What happened to this group?
LBS
Paul Barrett
LBS: Two years and no posts. What happened? Has interest in the topic completely died out?
I suspect it’s a ‘done deal’ now among those who bother reading about such matters. There is nothing much left to talk about apart from restating the “bleeding obvious”!
For me, Joel Michell and Mike Maraun between them have set out precisely the conditions required to instantiate a claim of quantity and ’measurement’.
Apart from the occasional defence of “anything goes/It’ll be alright on the night” articles like that from Bringmann, L.F., & Eronen, M.I. (2015). Heating up the measurement debate: What psychologists can learn from the history of physics. Theory and Psychology, In Press, , 1-17, most psychologists simply ignore the entire issue and concentrate on using MPLUS, SEM, ESEM, and inventing variants of a variety of latent-variable-oriented claptrap.
I’m also a huge fan of James Grice’s Observational Oriented Modeling, as a way of exploring causal explanatory theory that does not invoke the quantity assumptions, but works very nicely with qualities and orders.
He has a nice article: Grice, J. (2015). From means and variances to persons and patterns. Frontiers in Psychology: Quantitative Psychology and Measurement (http://dx.doi.org/10.3389/fpsyg.2015.01007 ), 6:1007, , 1-12, followed by some lively debate with a dyed-in-the-wool psychology ‘quant‘ statistician, obsessed with probability as a means to undertanding cause.
However, as David Deutsch, the quantum physicist said recently:
“PROBABILITY theory is a quaint little piece of mathematics. It is about sets of nonnegative numbers that are attached to actual and possible physical events, that sum to 1 and that obey certain rules. It has numerous practical applications. So does the flat-Earth theory: for instance, it’s an excellent approximation when laying out your garden. ”
And
“Similarly, conceiving of the world as being literally probabilistic may not prevent you from developing quantum technology. But because the world isn’t probabilistic, it could well prevent you from developing a successor to quantum theory. In particular, constructor theory – the framework that I have advocated for fundamental physics, within which I expect successors to quantum theory to be developed – is deeply incompatible with physical randomness. ”
It’s from an interesting opinion-piece in the 30th September, New Scientist magazine, Entitled: Probability is as useful to physics as flat- Earth theory
But that’s just me … I’m now much more interested in the computational modeling/exploration of the causes of psychological and other related phenomena, evolved over time.
Regards .. Paul
Chief Research Scientist
Cognadev.com
__________________________________________________________________________________
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Caroline Long
>>> LBS <benjami...@monash.edu> 12/08/15 6:45 AM >>>
Garett Howardson
Assistant Professor of Psychology
Paul Barrett
Hello Garrett
Specifically, how might one pursue the computational modeling aspects of psychology without acknowledging some sort of continuum?
Easily. You just acknowledge you have no evidence for demonstrating a phenomenon varies as a particular form of continuum.
But, in most cases we can distinguish ‘good enough’ orders and classes .. but have no idea if these represent a continuum whose magnitudes can be represented by the real number system or just a crude one fashioned from a few simple ordered classes.
So, you accept that research right now is about establishing evidence-bases about the causes of orders and classes of psychological attributes/phenomenal outcomes- where accurate claims of causal effect is limited to ‘good enough’ orders and classes of things, and ‘good enough’ classifications of outcomes.
Fact is we can barely achieve that right now unless we begin with very broad classes and categories of ‘things’, or where the outcome can actually be counted (as in actuarial recidivist risk assessment).
But, I’m talking about the kinds of psychological attributes which are found in areas of research like personality, motivation, emotionality, pathological behaviours, consciousness, values, morality, with outcomes drawn from a variety of real-world phenomena associated with day-to-day living, work, and ‘just being alive’.
For me, I’ll use quantitative relations as a handy way of working with data, along with hand-crafted,ad-hoc ‘production-rule’ algorithms - but remembering that any precision afforded by those numbers is illusory. But then, I only seek to predict ‘good enough’ outcomes which are invariably categories or ordered classes.
When I say ‘good enough’, in a very real sense I’m using the concept of Brunswik Symmetry here (Werner Wittman .. see http://www.osi.uni-mannheim.de/unterdokumente/sanfrancisco_2007/www_sanfrancisco_2007.pdf) where I’m accepting that right now claims of precise measurement or precise outcomes is technically impossible - so I’m working across the outer boundaries of both sides of the “Lens’.
If someone wants to invoke physics SI-extensive/derived unit assumptions for their latent variables or whatever, that’s fine. But, I do ask them to justify that assumption beyond - “it’s what MPLUS or whatever statistical methods I’m using require I must assume this”. For example, I’m always interested to hear why someone thinks a nebulous construct like Extraversion, Leadership, Employee Engagement, or Intelligence varies in the manner of electric current.
