Resilience Constructions: How to Make the Differences Between Theoretical Concepts Visible?

Abstract

The concept of resilience has performed an amazing career. Starting out in some selected disciplines, such as psychology and ecology, it has been applied in a vast variety of disciplines including natural sciences, humanities, and social sciences. Resilience deals with the characteristics of individuals, units—more abstractly: entities—that enable them to not only maintain their identity in face of unusual or critical situations, but to potentially even emerge strengthened from such stressful situations.

Appendix

List of projects from the research consortium ForChange (see Böschen et al. 2017, p. 227)

Topic	Question
Background discipline	Which discipline(s) is (are) the basis for your own work (regarding prior assumptions and methods?	A1
Research focus and research question	Which central questions (tasks) are to be answered by resilience analysis? Why should resilience of an entity by analysed?	B1
Examined resilience entities (which system/object/entity does resilience refer to?)	Which system (or which entity/which object) does the resilience refer to?	C1
	In what or against which influences/factors/etc. must the entity be resilient?	C2
	Who are central actors/elements/functions?	C3
	Which role/task/function do these have in their system (their entity)?	C4
1st and 2nd order resilience	What kind of differentiation between 1st and 2nd order resilience is sensible in the scope of this project?	D1
	If so, please specify the level in the following questions, or state when the answer is about 1st or 2nd order resiliences.	D2
Time	What is the relevant time horizon for resilience analysis? (estimate if necessary)	E1
Risks, Uncertainties	Which risks/uncertainties influence resilience (of the entity)?	F1
	Can these be measured and evaluated, and how?	F2
	How can they be dealt with?	F3
Thresholds	What relevant system-internal/entity-internal thresholds (bifurcation points) or sensitive balances are there and what are they made of? Are these developments reversible?	G1
	Which attracting conditions (‘attractor,’ ‘Basin of Attraction;’ conditions that require a much higher effort to change) are there?	G2
	Which thresholds lead to total loss of resilience and/or identity (irreversibility) of the examined entity?	G3
	Can these be measured, how and according to which parameters?	G4
	How robust is the entity regarding changes to certain parameters?	G5
	Are there important path dependencies or any other relevant historical observations on tipping points?	G6
Knowledge of the actors regarding examined systems and their dynamics	What knowledge do the central actors/elements/functions have?	H1
	How does the present knowledge relate to that which is actually necessary or applied?	H2
	How is knowledge distributed (also within these actors) and which structures are there for the information flow?	H3
	What role do which communication processes play to spread knowledge and the flow of information?	H4
Driving moments of the actors	What drives the actors/elements/functions? Which values and leading images do these have (implicit/explicit if applicable)?	I1
	What standards and indicators (as operationalisation of the values and leading images) influence the actions of the actors?	I2
Options for action of the actors	Which options for action are there for which actor/element/function?	J1
	Which of these action options are actually implemented?	J2
	How can the action options or their implementation be improved?	J3
Diversity	How high is the diversity of functional groups/elements/actors/functions? How many G/E/A/F are there? How many action options do the G/E/A/F have and how diverse are they?	K1
	How does the existing diversity influence resilience? (Does it increase or reduce resilience?)	K2
	Can different groups/elements/actors take the same function in the system?	K3
	How does this redundancy influence resilience? (Does it increase or reduce resilience?)	K4
Types and functions of the institutions that prevail in the system	What are the most important institutions (within the system/entity)?	L1
	Is its performance appropriate for the task field/resilience of the relevant entity?	L2
	How may they need to be adjusted?	L3
Connectivity	Which other actors/entities/system components are relevant outside of the entity?	M1
	Which central interdependencies are there with them?	M2
	Where are there interdependencies between the scales and actors (if appl., divided into within and outside of the “system border”)?	M3
	Is there any specified structure between scales/actors/elements or functions (governance) and what is it made of?	M4
	How are the actors to be weighed regarding interdependencies and resilience?	M5
	Where is there a need for action? Where should interdependencies be increased or reduced?	M6
	What roles do communication and connectivity and interdependence play for each other?	M7
Adaptability	Which of the entity under observation or any important actors show adaptability (incremental adaptability)?	N1
	Which of the entity or any important actors show transformability (fundamental adaptability)?	N2
	Which of the entity or any important actors show persistence (toughness/self-preservation/robustness)?	N3
Normative aspects of resilience	When is resilience good for other entities or systems? (see 2nd order resilience)	O1
	What is the normative evaluation framework (laws, values, etc.) of resilience?	O2
	When should resilience be promoted in an entity?	O3

Annex for factor analysis:

This covariance matrix Σ of the reduced (demeaned) responses X was decomposed with

$$ \Sigma = \Gamma \varLambda \Gamma^{\rm T} $$

into a diagonal matrix Λ of the eigenvalues of Σ and the orthogonal matrix Γ of the eigenvectors Σ (see here and below: Hartung and Elpelt 2007). While matrix Λ contains the explained variances on the diagonal Γ, the matrix Γ shows the factor loadings; this means that it states how strongly a factor is determined by a group of questions.

The matrix decomposition based on the idea that the first factor explains the maximum possible variance of the data. Graphically, this means that the first factor is a (straight) line through the set of data points of the answers to explain the maximum variance. The second line then is orthogonal to the first one and explains the set of data points second-best. After having placed one line in each dimension and thus determined one factor each, the same number of factors as groups of question in the individual projects results; however, they are differently suitable for explaining the data and therefore have a different amount of information content (explained variance to total variance). This case results in the following image (Fig. 1).

Fig. 1

Share of explained variance by the factors of a principal component analysis (percent variability explained by principal components number n in blue, percent variability explained by the first n principal components in red)

According to the Kasier-Guttmann criterion, it is evident that the first 5 factors suffice to explain 86% of the answer variance (Dunteman 1989). In order to better interpret the first five factors, the factors can be transformed. Therefore, the factor axes are rotated further, while keeping the origin of the coordinates the same. This technically corresponds to multiplication of the matrix of factor loadings with a transformation matrix T:

$$ \Gamma^{*} = \Gamma {\rm T} $$

The criterion according to which the turn takes place is decisive for the interpretation. The Varimax is one of the most common procedures here (see Kaiser 1958), in which factor axes are orthogonally rotated until the variance of the squared charges per factors has reached its maximum. The loadings are the weights (shares) that individual groups of questions have in the respective factor. The process thus maximises the share of the respective groups of question.

In the last step, the factor variations in the four theory models are determined. For this, the variations of factors 1–5 for the individual projects Y (see Hartung and Elpelt 2007)

$$ {\text{Y}} = \Gamma^{\rm T} {\rm X} $$

are determined and then the arithmetic average is calculated across all projects that were assigned to a model in the cluster analysis at Böschen et al. (2017).