For some years, I’ve been partly involved in the Let’s Move It intervention project, which targeted dysfunctional physical activity and sedentary behaviour patterns of older adolescents, by affecting their school environment as well as social and psychological factors.
I held a talk at the closing seminar; it was live streamed and is available here (on stage starting from about 1:57:00 in the recording). But if you were there, or are otherwise interested in the slides I promised, they are now here.
For a demonstration of non-stationary processes (which I didn’t talk about but which are mentioned in these slides), check out this video and an experimental mini-MOOC I made. Another blog post touching on some of the issues is found here.
The gist: to avoid getting fooled by them, we need to name our simplifying assumptions when modeling social scientific data. I’m experimenting with this visual approach to delivering information to those who think modeling is boring; feedback and improvement suggestions very welcome! [Similar presentation with between-individual longitudinal physical activity networks, presented at the Finnish Health Psychology conference: here]
I’m not as smooth as those talking heads on the interweb, so you may want just the slides. Download by clicking on the image below or watch at SlideShare.
Note: Jan Vanhove thinks we shouldn’t become paranoid with model assumptions; check his related blog post here!
It was recently brought to my attention that there exist such things as time and context, the flow of which affects human affairs considerably. Then there was this Twitter conversation about what habits actually are. In this post, I try to make sense of how to view health behavioural habits from the perspective of dynamical systems / complexity theory. I mostly draw from this article.
Habits are integral to human behaviour, and arguably necessary to account for in intervention research 1–3. Gardner 1 proposes a definition of habit as not a behaviour but “a process by which a stimulus generates an impulse to act as a result of a learned stimulus-response association”. Processes being seldom stable for all eternity, a complex dynamical systems perspective would propose some consequences of this definition.
What does it mean, when a process—such as habit—is stable? One way of conceiving this is considering the period of stability as a particular state a system can be in, while being subject to change. Barrett 4 proposes four features of dynamic system stability, in which a system’s states depend on the interactions among its components, as well as the system’s interactions with its environment.
First of all, stability always has a time frame, and stabilities at different time frames (such as stability over a month and a year) are interdependent. We ought to consider, how these time scales interact. For example, some factors which determine one’s motivation to go to the gym, such as mood, fluctuate on the scale from minutes to hours. Others may fluctuate on the daily level, and can be influenced by how much one slept the previous night or how stressful one’s workday was, whereas others fluctuate weekly. Then again, some—which increasingly resemble dispositions or personality factors—may be quite stable across decades. When inspecting a health behaviour, we ought to be looking at minimum the process which takes place on a time scale one level faster, and one lever slower than the one we are purportedly interested in 4. For example, how do daily levels of physical activity relate to weekly ones, and how do montly fluctuations affect the weekly fluctuations? Health psychologists could also classify each determinant of a health behaviour, based on the time scale it is thought to operate on. For example, if autonomous forms of motivation 5 seem to predict physical activity quite well cross-sectionally, we could attempt to measure it for a hundred days and investigate what the relevant time-scales of fluctuations are, in relation to those of the target behaviour. Such an exercise could also be helpful for deciding on the sampling frequency of experience sampling studies.
Second, processes in systems such as people have their characteristic attractor landscapes, and these landscapes can possibly be spelled out, along with the criteria associated with them. By attractors I mean here behaviours a person is drawn to, and an attractor landscape is the conglomerate of these behaviours. The cue-structure of the behaviours can be quite elaborate. For example, a person may smoke only, when they have drank alcohol (1) in a loud environment (2), among a relatively large group (3) of relatively unfamiliar people (4), one or two of whom are smokers (5); a situation where it is easier to have a private conversation if one joins another to go out for a cigarette. This highlights how the process of this person’s smoking habit can be very stable (mapping to the traditional conception of “habitual”), while also possibly being highly infrequent.
Note: Each of the aforementioned conditions for this person to smoke are insufficient by themselves, although all are needed to trigger smoking in this context. As a whole, they are sufficient to cause the person to smoke, but not always necessarily needed, because the person may smoke in some more-or-less limited other conditions, too. These conditions can also be called INUS (referring to Insufficient but Necessary criteria of an Unnecessary but Sufficient context for the behaviour) 6. Let that sink in a bit. As a corollary, if a criterion really is necessary, it may be an attractive target for intervention.