Same as those who use conventional statistical methodologies .. I just provide a little reminder to them to go read:
Freedman, D.A., & Berk, R.A. (2003). Statistical assumptions as empirical commitments. In T.G. Blomberg & S.Cohen (Eds.). Law, Punishment, and Social Control: Essays in Honor of Sheldon Messinger, 2nd ed. (pp. 235-254). Aldine de Gruyter.
For me Garrett, none of this is at all difficult anymore. I can conceive of doing excellent research without invoking any assumptions about quantity or continua. As evidence accrues, explanatory accuracies increases, and ‘normative rules surrounding the detection and measurement of a phenomenon’ begin to cohere, it may well be possible to reconsider/redefine the status of either the quantity or continuum assumptions.
But right now I think we may be dealing with eqifinality and multifinality, with synergistic response functions. To untangle these requires much more thought and analysis approaches than a few linear or conventional non-linear statistics and associated assumptions of quantity and continua.
Hence, I like the possibilities offered by program such as Netlogo (https://ccl.northwestern.edu/netlogo/ )- you only have to run the altruism vs selfish population simulations to see the value of such work as a means to explore ideas about causality.
But, this kind of non-quantitative exploratory work requires an adherence to technically-specified theory-claims and evolved-over-time modeling, where all assumptions are stated in advance and directly embedded in the code. In a sense, it’s like psychological engineering .. you seek to build-simulate and physically test that which a theory of the causes of a phenomenon say should be so.
As I say, this just me. Whether or not Michell “takes some liberties with the history of mathematical philosophy.” is irrelevant to me. What mattered greatly to me was his presentation of the axioms of quantity, classical measurement theory, and the manner in which natural scientists produced a body of empirical work in phenomenon detection and accompanying explanatory theory for those phenomena, ending up where we are now with the SI unit measurement system.
While I was reading Michell, I was also reading Stehle, P. (1994). Order, Chaos, Order: The Transition from Classical to Quantum Physics. Oxford University Press. ISBN: 0-19-507513-7. Two centuries spanning non-quantitative physics to that numerically precise physics we take for granted now.
Anyway, I think it’s time others perhaps responded with their views (if any) - and I took a back-seat. I really don’t have anything of any real interest to say or argue about, as it all seems so ‘obvious’ to me now.
But then, I gave up the notion of measuring any psychological attribute or ‘psychologically interesting’ real-world outcome as a ‘quantity’ many years ago. Which opened up many new imaginative ways to think about phenomenon detection, cause, analysis techniques, and the simple contrast between pragmatic vs scientific modes of working.
However, I have to do all this in my ‘spare time’ as my day job is working for a commercial test-publisher/consultancy organization. I was once told to apply to the Santa Fe Institute (http://www.santafe.edu/) … I should have done so at the time (many years ago)! I suspect it is only in such an institution where this kind of ‘next generation’ exploratory causal theory and research could ever be attempted. Ah well, such is life!
Regards .. Paul
Chief Research Scientist
Cognadev.com
__________________________________________________________________________________
Paul Barrett
Hello Garett,
sorry for misspelling your name in my previous email!
Regards .. Paul
Chief Research Scientist
Cognadev.com
__________________________________________________________________________________
From: talking-m...@googlegroups.com [mailto:talking-m...@googlegroups.com] On Behalf Of Garett Howardson
Sent: Wednesday, December 9, 2015 3:46 AM
To: talking-m...@googlegroups.com
Garett Howardson
Specifically, how might one pursue the computational modeling aspects of psychology without acknowledging some sort of continuum?
Easily. You just acknowledge you have no evidence for demonstrating a phenomenon varies as a particular form of continuum.
But, in most cases we can distinguish ‘good enough’ orders and classes .. but have no idea if these represent a continuum whose magnitudes can be represented by the real number system or just a crude one fashioned from a few simple ordered classes.
So, you accept that research right now is about establishing evidence-bases about the causes of orders and classes of psychological attributes/phenomenal outcomes- where accurate claims of causal effect is limited to ‘good enough’ orders and classes of things, and ‘good enough’ classifications of outcomes.
Fact is we can barely achieve that right now unless we begin with very broad classes and categories of ‘things’, or where the outcome can actually be counted (as in actuarial recidivist risk assessment).
But, I’m talking about the kinds of psychological attributes which are found in areas of research like personality, motivation, emotionality, pathological behaviours, consciousness, values, morality, with outcomes drawn from a variety of real-world phenomena associated with day-to-day living, work, and ‘just being alive’.
For me, I’ll use quantitative relations as a handy way of working with data, along with hand-crafted,ad-hoc ‘production-rule’ algorithms - but remembering that any precision afforded by those numbers is illusory. But then, I only seek to predict ‘good enough’ outcomes which are invariably categories or ordered classes.
