philosophy of science – … And Out Come the Systems

I recently had a great experience with a StackOverflow question, when I was thinking about how to visualise ordinal data. This post shows an option for how to do that. Code for the plots is in the end of this post.

Update: here’s an FB discussion, which mentions e.g. a good idea of making stacked % graphs (though I like to see the individuals, so they won’t sneak up behind me) and using the package TramineR to visualise and analyse change.

Update 2: Although they have other names too, I’m going to call these things flamethrower plots. Just because it reflects the fact, that even though you have the opportunity to do it, it may not always be the best idea to apply them.

Say you have scores on some likert-type scale questionnaire items, like motivation, in two time points, and would like to visualise them. You’re especially interested in whether you can see detrimental effects, e.g. due to an intervention. One option would be to make a plot like this: each line in the plot below is one person, and the lighter lines indicate bigger increases in motivation scores, whereas the darker lines indicate iatrogenic development. The data is simulated so, that the highest increases take place in the item in the leftmost plot, the middle is randomness and the right one shows iatrogenics.

I have two questions:

Do these plots have a name, and if not, what should we call them?
How would you go about superimposing model-implied-changes, i.e. lines showing that when someone starts off at, for example, a score of four, where are they likely to end up in T2?

flaming pillars

The code below first simulates 500 participants for two time points, then draws plot. If you want to use it on your own data, transform the variables in the form scaleName_itemNumber_timePoint (e.g. “motivation_02_T1”).

<br /># Simulate data:
data <- data.frame(id = 1:500,
Intrinsic_01_T1 = sample(1:5, 500, replace = TRUE),
Intrinsic_02_T1 = sample(1:5, 500, replace = TRUE),
Intrinsic_03_T1 = sample(1:5, 500, replace = TRUE),
Intrinsic_01_T2 = sample(1:5, 500, replace = TRUE, prob = c(0.1, 0.1, 0.2, 0.3, 0.3)),
Intrinsic_02_T2 = sample(1:5, 500, replace = TRUE),
Intrinsic_03_T2 = sample(1:5, 500, replace = TRUE, prob = c(0.3, 0.3, 0.2, 0.1, 0.1)))

pd <- position_dodge(0.4) # X-axis jitter to make points more readable

# Draw plot:

data %>%
tidyr::gather(variable, value, -id) %>%
tidyr::separate(variable, c("item", "time"), sep = "_T") %>%
dplyr::mutate(value = jitter(value, amount = 0.1)) %>% # Y-axis jitter to make points more readable
group_by(id, item) %>%
mutate(slope = (value[time == 2] - value[time == 1]) / (2 - 1)) %>%
ggplot(aes(x = time, y = value, group = id)) +
geom_point(size = 1, alpha = .2, position = pd) +
geom_line(alpha = .2, position = pd, aes(color = slope), size = 1.5) +
scale_color_viridis_c(option = "inferno")+
ggtitle('Changes in indicators of motivation scores') +
ylab('Intrinsic motivation scores') +
xlab('Time points') +
facet_wrap("item")

In the post-replication-crisis world, people are increasingly arguing, that even applied people should actually know what they’re doing when they do what they call science. In this post I expand upon some points I made in these slides about the philosophy of science behind hypothesis testing in interventions.

How does knowledge grow when we do intervention research? Evaluating whether an intervention worked can be phrased in relatively straightforward terms; “there was a predicted change in the pre-specified outcome“. This is, of course, a simplification. But try and contrast it with the attempt to phrase what you mean when you want to claim how the intervention worked, or why it did not. To do this, you need to spell out the program theory* of the intervention, which explicates the logic and causal assumptions behind intervention development.

* Also referred to as programme logic, intervention logic, theory-based (or driven) evaluation, theory of change, theory of action, impact pathway analysis, or programme theory-driven evaluation science… (Rogers, 2008). These terms are equivalent for the purposes of this piece.