Third, the path through which change happens matters, a lot. Even when all determinants of behaviour are at a same value, the outcome may be very different depending on previous values of the outcome. This phenomenon is known as hysterisis, and it has been observed in various fields from physics (e.g. the form of a magnetic field depends on its past) to psychology (e.g. once a person becomes depressed due to excess stress, the stress level must be much lower to switch back to the normal state, than was needed for the shift to depression; 7). As a health behaviour example, just imagine how much easier it is to switch from a consistent training regime to doing no exercise at all, compared to doing it the other way around. Another way to think about is to consider that systems are “influenced by the residual stability of an antecedent regime” 4. As a consequence of stability being “just” a particular type of a path-dependent dynamic process 4,8, we need to consider the history leading up to the period where a habit is active. This forces investigators to consider attractor patterns and sensitivity to initial conditions: When did this stable (or attractor) state come about? If interactions in a system create the state of the system, which bio-psycho-social interactions are contributing to the stable state in question?
Fourth, learning processes such as those happening due to interventions usually affect a cluster of variables’ stabilities, not just one of them. To change habits, we naturally need to consider which changeable processes should be targeted, but it is probably impossible to manipulate these processes in isolation. This has been dubbed the “fat finger problem” (Borsboom 2018, personal communication); trying to change a specific variable, like attempting to press a specific key on the keyboard with gloves on, almost invariably ends up affecting neighbouring variables. Our target is dynamic and interconnected, often calling for coevolution of the intervention and the intervened.
It is obvious that people can relapse to their old habitual (attractor) behaviour after an intervention, and likely that extinction, unlearning and overwriting of cue-response patterns can help in breaking habits, whatever the definition. But the complex dynamics perspective puts a special emphasis on understanding the time scale and history of the intervenable processes, as well as highlighting the difficulty of changing one process while holding others constant, as the classical experimental setup would propose.
I would be curious of hearing thoughts about these clearly unfinished ideas.
Gardner, B. A review and analysis of the use of ‘habit’ in understanding, predicting and influencing health-related behaviour. Health Psychol. Rev.9, 277–295 (2015).
Wood, W. Habit in Personality and Social Psychology. Personal. Soc. Psychol. Rev.21, 389–403 (2017).
Wood, W. & Rünger, D. Psychology of Habit. Annu. Rev. Psychol.67, 289–314 (2016).
Barrett, N. F. A dynamic systems view of habits. Front. Hum. Neurosci.8, (2014).
Ryan, R. M. & Deci, E. L. Self-determination theory: Basic psychological needs in motivation, development, and wellness. (Guilford Publications, 2017).
Mackie, J. L. Causes and Conditions. Am. Philos. Q.2, 245–264 (1965).
Cramer, A. O. J. et al. Major Depression as a Complex Dynamic System. PLoS ONE11, (2016).
Roe, R. A. Test validity from a temporal perspective: Incorporating time in validation research. Eur. J. Work Organ. Psychol.23, 754–768 (2014).
In this post, I wonder what complex systems, as well as the nuts and bolts of mediation analysis, imply for studying processes of health psychological interventions.
Say we make a risky prediction and find an intervention effect that replicates well (never mind for now that replicability is practically never tested in health psychology). We could then go on to investigating boundary conditions and intricacies of the effect. What’s sometimes done is a study of “mechanisms of action”, also endorsed by the MRC guidelines for process evaluation (1), as well as the Workgroup for Intervention Development and Evaluation Research (WIDER) (2). In such a study, we investigate whether the intervention worked as we thought it should have worked (in other words, to test the program theory; see previous post). It would be spectacularly useful to decision makers, if we could disentangle the mechanisms of the intervention; “by increasing autonomy support, autonomous motivation goes up and physical activity ensues”. But attempting to evaluate this opens a spectacular can of worms.