When I say ‘good enough’, in a very real sense I’m using the concept of Brunswik Symmetry here (Werner Wittman .. see http://www.osi.uni-mannheim.de/unterdokumente/sanfrancisco_2007/www_sanfrancisco_2007.pdf) where I’m accepting that right now claims of precise measurement or precise outcomes is technically impossible - so I’m working across the outer boundaries of both sides of the “Lens’.
If someone wants to invoke physics SI-extensive/derived unit assumptions for their latent variables or whatever, that’s fine. But, I do ask them to justify that assumption beyond - “it’s what MPLUS or whatever statistical methods I’m using require I must assume this”. For example, I’m always interested to hear why someone thinks a nebulous construct like Extraversion, Leadership, Employee Engagement, or Intelligence varies in the manner of electric current.
Same as those who use conventional statistical methodologies .. I just provide a little reminder to them to go read:
Freedman, D.A., & Berk, R.A. (2003). Statistical assumptions as empirical commitments. In T.G. Blomberg & S.Cohen (Eds.). Law, Punishment, and Social Control: Essays in Honor of Sheldon Messinger, 2nd ed. (pp. 235-254). Aldine de Gruyter.
For me Garrett, none of this is at all difficult anymore. I can conceive of doing excellent research without invoking any assumptions about quantity or continua. As evidence accrues, explanatory accuracies increases, and ‘normative rules surrounding the detection and measurement of a phenomenon’ begin to cohere, it may well be possible to reconsider/redefine the status of either the quantity or continuum assumptions.
But right now I think we may be dealing with eqifinality and multifinality, with synergistic response functions. To untangle these requires much more thought and analysis approaches than a few linear or conventional non-linear statistics and associated assumptions of quantity and continua.
Hence, I like the possibilities offered by program such as Netlogo (https://ccl.northwestern.edu/netlogo/ )- you only have to run the altruism vs selfish population simulations to see the value of such work as a means to explore ideas about causality.
adherence to technically-specified theory-claims and evolved-over-time modeling, where all assumptions are stated in advance and directly embedded in the code. In a sense, it’s like psychological engineering .. you seek to build-simulate and physically test that which a theory of the causes of a phenomenon say should be so.
As I say, this just me. Whether or not Michell “takes some liberties with the history of mathematical philosophy.” is irrelevant to me. What mattered greatly to me was his presentation of the axioms of quantity, classical measurement theory, and the manner in which natural scientists produced a body of empirical work in phenomenon detection and accompanying explanatory theory for those phenomena, ending up where we are now with the SI unit measurement system.
Paul Barrett
Hello Garett!
Would you disagree that the distinction between continuous and class-based evidence is itself a class-based form of reasoning? If so, such perspective pre-supposes that at the highest, most abstract level of scientific conceptualization achievable (classes or continua) exists a class. Speaking formally in mathematics, we can also think of a class as a set of mathematical objects.
So in other words, your argument seems to state that the most abstract conceptualization of scientific psychology possible is a set (let's call it aleph-naught) containing at least two objects: sub-classes/sub-orders and a continua. This still brings us back to the problem how we can know that aleph-naught is itself not a member of an even higher-yet order set/class, which is the classic problem of Russell's paradox and Gödel's, Turing's and Church's work showing that we cannot know what the highest level of abstraction is, we can only use human judgement and logic to figure that out, which I don't think disagrees with your stance.
Probably! All I’m saying is that without evidence to date showing that a psychological attribute varies as a continuous quantity, or any theory that claims (with some kind of formal justification) that an attribute should vary in this manner, I’m reduced to exploration of phenomena which starts from a more ‘gentle’ position where I can at least provide some kind of reasoned justification for looking at classes or orders. The ‘ideal’ goal within this perspective is to provide a body of work that begins to inform us just how an attribute varies, what is causal for it, and whether or not something more precise than a broad classification can be imposed on the observed variations. I don’t have any more ambition than that right now.
Have you ever read about Brouwer's choice sequences? It's an interesting compromise between the classes and continua perspective that directly relies on the mathematician's judgement. This type of work was developed in reaction to the axiomatic approach (championed by the Greek's and Hilbert) from which Michell draws (and the logical paradigm of Russell).
I’m afraid not. But then I’m not looking to impose a continuum model of any variety other than the most basic ordered-class, then if I can show that I can at least explain these broad ‘classes’, begin to further refine the possible ‘gaps’ between the broad classes, and determine whether a theory I have in mind (fed by previous research) can account for a more refined set of orders, and so on.
