Section 3 Causal maps: a unifying idea
Social scientists and programme evaluators often use a particular kind of diagram to represent causal relationships: boxes joined by arrows, to show what causes what. In this post we revive the term “causal map” as a broad name for this kind of diagram. Causal maps can be found throughout a whole range of traditions, from strictly quantitative to thoroughly qualitative. This fact alone makes the concept interesting as a unifying idea.
Causal maps are not peripheral things. They are central to much research and evaluation: a way of expressing the main findings, what we really wanted to know: does X causally influence Y? Did B contribute to C? What else has to happen? How sure can we be?
In this post we will briefly look at some different, overlapping approaches (which we will call “paradigms”) for drawing and understanding different kinds of causal map. Some of these paradigms are well developed, such as those coming from fuzzy logic and causal statistics, some are less clearly defined, such as the idea of a “program theory” in evaluation; but, as causal maps, they all have a few key points in common.
This matters to us because we’d like our causal map app to be useful for people working with maps from a wide range of different paradigms.
A rough definition:
A causal map is a model of causal relationships, in the form of a directed graph in which the items (nodes, elements ) are linked by arrows, together with translation rules which tell us how to interpret the arrows, namely that an item with one or more arrows pointing to it is in some sense causally influenced by the item(s) at the start of those arrow(s).1
This definition says that a causal map comes with explicit or implied translation rules which let us go from it to a set of causal claims and back again. These rules are a bit like a “legend” at the side of the map. The key thing about the definition is that the fundamental translation rule is expressed at the level of the individual causal pieces, which we call “mini-maps”.
A (causal) mini-map is one item together with all the items directly pointing to it, i.e. directly influencing it.
The mini-map rule helps us translate “drought –> hunger” to the equivalent causal claim (“drought causally influences hunger”), and back again. Larger causal maps are built up from bunches of mini-maps.
Fig 1. A mini-map Fig 2. Another mini-mapDifferent kinds of causal maps can have radically different translation rules: what precise flavour of causation is meant? The causal arrow might mean “…completely determines…” or “…is sufficient for…”. Or arrows might have numbers associated with them, and the arrow might be interpreted as something like “…increases by a factor of .5 the probability of …”. In most causal maps which programme evaluators have to deal with, the meaning of these arrows can be mixed and unclear, often meaning just “… causally influences in some way …”
The elements within different kinds of causal map (like “drought”) differ correspondingly. In some of the cases above, the elements might be propositions like “drought happened”; in others, they are continuous variables; other kinds are possible too.
But a causal map’s translation rules have to be explicitly causal. As Pearl points out, a genuinely causal arrow can be understood as something like “if you do X, Y will happen (perhaps, with probability \(p\))”, whereas, for example, Bayesian belief networks are not causal maps because the arrows say “if you observe X, you will observe Y (perhaps with the probability \(p\))”. Causation is not correlation.
To make them useful, causal maps nearly always come with additional combination rules which tell us how we can piece together a larger map out of smaller ones, and how to understand it on the basis of our understanding of its constituent parts. We can use these rules for example to make deductions about maps or to derive a simpler version of a larger map. As both Realist theorists and the Pearlian school point out, our real-life knowledge is composed of relatively portable, transferrable small units like mini-maps.
For example, if we know that
drought –> hunger
and
hunger –> revolution
can we deduce
drought –> revolution?
If we are told to interpret “–>” as “completely determines”, this is arguably an acceptable conclusion; likewise with “may have some causal influence on”. But if we interpret it as “increases the probability of X by 50%”, this conclusion doesn’t work, because we are trying to describe a partial influence which we expect to attenuate as we go down the causal chain. Concretely, we’d then expect the influence of drought on hunger to be less than 50%.
So, the explicit or implicit rules which come with a causal map also help us to make deductions with maps.
3.1 Causal map paradigms
We don’t have to set up these kinds of rule for understanding causal arrows every time we draw a causal map. Instead, we make use of an established paradigm: we only need to say “this is a structural equation model” or “this is a fuzzy cognitive map”, and the rules are understood. A causal map paradigm is just a frequently-used set of rules for understanding and manipulating a whole genre of causal maps.
Particular kinds of causal map may have any number of additional properties and characteristics. For example, the arrows might include information about the degree of certainty we have in that causal link. And the corresponding mini-map rule and combination rules might help us to do deductions with that kind of information. For example, if we are only partially certain that X causes Y and only partially certain that Y causes Z, the rules should tell us that we are even less certain that X causes Z.
Many causal maps are not just timeless statements of connections; they also include factual information about how things actually are. For example, this mini-map:
The horse kicked me –> I screamed
probably contains not only the background information that horses kicking people makes them scream, but also the information that both things actually happened. We call these maps “propositional” because they also contain this kind of factual information.