Complex interventions include multiple interacting components, targeting several facets of a behaviour on different levels of the environment the individual operates in (1). This environment itself can be described as a complex system (3). In complex, adaptive systems such as the society or a human being, causality is thorny issue (4): Feedback loops, manifold interactions between variables over time, path-dependence and sensitivity to initial conditions make it challenging at best to state “a causes b” (5). But what does it even mean to say something causes something else?
Bollen (6) presents three conditions for causal inference: isolation, association and direction. Isolation means that no other variable can reasonably cause the outcome. This is usually impossible to achieve strictly, which is why researchers usually aim to control for covariates and thus reach a condition of pseudo-isolation. A common, but not often acknowledged problem is overfitting; adding covariates to a model leads to also fitting the measurement error they carry with them. Association means there should be a connection between the cause and the effect – in real life, usually a probabilistic one. In social sciences, a problem arises as everything is more or less correlated with everything else, and high-dimensional datasets suffer of the “curse of dimensionality”. Direction, self-evidently, means that the effect should flow from one direction to the other, not the other way around. This is highly problematic in complex systems. For an example in health psychology, it seems obvious that depression symptoms (e.g. anxiety and insomnia) feed each other, resulting in self-enforcing feedback loops (7).
When we consider the act of making efficient inferences, we want to be able to falsify our theories of the world (9); something that’s only recently really starting to be understood among psychologists (10). An easy-ish way about this, is to define the smallest effect size of interest (SESOI) a priori, ensure one has proper statistical power and attempt to reject the hypotheses that effects are larger than the upper bound of the SESOI, and lower than the lower bound. This procedure, also known as equivalence testing (11) allows for rejecting the falsification of statistical hypotheses in situations, where a SESOI can be determined. But when testing program theories of complex interventions, there may be no such luxury.
The notion of non-linear interactions with feedback loops makes the notion of causality in a complex system an evasive concept. If we’re dealing with complexity, it is a situation where even miniscule effects can be meaningful when they interact with other effects: even small effects can have huge influences down the line (“the butterfly effect” in nonlinear dynamics; 8). It is hence difficult to determine the SESOI for intermediate links in the chain from intervention to outcome. And if we only say we expect an effect to be “any positive number”, this leads to the postulated processes, as described in intervention program theories, being unfalsifiable: If a correlation of 0.001 between intervention participation and a continuous variable would corroborate a theory, one would need more than six million participants to detect it (at 80% power and an alpha of 5%; see also 12, p. 30). If researchers are unable to reject the null hypothesis of no effect, they cannot determine whether there is evidence for a null effect, or if a more elaborate sample was needed (e.g. 13).
Side note: One could use Bayes factors to compare whether a point null data generator (effect size being zero) would predict the data better than, for example, an alternative model where most effects are near zero but half of them over d = 0.2. But still, the smaller effects you consider potentially important, the less the data can distinguish between alternative and null models. A better option could be to estimate, how probable it is that the effect has a positive sign (as demonstrated here).
In sum, researchers are faced with an uncomfortable trade-off: Either they must specify a SESOI (and thus, a hypothesis) which does not reflect the theory under test or, on the other hand, unfalsifiability.
A common way to study mechanisms is to conduct a mediation analysis, where one variable’s (X) impact on another (Y) is modelled to pass through a third variable (M). In its classical form, one expects the path X-Y to go near zero, when M is added to the model.
The good news is, that nowadays we can do power analyses for both simple and complex mediation models (14). The bad news is, that in the presence of randomisation of X but not M, the observed M-Y relation entails strong assumptions which are usually ignored (15). Researchers should e.g. justify why there exist no other mediating variables than the ones in the model; leaving variables out is effectively the same as assuming their effect to be zero. Also, the investigator should demonstrate why no omitted variables affect both M and Y – if there are such variables, the causal effect may be distorted at best and misleading at worst.
Now that we know it’s bad to omit variables, how do we avoid overfitting the model (i.e. be fooled by looking too much into what the data says)? It is very common for seemingly supported theories to fail to generalise to slightly different situations or other samples (16), and subgroup claims regularly fail to pan out in new data (17). Some solutions include ridge regression in the frequentist framework and regularising priors in the Bayesian one, but the simplest (though not the easiest) solution would be cross-validation. In cross-validation, you basically divide your sample in two (or even up to n) parts, use the first one to explore and the second one to “replicate” the analysis. Unfortunately, you need to have a large enough sample so that you can break it down to parts.
