Pathways and complexity in behaviour change research

These are slides of a talk given at the Aalto University Complex Systems seminar. Contrasts two views to changing behaviour; the pathway view and the complexity view, the latter being at its infancy. Presents some Secret Analysis Arts of Recurrence, which Fred Hasselman doesn’t want you to know about. Includes links to resources. If someone perchance saw my mini-moocs (1, 2) and happened to find them useful, drop me a line and I’ll make one of this.

Lifestyle factors are hugely relevant in preventing disease in modern societies; unfortunately people often fail in their attempts to change health behaviour – both their own, as well as that of others’. In recent years, behaviour change design has been conceived as a process where one identifies deficiencies in factors influencing the behaviours (commonly called “determinants”). Complexity thinking suggests putting emphasis on de-stabilisation instead.

The perspective taken here is mostly at the idographic level. At the time of writing, we have behaviour change methods to affect e.g. skills, perceived social norms, attitudes and so forth – but very little on general de-stabilisation of the motivational system as an important predictor of change.

Perspectives are welcome!

ps. Those of you to worry about brainwashing and freedom of thought: Chill. Stuff that powerful doesn’t really exist, and if it did, marketers would know about it and probably rule the world. [No, they don’t rule the world, I’ve been there]

pps. Forgot to put it in the slides, but this guy Merlijn Olthof will perhaps one day tweet about his work about destabilisation in psychotherapy contexts. Meanwhile, you can e.g. be his 10th Twitter follower, or keep checking his Google Scholar profile, as there’s a new piece coming out soon!

Randomised experiments (mis?)informing social policy in complex systems

In this post, I vent about anti-interdisciplinarity, introduce some basic perspectives of complexity science, and wonder whether decisions on experimental design actually lead us to end up in a worse place than where we were, before we decided to use experimental evidence to inform social policy.

People in our research group recently organised a symposium, Interdisciplinary perspectives on evaluating societal interventions to change behaviour (talks watchable here), as part of a series called Behaviour Change Science & Policy (BeSP). The idea is to bring together people from various fields from philosophy to behavioural sciences, medicine and beyond, in order to better tackle problems such as climate change and lifestyle diseases.

One presentation touched upon Finland’s randomised controlled trial to test the effects of basic income on employment (see also report on first year results). In crude summary, they did not detect effects of free money on finding employment. (Disclaimer: They had aimed for 80% statistical power, meaning that if all your assumptions regarding the size of the effect are correct, in the long term, 20% of the time you’d get no statistically significant effect in spite of there being a real effect.)

During post-symposium drinks, I spoke with an economist about the trial. I was wondering, how come they used individual instead of cluster randomisation – randomising neighbourhoods, for example. The answer was resource constraints; much larger sample sizes are needed for the statistics to work. To me it seemed clear, that it’s a very different situation if one person in a network of friends got free money, as compared to if everyone did. The economist wondered: “How come there could be second-order effects when there were no first-order effects?” The conversation took a weird turn. Paraphrasing:

Me: Blahblah compelling evidence from engineering and social sciences to math and physics that “more is different”, i.e. phenomena play out differently depending on the scale at consideration… blahblah micro-level interactions create emergent macro-level patterns blahblah.

Economist: Yeah, we’re not having that conversation in our field.

Me: Oh, what do you mean?

Economist: Well, those are not things discussed in our top journals, or considered interesting subjects to research.

Me: I think they have huge consequences, and specifically in economics, this guy in Oxford just gave a presentation on what he called “Complexity economics“. He had been doing it for some decades already, I think he originally had a physics background…

Economist: No thanks, no physicists in my economics.

Me: Huh?

Economist: [exits the conversation]

Now, wasn’t that fun for a symposium on interdisciplinary perspectives.

I have a lot of respect for the mathematical prowess of economists and econometricians, don’t get me wrong. One of my favourites is Scott E. Page, though I only know him due to an excellent course on complexity (also available as an audio book). I do probably like him, because he breaks out of the monodisciplinary insulationist mindset economists are often accused of. Page’s view of complexity actually relates to our conversation. Let’s see how.

First off, he describes complexity (and most social phenomena of interest) as arising from four factors, which can be thought as tuning knobs or dials. Complexity arises, when each dial is not tuned into either of the extremes, which is where equilibria arise, but somewhere in the middle. And complex systems tend to reside far from equilibrium, permanently.

To dig more deeply into how the attributes of interdependence,
connectedness, diversity, and adaptation and learning generate
complexity, we can imagine that each of these attributes is a dial that
can be turned from 0 (lowest) to 10 (highest).