3.2 Mini-maps with more than one influencing item
Many causal map paradigms assume that causal influences are always between a single cause and a single effect. This is a very useful simplification. But sometimes we need to take into account causal connections in which something is affected by sets of more than one influence. For example, what if we want to draw a causal map to show that you need both oxygen and a spark to cause a fire? This can’t be assembled from two separate diagrams:
We need a diagram in which “fire” has two different things pointing to it at once, and we need to note down how those two things interact, e.g. by writing AND where the arrows join.
This can’t be expressed like this:
3.3 Semi-formal definition of a causal map paradigm
A causal map paradigm is a set of rules for constructing and understanding causal maps. It should contain as a minimum:
A mini-map rule defining what counts as a “mini-map” within this paradigm (roughly, a “consequence” element with one or more “influence” elements pointing to it); it may have other attributes too like factual information about the actual state of things, or the strength of the influences, the amount of trust in the information, etc. The rule has two parts saying (syntax): any such mini-map counts as a causal map and (semantics): how to translate such a mini-map into a particular kind of causal claim, and back.
Combination rules showing how to build up larger maps. The rules each have two parts saying (syntax): mini-maps joined in such-and-such a way also count as causal maps and (semantics): what does the composite map mean in terms of the meanings of its elements?
There are some important combination rules for joining two mini-maps. These different ways of combining elementary maps into composite maps embody some interesting social science questions.
- joining two maps on a shared item (what counts as the same thing? is “hunger” according to one person’s report the same as “starvation” in another?)
- joining two maps on a shared consequence item (this is surprisingly difficult in the general case which includes problems of multi-causation or overdetermination). Many paradigms make the assumptions that different influences can in some sense just be added together, so that the influence of X on Z is always independent of the influence of Y on Z. But other paradigms (like perhaps QCA) specialise in combining influences which are not independent of one another
- joining two maps on a shared influence item (usually unproblematic)
- merging several co-terminal arrows from different maps into one (what does it mean when we have overlapping information from different sources about the same causal influence? how do we combine them if they agree or if they disagree?)
- whether or not to allow joining two mini-maps in such a way that a loop is created, and if so, what does this mean? Fuzzy Cognitive Maps deals with this kind of composite map.
Plus, individual paradigms will have their own rules about how to combine any additional information which they allow for (e.g. level of trust).
3.4 Hybrid sets of rules
In real life, programme evaluators often have to deal with maps set up with hybrid rules. We might have to combine, say, information from publications in the field with data from a randomised controlled trial and information from stakeholder interviews into a larger “programme theory”. In this case we might have to resort to a mixed toolbox containing a larger set of rules.
3.5 Causal multi-maps?
In the approaches listed above, the information underlying them can usually be considered to come from just one source: one book, or one experiment, or one survey, or one expert; or the question “what is the source for that” isn’t even raised at all. We can call these kinds of maps “causal mono-maps”. They are particularly interesting for us at Bath SDR because they are at the heart of the QuIP methodology. Our causal map app is specialised in dealing with them.
A causal multi-map is a kind of causal map in which information about the source of each causal link (or more generally of each mini-map with several influencing items) is firmly attached to it and taken very seriously. The rules for this kind of map need to take this information into account, as in the following example.
If the homoeopath tells us that the right potency of gold is a cause of a well functioning liver, and the doctor tells us that a well functioning liver is a cause of clean blood, does that mean we know that the right potency of gold is a cause of clean blood? No, we can’t necessarily deduce from:
H believes that X causally influences Y
plus
D believes that Y causally influences Z
to
X causally influences Z
..… and we can’t even necessarily deduce this:
Some people believe that X causally influences Z
There are lots of similar challenges in joining together fragments of causal information. If a reliable source tells us they are almost certain that the link between X and Y is strong, whereas a hundred less reliable sources tell us they believe that there is no such link, how do we combine that information?
Is there a plausible set of rules for amalgamating fragments of causal information? Can those rules be adapted to cope with the different kinds of paradigms mentioned above?
We haven’t found many formal approaches to this solve this problem directly (Markiczy and Goldberg (1995)).
The term “causal mapping” has often been used to acknowledge the possibility that causal information may comes from different sources and explicitly opens the challenge of how to meaningfully aggregate that information.
3.6 A brief overview of different causal map paradigms
3.6.1 Approaches already called “Causal Mapping”
There are a number of approaches which have been explicitly used the terms “causal maps” or “causal mapping” Laukkanen and Wang (2016),Laukkanen and Eriksson (2013),Bryson et al. (2004),Nadkarni and Shenoy (2004).
Causal mapping in this sense is loosely based on “Concept mapping”, which has itself been used widely in some areas of evaluation. A special edition Trochim (2017) 2017 presents it as a relatively standardized area with standard steps (preparation, generation, structuring, representation, interpretation and utilization).