What does all this tell us? Mainly, that investigators would do well to heed Kenny’s (18) admonition: “mediation is not a thoughtless routine exercise that can be reduced down to a series of steps. Rather, it requires a detailed knowledge of the process under investigation and a careful and thoughtful analysis of data”. I would conjecture that researchers often lack such process knowledge. It may also be, that under complexity, the exact processes become both unknown and unknowable (19). Tools like structural equation modelling are wonderful, but I’m curious if they are up to the task of advising us about how to live in interconnected systems, where trends and cascades are bound to happen, and everything causes everything else.
These are just relatively disorganised thoughts, and I’m curious to hear if someone can shed hope to the situation. Specifically, hearing of interventions that work consistently and robustly, would definitely make my day.
ps. If you’re interested in replication matters in health psychology, there’s an upcoming symposium on the topic in EHPS17 featuring Martin Hagger, Gjalt-Jorn Peters, Rik Crutzen, Marie Johnston and me. My presentation is titled “Disentangling replicable mechanisms of complex interventions: What to expect and how to avoid fooling ourselves?“
pps. A recent piece in Lancet (20) called for a complex systems model of evidence for public health. Here’s a small conversation with the main author, regarding the UK Medical Research Council’s take on the subject. As you see, the science seems to be in some sort of a limbo/purgatory-type of place currently, but smart people are working on it so I have hope 🙂
Moore GF, Audrey S, Barker M, Bond L, Bonell C, Hardeman W, et al. Process evaluation of complex interventions: Medical Research Council guidance. BMJ. 2015 Mar 19;350:h1258.
Abraham C, Johnson BT, de Bruin M, Luszczynska A. Enhancing reporting of behavior change intervention evaluations. JAIDS J Acquir Immune Defic Syndr. 2014;66:S293–S299.
Shiell A, Hawe P, Gold L. Complex interventions or complex systems? Implications for health economic evaluation. BMJ. 2008 Jun 5;336(7656):1281–3.
Sterman JD. Learning from Evidence in a Complex World. Am J Public Health. 2006 Mar 1;96(3):505–14.
Resnicow K, Page SE. Embracing Chaos and Complexity: A Quantum Change for Public Health. Am J Public Health. 2008 Aug 1;98(8):1382–9.
Bollen KA. Structural equations with latent variables. New York: John Wiley. 1989;
Borsboom D. A network theory of mental disorders. World Psychiatry. 2017 Feb;16(1):5–13.
Hilborn RC. Sea gulls, butterflies, and grasshoppers: A brief history of the butterfly effect in nonlinear dynamics. Am J Phys. 2004 Apr;72(4):425–7.
LeBel EP, Berger D, Campbell L, Loving TJ. Falsifiability Is Not Optional. Accepted pending minor revisions at Journal of Personality and Social Psychology. [Internet]. 2017 [cited 2017 Apr 21]. Available from: https://osf.io/preprints/psyarxiv/dv94b/
I recently peer reviewed a partly shocking piece called “Reproducibility in Psychological Science: When Do Psychological Phenomena Exist?“ (Iso-Ahola, 2017). In the article, the author makes some very good points, which unfortunately get drowned under very strange statements and positions. Me, Eiko Fried and Etienne LeBel addressed those shortly in a commentary (preprint; UPDATE: published piece). Below, I’d like to expand upon some additional thoughts I had about the piece, to answer Martin Hagger’s question.
When all parts do the same thing on a certain scale (planets on Newtonian orbits), their behaviour is relatively easy to predict for many purposes. Same thing, when all molecules act independently in a random fashion: the risk that most or all beer molecules in a pint move upward at the same time is ridiculously low, and thus we don’t have to worry about the yellow (or black, if you’re into that) gold escaping the glass. Both situations are easy-ish systems to describe, as opposed to complex systems where the interactions, sensitivity to initial conditions etc. can produce a huge variety of behaviour and states. Complexity science is the study of these phenomena, which have become increasingly common since the 1900s (Weaver, 1948).
