed graph

35 A A D Undirected Unweighted B D Undirected Weighted B C C A A D Directed Unweighted B D Directed Weighted B C C

36 A directed network with no cycles is called a Directed Acyclic Graph (DAG) A cycle means that you can not start at a node and encounter it again by following directed edges This includes no self-loops As we will see in later lectures, DAGs are very useful in that they represent a clear dependency structure between the nodes But, the assumption on acylicness is very strict and often not tenable

37 A A D Cyclic B D Acyclic B C C

38 Mathematical notation In mathematics, a graph G is considered an ordered pair of a set V of vertices (nodes) and a set E edges: 1 G = {V, E} V = {1, 2, 3} E = {(1, 2), (2, 3), (3, 1)} 3 2

39 Adjacency matrices Let V be the number of nodes. An adjacency matrix is a square V V matrix in which each element is 0 or 1. If there is a 1 in row i and column j it means there is an edge from node i to node j A 0 denotes that there is no edge Undirected networks are encoded with a symmetrical adjacency matrix

40 Adjacency matrices A =

41 Adjacency matrices A =

42 Weights Matrices An weights matrix is identical to an adjacency matrix except it encodes the weight of the edge A 0 still indicates no edge Higher absolute values indicate stronger edges Undirected networks are encoded with a symmetrical adjacency matrix

43 Weights matrices W =

44 Weights matrices W =

45 Edgelist Let E be the number of nodes. An edgelist is a E 2 matrix containing a row for each edge The first column contains the node of origin and the second column the node of destination In weighted networks, a third column indicates the edge weight

46 Edgelist 1 2 E =

47 Edgelist 1 2 E =

48 Edgelist E =

49 Edgelist E =

50 Interpreting Networks A network can be interpreted in different ways: As a model of interacting components Information can spread from node to node via edges As a causal model (weeks 4-5) As a predictive model (week 6)

51 Interacting components

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62 Friendship

63 Friendship

64 elationships

65 Sexual contacts

66 Networks can be simulated given sufficient information about a population:

67 If a real network can not be obtained an approximation can be simulated.

68 virus...

69 Generalized Anxiety: Chronic Anxiety Anxiety about more than one event Irritability No control of anxiety Muscle tension Sleep Disturbances Concentration problems estlessness Fatigue Major Depression: Depressed mood Loss of interest in pleasurable things Weight problems Self-reproach (thoughts of) suicide Sleep disturbances Concentration problems estlessness Fatigue

70 Generalized Anxiety: Chronic Anxiety Anxiety about more than one event Irritability No control of anxiety Muscle tension Sleep Disturbances Concentration problems estlessness Fatigue Major Depression: Depressed mood Loss of interest in pleasurable things Weight problems Self-reproach (thoughts of) suicide Sleep disturbances Concentration problems estlessness Fatigue

71 (Cramer, Waldorp, van der Maas, Borsboom, et al., 2010)

72 Disorders usually first diagnosed in infancy, childhood or adolescence Delirium, dementia, and amnesia and other cognitive disorders Mental disorders due to a general medical condition Substance related disorders Schizophrenia and other psychotic disorders Mood disorders Anxiety disorders Somatoform disorders Factitious disorders Dissociative disorders Sexual and gender identity disorders Eating disorders Sleep disorders Impulse control disorders not elsewhere classified Adjustment disorders Personality disorders Symptom is featured equally in multiple chapters Disorders usually first diagnosed in infancy, childhood or adolescence Delirium, dementia, and amnesia and other cognitive disorders Mental disorders due to a general medical condition Substance related disorders Schizophrenia and other psychotic disorders Mood disorders Anxiety disorders Somatoform disorders Factitious disorders Dissociative disorders Sexual and gender identity disorders Eating disorders Sleep disorders Impulse control disorders not elsewhere classified Adjustment disorders Personality disorders Symptom is featured equally in multiple chapters (Borsboom, Cramer, Schmittmann, Epskamp, & Waldorp, 2011)

73 0.7 Correlation Average Shortest Path Length MDE x DYS MDE x AGPH MDE x SOP MDE x SIP MDE x PD MDE x APD DYS X AGPH DYS X SOP DYS X SIP DYS X PD DYS X APD AGPH X SOP AGPH X SIP AGPH X PD AGPH X APD SOP X SIP SOP X PD SOP X APD SIP X PD SIP X APD PD X APD

74 For Thursday, read:, a Network Perspective The Network Takeover A (very) short introduction to

75 I Borsboom, D., Cramer, A. O., Schmittmann, V. D., Epskamp, S., & Waldorp, L. J. (2011). The small world of psychopathology. PloS one, 6(11), e Cramer, A. O., Waldorp, L. J., van der Maas, H. L., Borsboom, D., et al. (2010). : A network perspective. Behavioral and Brain Sciences, 33(2-3), Van der Maas, H. L. J., Dolan, C. V., Grasman,. P. P. P., Wicherts, J. M., Huizenga, H. M., & aijmakers, M. E. J. (2006). A dynamical model of general intelligence: the positive manifold of intelligence by mutualism. Psychological review, 113(4), 842.