“Causal (aka cognitive) mapping (CM) first emerged in political science (Axelrod, 1976) and organizational studies (Bougon et al., 1977) as an innovative method for operationalizing and analysing the causal knowledge and beliefs of social actors.” It is mainly used in project management.
These are amongst the few addressing problems of merging and aggregating maps from different sources
A rare and early exception is Markiczy and Goldberg (1995); they even derive a Distance Ratio method for measuring similarity between pairs of maps.
Scavarda et al Scavarda et al. (2006) discuss a method for creating a combining causal maps from multiple sources using a Delphi-like method. Their causal links have a default interpretation (if-then, although the meaning and restrictions of this are not further explored) and always have just one influence and one consequence variable. The method includes an algorithmic stage which uses hierarchical cluster analysis.
3.6.2 (Comparative) Cognitive Mapping
3.6.3 Theories of Change for a project or programme,
even (in a very restricted sense) Logical Frameworks
Some assume a sufficient connection, embedded in the mantras “if this then that” and “development hypothesis”.
3.6.4 Programme theories in theory-based evaluation
3.6.5 Fuzzy Cognitive Maps
3.6.6 Contribution analysis
3.6.7 Systems Diagrams
3.6.8 DAGs as promoted by Judea Pearl
Judea Pearl (Pearl 2000) and colleagues - mostly statistics-based, though the theory is generalised to cover non-parametric cases.
Different kinds of causal maps have been well studied by statisticians, and recently Judea Pearl and colleagues have made giant strides to showing their utility as part of an approach to statistics which is better adapted than traditional statistics to dealing directly with causality rather than only with correlation.
3.6.9 Structural Equation Models
3.6.10 Bayesian belief networks
probably not, see Pearl (1986)
3.6.11 (arguably) diagrams used in Realist Evaluation
3.6.12 (sometimes) diagrams used in Outcome Harvesting
3.6.13 Causal Maps as constructed in QuIP
3.6.14 Mental models
Moon et al. (2019) from the field of conservation, with a lot of emphasis on complexity and systems. Also ask about what respondents say should be the case. Use 1, 2, or 3 for strength.
Elicits maps of the same domain from different stakeholders and compare in a narrative way.
“The progressive emergence of a shared vision can lead to a revision of assumptions (double-loop learning) and exploration of underlying values and beliefs (triple-loop learning)”
This approach is only monocausal/additive; it does not allow for multiple, interacting influences on a downstream variable.
There is a focus on different individuals’ different maps. They can be elicited with interviews, by drawing cognitive maps, Bayesian belief networks.
3.6.15 Knowledge graphs, semantic networks
Sometimes the phrase “knowledge graph” is used for any representation of knowledge in the form of a graph. In that sense, our causal maps are knowledge graphs. See also “ontologies” in philosophy and computer science -– tension between formal and practical interests (e.g. Google’s own “knowledge graph”).
The term “semantic network” is used for networks in which there is a wide variety of types of relations, whereas a “knowledge graph” has a very restricted set of relations.
The task of calculating the values of downstream nodes is very similar to calculating downstream activity levels in a neural network. One difference is that in a neural network, the contributions of each parent neuron to a child neuron can be simply summed (and then usually transformed by a sigmoid-type function to bring the activity levels back in the range 0 to 1). In other words, there is a pre-engineered solution to the question of how to combine the influences.
3.6.16 NCA (Necessary Condition Analysis)
This is one of many approaches which are not in essence graphical (because they focus on individual causal combinations rather than constructing larger edifices from those combinations Dul (2016) .) However they do address some relevant issues.
3.6.17 Influence diagrams
3.6.18 Paradigms which include the aspect of belief
Modal logic of belief, Dempster-Shafer theory
3.6.19 “System Effects”
3.6.20 QuIP maps
The raw output of a QuIP-type coding exercise is a set of directed paths or arrows between a set of nodes or factors, in which the arrows might have additional attributes like respondent characteristics, question number / domain etc. One or more arrows B, maybe also C, D, ..… coming into a node E encode a causal claim about how B (and maybe C and D..…) influence E.
3.6.21 Maps of maps
There are causal maps which incorporate elements which are themselves embodiments of causal maps, as we need to do when trying to model stakeholder behaviour.
3.7 Summary
A causal map is a directed graph which is intended to model causal relationships, in which the items (nodes, elements) are linked by arrows which mean that the item at the start of the arrow causally influences the item at the end of the arrow. This is a broad definition which covers many different existing “paradigms” of causal modelling. In general, the individual causal connections in a causal map may be based on information from more than one source.
The causal map app is a tool which helps social scientists and programme evaluators to extract causal claims from texts (e.g. interview data) from different sources, and to combine and present it visually.
In most cases the model is literally drawn in the form of a network, but other ways of representing the same ideas are possible too, for example a set of narrative claims.↩