Iso-Ahola (2017) quotes (though somewhat unfaithfully) the complexity scientist Bar-Yam (2016b): “for complex systems (humans), all empirical inferences are false… by their assumptions of replicability of conditions, independence of different causal factors, and transfer to different conditions of prior observations”. He takes this to mean that “phenomena’s existence should not be defined by any index of reproducibility of findings” and that “falsifiability and replication are of secondary importance to advancement of scientific fields”. But this is a highly misleading representation of the complexity science perspective.
In Bar-Yam’s article, he used an information theoretic approach to analyse the limits of what we can say about complex systems. The position is that while full description of systems via empirical observation is impossible, we should aim to identify the factors which are meaningful in terms of replicability of findings, or the utility of the acquired knowledge. As he elaborates elsewhere: “There is no utility to information that is only true in a particular instance. Thus, all of scientific inquiry should be understood as an inquiry into universality—the determination of the degree to which information is general or specific” (Bar-Yam, 2016a, p. 19).
This is fully in line with the Fisher quote presented in Mayo’s slides:
The same goes for replications; no single one-lab study can disprove a finding:
“’Thus a few stray basic statements contradicting a theory will hardly induce us to reject it as falsified. We shall take it as falsified only if we discover a reproducible effect which refutes the theory. In other words, we only accept the falsification if a low-level empirical hypothesis which describes such an effect is proposed and corroborated’ (Popper, 1959, p. 66)” (see Holtz & Monnerjahn, 2017)
So, if the high-quality non-replication replicates, one must consider that something may be off with the original finding. This leads us to the question of what researchers should study in the first place.
On research programmes
Lakatos (1971) posits a difference between progressive and degenerating research lines. In a progressive research line, investigators explain a negative result by modifying the theory in a way which leads to new predictions that subsequently pan out. On the other hand, coming up with explanations that do not make further contributions, but rather just explain away the negative finding, leads to a degenerative research line. Iso-Ahola quotes Lakatos to argue that, although theories may have a “poor public record” that should not be denied, falsification should not lead to abandonment of theories. Here’s Lakatos:
“One may rationally stick to a degenerating [research] programme until it is overtaken by a rival and even after. What one must not do is to deny its poor public record. […] It is perfectly rational to play a risky game: what is irrational is to deceive oneself about the risk” (Lakatos, 1971, p. 104)
As Meehl (1990, p. 115) points out, the quote continues as follows:
“This does not mean as much licence as might appear for those who stick to a degenerating programme. For they can do this mostly only in private. Editors of scientific journals should refuse to publish their papers which will, in general, contain either solemn reassertions of their position or absorption of counterevidence (or even of rival programmes) by ad hoc, linguistic adjustments. Research foundations, too, should refuse money.” (Lakatos, 1971, p. 105)
Perhaps researchers should pay more attention which program they are following?
As an ending note, here’s one more interesting quote: “Zealotry of reproducibility has unfortunately reached the point where some researchers take a radical position that the original results mean nothing if not replicated in the new data.” (Iso-Ahola, 2017)
For explorative research, I largely agree with these zealots. I believe exploration is fine and well, but the results do mean nearly nothing unless replicated in new data (de Groot, 2014). One cannot hypothesise and confirm with the same data.
Perhaps I focus too much on the things that were said in the paper, not what the author actually meant, and we do apologise if we have failed to abide with the principle of charity in the commentary or this blog post. I do believe the paper will best serve as a pedagogical example to aspiring researchers, on how strangely arguments could be constructed in the olden times.
ps. Bar-Yam later commented on this blog post, confirming the mis(present/interpr)etation of his research by the author of the reproducibility paper:
pps. Here’s Fred Hasselman‘s comment on the article, from the Frontiers website (when you scroll down all the way to the bottom, there’s a comment option):
1. Whether or not a posited entity (e.g. a theoretical object of measurement) exists or not, is a matter of ontology.
2. Whether or not one can, in principle, generate scientific knowledge about a posited entity, is a matter of epistemology.