Scott E. Page

  • Interdependence means the extent of how much one person’s actions affect those of another’s. This dial ranges from complete independence, where one person’s actions do not affect others’ at all, to complete dependence, where everyone observes and tries to perfectly match all others’ actions. In real life, we see both unexpected cascades (such as the US decision makers’ ethanol regulations, leading to the Arab Spring), as well as some, but never complete, independence – that is, manifestations that do not fit into either extreme of the dial, but lie somewhere in between.
  • Connectedness refers to how many other people a person is connected to. The extremes range from people living in a cabin in the woods all alone, to hypersocial youth living in Instagram trying to keep tabs on everyone and everything. The vast majority of people lie somewhere in between.
  • Diversity is the presence of qualitatively different types of actors: If every person is a software engineer, mankind is obviously doomed… But the same happens if there’s only one engineer, one farmer etc. Different samples of real-world social systems (e.g. counties) consist of intermediate amounts of diversity, lying somewhere in between.
  • Adaptation and learning refer to the extent of the actors’ smartness. This ranges from following simple, unchanging rules, to being perfectly rational and informed, as assumed in classical economics. In actual decision making, we see “bounded rationality”, reliance on rules of thumb and tradition, as well as both optimising and satisficing behaviours – the “somewhere in between”.

The complexity of complex systems arises, when diverse, connected people interact on the micro-level, and by doing so produce “emergent” macro-level states of the world, to which they adapt, creating new unexpected states of the world.

You might want to read that one again.

Back to basic income: When we pick 2000 random individuals around the country and give them free money, we’re implicitly assuming they are not connected to any other people, and/or that they are completely independent the actions of others’. We’re also assuming that they are either the same, or that it’s not interesting that they are of different types. And so forth. If we later compare their employment data to that of those who were not given basic income, the result we get is an estimate of the causal effect in the population, if all assumptions would hold.

But consider how these assumptions may fail. If the free money was perceived as a permanent thing, and given to people’s whole network of unemployed buddies, it seems quite plausible that they would adapt their behaviour as a response of the dynamics of their social network changing. This might even be different in cliques of certain people, who might use the safety net of basic income to collectively found companies and take risks, and cliques of other people, who might alter their daily drinking behaviour to match the costs with the predictable income – for better or worse. But when you randomise individually and ignore how people cluster in networks, you’re studying a different thing. Whether it’s an interesting thing or a silly thing, is another issue.

Now, it’s easy to come up with these kinds of assumption-destroying scenarios, but a whole different ordeal to study them empirically. We need to simplify reality in order to deal with it. The question is this: How much of an abstraction can a map (i.e. a model in a research study, making those simplified assumptions) be, in order to still represent reality adequately? This is also an ontological question, because if you take the complexity perspective seriously, you say bye-bye to the kind of thinking that allows you to dream up predictable effects a button-press (such as a policy change) has over the state of a system. People who act in—or try steering—complex systems, control almost nothing but influence almost everything.

An actor in a complex system controls almost nothing but influences almost everything.

Scott E. Page

Is some information, some model, still better than none? Maybe. Maybe not. In Helsinki, you’re better off without a map, than with a map of Stockholm – the so-called “Best map fallacy” (explained here in detail). Rare, highly influential events drive the behaviour of complex systems: the Finnish economy was not electrified by average companies starting to sell more, but by Nokia hitting the jackpot. And these events are very hard, if not impossible, to predict✱.

Ok, back to basic income again. I must say that the people who devised the experiment were not idiots, and included e.g. interviews of people to get some idea about unexpected effects. I think that this type of an approach is definitely necessary when dealing with complexity, and all social interventions should include qualitative data in their evaluation. But, again, unless the unemployed don’t interact, with randomisation done individually you’re studying a different thing than when it’s done in clusters. I do wonder if it would have been possible to include some matched clusters, to see if any qualitatively different dynamics take place, when you give basic income to a whole area instead of randomly picked individuals within it.

Complex systems organizational map.jpg
The society is a complex system, and must be studied as such. Figure: Hiroki Sayama (click to enlarge)

But, to wrap up this flow of thought, I’m curious if you think it is possible to randomise a social intervention individually AND always keep in mind that the conclusions are only valid if there are no interactions between people’s behaviour and that of their neighbours. Or is it inevitable that that the human mind smoothes out the details?

Importantly: Is our map better now, than it was before? Will this particular experiment go in history as—like the economist stated in “there were no first-order effects”—basic income not having any effect on job seeking? (remember, aim was only 80% statistical power). Lastly, I want to say I consider it unforgiveable to only work within one discipline and disregard the larger world you’re operating in: When we bring science to policy making, we must be doubly cautious of the assumptions our conclusions stand on. Luckily, transparent scientific methodology allows us to be explicit about them.

Let me hear your thoughts, and especially objections, on Twitter, or by email!

✱ One solution is to harness convexity, which can be oversimplified like this:

  1. Unpredictable things will happen, and they will make you either better or worse off.
  2. Magnitude of an event is different from it’s effect on you, i.e. there are huge events that don’t impact you at all, and small events that are highly meaningful to you. Often that impact depends on the interdependence and connectedness dials.
  3. To an extent, you can control the impact an event has on you.
  4. You want to control exposure in such a way, that surprise losses are bounded, while surprise gains are as limitless as possible.