The way I see it (for a more systematic approach, see intervention mapping), we have background theories (Theory of Planned Behaviour, Self-Determination Theory, etc.) and knowledge from earlier studies, which we synthesise into a program theory. This knowledge informs us about how we believe an intervention in our context would achieve its goals, regarding the factors (“determinants”) that determine the target behaviour. From (or during the creation of) this mesh of substantive theory and accompanying assumptions, we deduce a boxes-and-arrows diagram, which describes the causal mechanisms at play. These assumed causal mechanisms then help us derive a substantive hypothesis (e.g. “intervention increases physical activity”), which informs a statistical hypothesis (e.g. “accelerometer-measured metabolic equivalent units will be statistically significantly higher in the intervention group than the control group”). The statistical hypothesis then dictates what sort of observations we should be expecting. I call this the causal stream; each one of the entities follows from what came before it.

The inferential stream runs to the other direction. Hopefully, the observations are informative enough so that we can make judgements regarding the statistical hypothesis. The statistical hypothesis’ fate then informs the substantive hypothesis, and whether our theory upstream get corroborated (supported). Right?

Not so fast. What we derived the substantive and statistical hypotheses from, was not only the program theory (T) we wanted to test. We also had all the other theories the program theory was drawn from (i.e. auxiliary theories, A_t), as well as an assumption that the accelerometers measure physical activity as they are supposed to, and other assumptions about instruments (A_i). Not only this, we assume that the intervention was delivered as planned and all other presumed experimental conditions (C_n) hold, and that there are no other systematic, unmeasured contextual effects that mess with the results (“all other things being equal”; a ceteris paribus condition, C_p).

Program_link tells.png

We now come to a logical implication (“observational conditional”) for testing theories (Meehl, 1990b, p. 119, 1990a, p. 109). O_i is the observation of an intervention having taken place, and O_p is an observation of increased physical activity:

(T and A_t and A_i and C_n and C_p) → (O_i → O_p)

[Technically, the first arrow should be logical entailment, but that’s not too important here.] The first bracket can be thought of as “all our assumptions hold”, the second bracket as “if we observe the intervention, then we should observe increased physical activity”. The whole thing thus roughly means “if our assumptions (T, A, C) hold, we should observe a thing (i.e. O_i → O_p)”.

Now here comes falsifiability: if we observe an intervention but no increase in physical activity, the logical truth value of the second bracket comes out false, which also destroys the conjunction in the first bracket. By elementary logic, we must conclude that one or more of the elements in the first bracket is false – the big problem is that we don’t know which element(s) was or were false! And what if the experiment pans out? It’s not just our theory that’s been corroborated, but the bundle of assumptions as a whole. This is known as the Duhem-Quine problem, and it has brought misery to countless induction-loving people for decades.

EDIT: As Tal Yarkoni pointed out, this corroboration can be negligible unless one is making a risky prediction. See the damn strange coincidence condition below.

Program_link fails.png

EDIT: There was a great comment by Peter Holtz. Knowledge grows when we identify the weakest links in the mix of theoretical and auxiliary assumptions, and see if we can falsify them. And things do get awkward if we abandon falsification.

If wearing an accelerometer increases physical activity in itself (say people who receive an intervention are more conscious about their activity monitoring, and thus exhibit more pronounced measurement effects when told to wear an accelerometer), you obviously don’t conclude the increase is due to the program theory’s effectiveness. Also, you would not be very impressed by setups where you’d likely get the same result, whether the program theory was right or wrong. In other words, you want a situation where, if the program theory was false, you would doubt a priori that among those who increased their physical activity, many would have underwent the intervention. This is called the theoretical risk; prior probability p(O_p|O_i)—i.e. probability of observing increase in physical activity, given that the person underwent the intervention—should be low absent the theory (Meehl, 1990a, p. 199, mistyped in Meehl, 1990b, p. 110), and the lower the probability, the more impressive the prediction. In other words, spontaneous improvement absent the program theory should be a damn strange coincidence.

Note that solutions for handling the Duhem-Quine mess have been proposed both in the frequentist (e.g. error statistical piecewise testing, Mayo, 1996), and Bayesian (Howson & Urbach, 2006) frameworks.

What is a theory, anyway?