3. Whether or not the existence claim of a posited entity (or law) is scientifically plausible depends on the ability of a theory or nomological network to produce testable predictions (predictive power) and the accuracy of those predictions relative to measurement outcomes (empirical accuracy).
4. The comparison of the truth status of psychological theoretical constructs to the Higgs Boson is a false equivalence: One is formally defined and deduced from a highly corroborated model and predicts the measurement context in which its existence can be verified or falsified (the LHC), the other is a common language description of a behavioural phenomenon “predicted” by a theory constructed from other phenomena published in the scientific record of which the reliability is… unknown.
5. It is the posited entity itself -by means of its definition in a formalism or theory that predicts its existence- that decides how it can be evidenced empirically. If it cannot be evidenced using population statistics, don’t use it! If the analytic tools to evidence it do not exist, develop them! Quantum physics had to develop a new theory of probability, new mathematics to be able to make sense of measurement outcomes of different experiments. Study non-ergodic physics, complexity science, emergence and self-organization in physics, decide if it is sufficient, if not, develop a new formalism. That is how science advances and scientific knowledge is generated. Not by claiming all is futile.
To summarise: The article continuously confuses ontological and epistemic claims, it does not provide a future direction even though many exist or are being proposed by scholars studying phenomena of the mind, moreover the article makes no distinction between sufficiency and necessity in existence claims, and this is always problematic.
Contrary to the claim here, a theory (and the ontology and epistemology that spawned it) can enjoy high perceived scientific credibility even if some things cannot be known in principle, or if there’s always uncertainty in measurements. It can do so by being explicit about what it is that can and cannot be known about posited entities.
E.g. Quantum physics is a holistic physical theory, also in the epistemic sense: It is in principle not possible to know anything about a quantum system at the level of the whole, based on knowledge about its constituent parts. Even so, quantum physical theories have the highest predictive power and empirical accuracy of all scientific theories ever produced by human minds!
As evidenced by the history of succession of theories in physics, successful scientific theorising about the complex structure of reality seems to be a highly reproducible phenomenon of the mind. Let’s apply it to the mind itself!
Bar-Yam, Y. (2016a). From big data to important information. Complexity, 21(S2), 73–98.
Bar-Yam, Y. (2016b). The limits of phenomenology: From behaviorism to drug testing and engineering design. Complexity, 21(S1), 181–189. https://doi.org/10.1002/cplx.21730
de Groot, A. D. (2014). The meaning of “significance” for different types of research [translated and annotated by Eric-Jan Wagenmakers, Denny Borsboom, Josine Verhagen, Rogier Kievit, Marjan Bakker, Angelique Cramer, Dora Matzke, Don Mellenbergh, and Han L. J. van der Maas]. Acta Psychologica, 148, 188–194. https://doi.org/10.1016/j.actpsy.2014.02.001
Holtz, P., & Monnerjahn, P. (2017). Falsificationism is not just ‘potential’ falsifiability, but requires ‘actual’ falsification: Social psychology, critical rationalism, and progress in science. Journal for the Theory of Social Behaviour. https://doi.org/10.1111/jtsb.12134
In this post, I argue against the intuitively appealing notion that, in a deterministic world, we just need more information and can use it to solve problems in complex systems. This presents a problem in e.g. psychology, where more knowledge does not necessarily mean cumulative knowledge or even improved outcomes.
Recently, I attended a talk where Misha Pavel happened to mention how big data can lead us astray, and how we can’t just look at data but need to know mechanisms of behaviour, too.
Later, a couple of my psychologist friends happened to present arguments discounting this, saying that the problem will be solved due to determinism. Their idea was that the world is a deterministic place—if we knew everything, we could predict everything (an argument also known as Laplace’s Demon)—and that we eventually a) will know, and b) can predict. I’m fine with the first part, or at least agnostic about it. But there are more mundane problems to prediction than “quantum randomness” and other considerations about whether truly random phenomenon exist. The thing is, that even simple and completely deterministic systems can be utterly unpredictable to us mortals. I will give an example of this below.
Even simple and completely deterministic systems can be utterly unpredictable.