Complexity considerations for intervention (process) evaluation

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.

 

blogiin kuva

Misleading simplifications and where to find them (Slides & Mini-MOOC 11min)

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.

SLIDE DECK:

misleading assumptions 1st slide

Mini-MOOC:

 

Note: Jan Vanhove thinks we shouldn’t  become paranoid with model assumptions; check his related blog post here!

The secret life of (complex dynamical) habits

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.

corpus clock
Corpus Clock of Cambridge, where I’m writing this. The clock behaves chaotically so that it’s accurate every five minutes. A time-eating locust on top reminds us that neither habits, nor other human endeavours, escape this passage. Photo: Jim Linwood

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.

  1. 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).
  2. Wood, W. Habit in Personality and Social Psychology. Personal. Soc. Psychol. Rev. 21, 389–403 (2017).
  3. Wood, W. & Rünger, D. Psychology of Habit. Annu. Rev. Psychol. 67, 289–314 (2016).
  4. Barrett, N. F. A dynamic systems view of habits. Front. Hum. Neurosci. 8, (2014).
  5. Ryan, R. M. & Deci, E. L. Self-determination theory: Basic psychological needs in motivation, development, and wellness. (Guilford Publications, 2017).
  6. Mackie, J. L. Causes and Conditions. Am. Philos. Q. 2, 245–264 (1965).
  7. Cramer, A. O. J. et al. Major Depression as a Complex Dynamic System. PLoS ONE 11, (2016).
  8. Roe, R. A. Test validity from a temporal perspective: Incorporating time in validation research. Eur. J. Work Organ. Psychol. 23, 754–768 (2014).

 

Is it possible to unveil intervention mechanisms under complexity?

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 🙂

complexity rutter twitter.PNG

https://twitter.com/harryrutter/status/876219437430517761

 

Bibliography

 

  1. 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.
  2. 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.
  3. Shiell A, Hawe P, Gold L. Complex interventions or complex systems? Implications for health economic evaluation. BMJ. 2008 Jun 5;336(7656):1281–3.
  4. Sterman JD. Learning from Evidence in a Complex World. Am J Public Health. 2006 Mar 1;96(3):505–14.
  5. 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.
  6. Bollen KA. Structural equations with latent variables. New York: John Wiley. 1989;
  7. Borsboom D. A network theory of mental disorders. World Psychiatry. 2017 Feb;16(1):5–13.
  8. 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.
  9. 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/
  10. Morey R D, Lakens D. Why most of psychology is statistically unfalsifiable. GitHub [Internet]. in prep. [cited 2016 Oct 23]; Available from: https://github.com/richarddmorey/psychology_resolution
  11. Lakens D. Equivalence Tests: A Practical Primer for t-Tests, Correlations, and Meta-Analyses [Internet]. 2016 [cited 2017 Feb 24]. Available from: https://osf.io/preprints/psyarxiv/97gpc/
  12. Dienes Z. Understanding Psychology as a Science: An Introduction to Scientific and Statistical Inference. Palgrave Macmillan; 2008. 185 p.
  13. Dienes Z. Using Bayes to get the most out of non-significant results. Quant Psychol Meas. 2014;5:781.
  14. Schoemann AM, Boulton AJ, Short SD. Determining Power and Sample Size for Simple and Complex Mediation Models. Soc Psychol Personal Sci. 2017 Jun 15;194855061771506.
  15. Bullock JG, Green DP, Ha SE. Yes, but what’s the mechanism? (don’t expect an easy answer). J Pers Soc Psychol. 2010;98(4):550–8.
  16. Yarkoni T, Westfall J. Choosing prediction over explanation in psychology: Lessons from machine learning. FigShare Httpsdx Doi Org106084m9 Figshare. 2016;2441878:v1.
  17. Wallach JD, Sullivan PG, Trepanowski JF, Sainani KL, Steyerberg EW, Ioannidis JPA. Evaluation of Evidence of Statistical Support and Corroboration of Subgroup Claims in Randomized Clinical Trials. JAMA Intern Med. 2017 Apr 1;177(4):554–60.
  18. Kenny DA. Reflections on mediation. Organ Res Methods. 2008;11(2):353–358.
  19. Bar-Yam Y. The limits of phenomenology: From behaviorism to drug testing and engineering design. Complexity. 2016 Sep 1;21(S1):181–9.
  20. Rutter H, Savona N, Glonti K, Bibby J, Cummins S, Finegood DT, et al. The need for a complex systems model of evidence for public health. The Lancet [Internet]. 2017 Jun 13 [cited 2017 Jun 17];0(0). Available from: http://www.thelancet.com/journals/lancet/article/PIIS0140-6736(17)31267-9/abstract