A lot of the above discussion hangs upon what we mean by a “theory” – and consequently, should we apply the process of theory testing to intervention program theories. [Some previous discussion here.] One could argue that saying “if I push this button, my PC will start” is not a scientific theory, and that interventions use theory but logic models do not capture them. It has been said that if the theoretical assumptions underpinning an intervention don’t hold, the intervention will fail, but that doesn’t make an intervention evaluation a test of the theory. This view has been defended by arguing that behaviour change theories underlying an intervention may work, but e.g. the intervention targets the wrong cognitive processes.

To me it seems like these are all part of the intervention program theory, which we’re looking to make inferences from. If you’re testing statistical hypotheses, you should have substantive hypotheses you believe are informed by the statistical ones, and those come from a theory – it doesn’t matter if it’s a general theory-of-everything or one that applies in very specific context such as the situation of your target population.

Now, here’s a question for you:

If the process described above doesn’t look familiar and you do hypothesis testing, how do you reckon your approach produces knowledge?

Note: I’m not saying it doesn’t (though that’s an option), just curious of alternative approaches. I know that e.g. Mayo’s error statistical perspective is superior to what’s presented here, but I’m yet to find an exposition of it I could thoroughly understand.

Please share your thoughts and let me know where you think this goes wrong!

With thanks to Rik Crutzen for comments on a draft of this post.

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. Paul Meehl’s wonderful seminar Philosophical Psychology can be found in video and audio formats here.

Bibliography:

Abraham, C., Johnson, B. T., de Bruin, M., & Luszczynska, A. (2014). Enhancing reporting of behavior change intervention evaluations. JAIDS Journal of Acquired Immune Deficiency Syndromes, 66, S293–S299.

Dienes, Z. (2008). Understanding Psychology as a Science: An Introduction to Scientific and Statistical Inference. Palgrave Macmillan.

Dienes, Z. (2014). Using Bayes to get the most out of non-significant results. Quantitative Psychology and Measurement, 5, 781. https://doi.org/10.3389/fpsyg.2014.00781

Hilborn, R. C. (2004). Sea gulls, butterflies, and grasshoppers: A brief history of the butterfly effect in nonlinear dynamics. American Journal of Physics, 72(4), 425–427. https://doi.org/10.1119/1.1636492

Howson, C., & Urbach, P. (2006). Scientific reasoning: the Bayesian approach. Open Court Publishing.

Lakatos, I. (1971). History of science and its rational reconstructions. Springer. Retrieved from http://link.springer.com/chapter/10.1007/978-94-010-3142-4_7

Mayo, D. G. (1996). Error and the growth of experimental knowledge. University of Chicago Press.

Meehl, P. E. (1990a). Appraising and amending theories: The strategy of Lakatosian defense and two principles that warrant it. Psychological Inquiry, 1(2), 108–141.

Meehl, P. E. (1990b). Why summaries of research on psychological theories are often uninterpretable. Psychological Reports, 66(1), 195–244. https://doi.org/10.2466/pr0.1990.66.1.195

Moore, G. F., Audrey, S., Barker, M., Bond, L., Bonell, C., Hardeman, W., … Baird, J. (2015). Process evaluation of complex interventions: Medical Research Council guidance. BMJ, 350, h1258. https://doi.org/10.1136/bmj.h1258

Rogers, P. J. (2008). Using Programme Theory to Evaluate Complicated and Complex Aspects of Interventions. Evaluation, 14(1), 29–48. https://doi.org/10.1177/1356389007084674

Shiell, A., Hawe, P., & Gold, L. (2008). Complex interventions or complex systems? Implications for health economic evaluation. BMJ, 336(7656), 1281–1283. https://doi.org/10.1136/bmj.39569.510521.AD

… And Out Come the Systems | Käyttäytymisarkkitehtuuri

Complex systems, health and well-being with uncertainty

Tag: philosophy of science

Assumptions, Schmassumptions; Did my intervention work or not?!

Visualising ordinal data with Flaming Pillars of Hell

The scientific foundation of intervention evaluation

What is a theory, anyway?

Evaluating intervention program theories – as theories