Let’s think of a very simple made-up model of physical activity, just to illustrate a phenomenon:
Say today’s amount of exercise depends only on motivation and exercise of the previous day. Let’s say people have a certain maximum amount of time to exercise each day, and that they vary from day to day, in what proportion of that time they actually manage to exercise. To keep things simple, let’s say that if a person manages to do more exercise on Monday, they give themselves a break on Tuesday. People also have different motivation, so let’s add that as factor, too.
Our completely deterministic, but definitely wrong, model could generalise to:
Exercise percentage today = (motivation) * (percentage of max exercise yesterday) * (1 – percentage of max exercise yesterday)
For example, if one had a constant motivation of 3.9 units (whatever the scale), and managed to do 80% of their maximum exercise on Monday, they would use 3.9 times 80% times 20% = 62% of their maximum exercise time on Tuesday. Likewise, on Wednesday they would use 3.9 times 62% times 38% = 92% of the maximum possible exercise time. And so on and so on.
We’re pretending this model is the reality. This is so that we can perfectly calculate the amount of exercise on any day, given that we know a person’s motivation and how much they managed to exercise the previous day.
Imagine we measure a person, who obeys this model with a constant motivation of 3.9, and starts out on day 1 reaching 50% of their maximum exercise amount. But let’s say there is a slight measurement error: instead of 50.000%, we measure 50.001%. In the graph below we can observe, how the error (red line) quickly diverges from the actual (blue line). The predictions we make from our model after around day 40 do not describe our target person’s behaviour at all. The slight deviation from the deterministic system has made it practically chaotic and random to us.
What are the consequences?
The model is silly, of course, as we probably would never try to predict an individual’s exact behaviour on any single day (averages and/or bigger groups help, because usually no single instance can kill the prediction). But this example does highlight a common feature of complex systems, known as sensitive dependence to initial conditions: even small uncertainties cumulate to create huge errors. It is also worth noting, that increasing model complexity doesn’t necessarily help us with prediction, due to a problems such as overfitting (thinking the future will be like the past; see also why simple heuristics can beat optimisation).
Thus, predicting long-term path-dependent behaviour, even if we knew the exact psycho-socio-biological mechanism governing it, may be impossible in the absence of perfect measurement. Even if the world was completely deterministic, we still could not predict it, as even trivially small things left unaccounted for could throw us off completely.
Predicting long-term path-dependent behaviour, even if we knew the exact psycho-socio-biological mechanism governing it, may be impossible in the absence of perfect measurement.
The same thing happens when trying to predict as simple a thing as how billiard balls impact each other on the pool table. The first collision is easy to calculate, but to compute the ninth you already have to take into account the gravitational pull of people standing around the table. By the 56th impact, every elementary particle in the universe has to be included in your assumptions! Other examples include trying to predict the sex of a human fetus, or trying to predict the weather 2 weeks out (this is the famous idea about the butterfly flapping its wings).
Coming back to Misha Pavel’s points regarding big data, I feel somewhat skeptical about being able to acquire invariant “domain knowledge” in many psychological domains. Also, as shown here, knowing the exact mechanism is still no promise of being able to predict what happens in a system. Perhaps we should be satisfied when we can make predictions such as “intervention x will increase the probability that the system reaches a state where more than 60% of the goal is reached on more than 50% of the days, by more than 20% in more than 60% of the people who belong in a group it was designed to affect”?
But still: for determinism to solve our prediction problems, the amount and accuracy of data needed is beyond the wildest sci-fi fantasies.
I’m happy to be wrong about this, so please share your thoughts! Leave a comment below, or on these relevant threads: Twitter, Facebook.
To learn about dynamic systems and chaos, I highly recommend David Feldman’s course on the topic, next time it comes around at Complexity Explorer.
… Meanwhile, the equation I used here is actually known as the “logistic map”. See this post about how it behaves.
Recently, I was happy and surprised to see a paper attempting to create a computational model of a major psychological theory. In a conversation, Nick Brown expressed doubt:
Do you agree? What are the alternatives? Do we have to content with vague statements like “the behaviour will fluctuate” (perhaps as in: fluctuat nec mergitur)? How should we study the dynamics of human behaviour?
Also: do see Nick Brown’s blog, if you don’t mind non-conformist thinking.