Fitting like a glove: New method for constructing networks

Fitting like a glove: New method for constructingnetworks from psychometric data

Claudia van Borkulo

University Medical Center GroningenUniversity of Amsterdam

Februari 13, 2014

Claudia van Borkulo New method for constructing networks 1 / 24

Outline

1 Typical psychopathology data

2 Psychological constructs as networks

3 New network estimation procedure: eLasso

4 R-package: IsingFit


Table of Contents






Typical data

◦ Item scores on questionnaires

◦ Example items concerning depression(from Beck Depression Inventory)

I do not feel sadI feel sadI am sad all the time and I can’t snap out of itI am so sad and unhappy that I can’t stand it

(from Inventory of Depressive Symptomatology)Falling Asleep:I never take longer than 30 minutes to fall asleepI take at least 30 minutes to fall asleep, less than half of the timeI take at least 30 minutes to fall asleep, more than half of the timeI take more than 60 minutes to fall asleep, less than half of the time


How is data analyzed?

◦ Commonly used to assess depression severityby generating total scoresinformation about individual symptoms is discarded

◦ Growing dissatisfaction with the non-specificity of major depression

◦ Many possible symptom constellations

◦ Latent class analyses: substantial heterogeneity in depressivesymptomatology

◦ Why not study depression on more fine-grained level?Surprisingly few studies do that



Bhar et al. (2008) Stewart & Harkness (2012)

Fournier et al. (2013)



◦ Possible option: inspect individual symptoms and how they relate toeach other

Associations between symptoms

◦ Small step to view associations as anetwork

◦ qgraph was very important for that ;-)


Table of Contents






Psychological constructs as networks of interacting parts

◦ View mental disorder as network of interacting symptoms

◦ New scientific field opens up: Network theory

◦ A lot of knowledge available (mathematics, physics)◦ Interesting measures of a network:

− Importance of single node (centrality measures, e.g., degree)− Network controllability (find smallest set of nodes whose control is

sufficient to fully control the system’s dynamics)


Psychological constructs as networks of interacting parts

◦ For psychology there is one big challenge

◦ Network structure for psychological constructs is unknown

◦ Compare to this network


Current network estimation

◦ Procedures to generate a network:

− Correlations− Partial correlations− Conditional independencies

◦ Problem with correlationsSpurious correlations


Current network estimation

◦ Problems with current network estimation proceduresHow to determine which connections are relevant?

− association is relevant if > .1− significance level


Table of Contents






New network estimation procedure: eLasso

Based on

◦ Ravikumar, Wainwright, & Lafferty (2010)− Ising model (well known in physics/mathematics) boils down to logistic

regressions− combines `1-regularized logistic regression with Extended Bayesian

Information Criterion (Chen & Chen, 2008)

◦ Foygel & Drton (2011)− showed that using EBIC renders networks that are asymptotically close

to true underlying network



The Ising model:

◦ variables can assume two states

◦ can be generalized to otherobjects in a network (voter,neuron, tree)

◦ objects/variables can interact,but only with direct neighbors

◦ Most essential part:neighborhood estimation

- - - + -+ + - - -- - + - -+ + + - -- + - + +



Estimation of neighborhood

◦ `1-regularized logistic regression

◦ lasso: least absolute shrinkage and selection operator (Tibshirani,1996)

◦ The ’lasso’ returns multiple sets of different neighbors

◦ ensures shrinkage of some regression coefficients

◦ puts other coefficients to zero

◦ results in an interpretable network structure



PΘ(x j | x\ j)=exp

[τ jx j + x j

∑k∈V\ j

β jkxk]

1+exp[τ j + ∑

k∈V\ j

β jkxk]

◦ L (θ | x)=P(x | θ)

◦ Given the data, what is the best set of regression coefficients (θ1, θ2,etc.)?

◦ Decision is based on extended BIC (EBIC)based on (log) likelihood

◦ Set with lowest EBIC fits best◦ Rule to construct final network:

If node A has node B in it’s set of neighbors AND node B has node A init’s set, than there is a connection (AND-rule)


Table of Contents






R-package: IsingFit

◦ Method is called eLasso*

◦ R-package IsingFit

◦ For binary variables

◦ For multiple independentobservations of variables(cross-sectional data)

* Van Borkulo, C.D., Borsboom, D., Epskamp, S., Blanken, T. F., Boschloo,L., Schoevers, R. A., & Waldorp, L. J. (2013). Fitting like a glove: Newmethodology for constructing networks from psychometric data.Manuscript in preparation.


R-package: IsingFit

Let’s do some R!


R-package: IsingFit


R-package: IsingFit


R-package: IsingFit

IsingFit is suitable for:◦ Basically any kind of psychological construct

Examples− Mental disorders (symptoms)− Attitudes (statements)− Math ability (different types of math questions)− Intelligence (different types of intelligence questions)− others?

◦ Future extensions:− continuous data− ordinal data− time series data


R-package: IsingFit

Thank you!

http://cran.r-project.org/web/packages/IsingFit/

[email protected]


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Fitting like a glove: New method for constructing networks