However, it goes back to the problem that we cannot know for certain how good those axioms are in an algorithmic way and must always (at least for now) rely on human judgment (e.g., Church, Turing, Gödel).
But, the axioms do define ‘quantity’, and we know they work in practice from the success of physics and its SI-unit system. Whether or not they are ‘true’ is immaterial given their success right now as the definition of quantity. Until someone shows they do not work as ‘stated’ (there is evidence to show they are not definitional of a quantity), they stand. And I think Michell’s 2012 article goes hand-in-hand with a further understanding of why the axiomatic definition works in practice ... Michell, J. (2012). Alfred Binet and the concept of heterogeneous orders. Download link:
http://www.frontiersin.org/quantitative_psychology_and_measurement/10.3389/fpsyg.2012.00261/abstract . Frontiers in Quantitative Psychology and Measurement, 3, 261, 1-8.
What's more, in response to the Feynman in that symposium lecture, I don't think he was too fond of the pure axiomatic approach to mathematics arguing that scientists tend to become too obsessed with proving the statements from axiom to conclusion that we overlook actual relationships in observed data. To be sure this seems to fit with your overall view but it simultaneously casts doubt in beginning with such axioms of measurement as truth.
Agreed. But I never claim the axioms are true; merely that right now there is no evidence to suggest they fail to account for how known ‘quantities’ vary in the manner that they do. A realist position if you like.
In a sense, I may have taken up what looks like a very sloppy position to some. I’m just saying “I don’t know how or why any psychological attribute should vary as a quantity; I’m not even sure how to define any attribute in such a way that it’s meaning is precisely specified and agreed upon by all researchers”. So, under those conditions, I’m seeing what another kind of approach to exploring the causes of phenomena in psychology might reveal; one that begins with Mike Maraun’s “Common or Garden” concepts .. and works from there to see if anything more is possible to attain. I’m the man (along with J.P. Rolland) who showed the lunacy of any meta-analysis when you have no consistent/precise definition of any construct (http://www.pbarrett.net/stratpapers/metacorr.pdf ). This is the reality of working within psychology today.
We have a rough idea about a lot, can make some good generalizations, can on rare occasions even be 100% accurate in our predictions of critical societal outcomes, but we lack any kind of accurate causal explanatory theory, let alone justifications for quantitative measurements of psychological phenomena/attributes.
However, some have come close. Two cases come to mind:
1) Metametrics Inc and the development of the Lexile measure (using experimentation and subsequent IRT models to develop measures of reading ability). Andrew Kyngdon provided a fine expository article on this whole venture (Kyngdon, A. (2013). Descriptive theories of behaviour may allow for the scientific measurement of psychological attributes. Theory and Psychology, 23, 2, 227-250.)
https://www.metametricsinc.com/
2) The British Army Ability Battery (using cognitive design theory/experiment results to construct items whose difficult is accurately predicted in advance of any presentation).
I’ve just reviewed this book for Personality and Individual Differences .. an utterly amazing feat of 25 years of assessment design, calibration, and deployment by the Plymouth University (UK) research team. I concluded the review:
“1. Joel Michell and others have repeatedly spoken of the need to understand what is causal for a ‘stimulus’, and how the response is entailed, before wandering off into advanced quantitative psychometric and statistical models which require attributes to vary quantitatively for their measurement claims to be considered valid. But that is precisely what the Plymouth team did, develop a clear picture of what was to be assessed, determine what is causal for variation in responses, and then develop a generative grammar which would produce items with a known difficulty. The only other research team I know of who really took the time to do the same are those at MetaMetrics Inc., under the leadership of Jack Stenner. A recent article by one of its previous senior scientists explains just how they did this (Kyngdon, 2013) as part of the overall construction of the Lexile framework for assessing/measuring reading ability.
2. While the Plymouth team chose to stay within a quantitative analysis framework, from my understanding and perspective having read the book, everything they achieved was perfectly possible if they had adopted methods of data analysis (e.g. reliability estimation, validity studies etc.) less dependent upon any assumptions of quantity, let alone ‘true scores’. I do not want to belabour this point as it is irrelevant to the content of the book. Computer generation of items with known difficulties works; BARB works.
In conclusion, this is a landmark book, not just for its description of a 25-30 year research project, its historical accounts of military research, and the sheer span and logistics of its problem area, but also with respect to its intellectual stimulus for the next generation of innovative test design. For every PhD student capable of computer programming (Java/Javascript, VB, Delphi, C++), and wanting to undertake a thesis project in some area of psychological assessment, think about what you might be able to undertake now you have the information and knowledge imparted by this book. Likewise for every large corporate test-publisher R&D department being persuaded to undertake some kind of latent variable or IRT-CAT development as ‘the next product’, don’t. Read this book cover to cover, and think very carefully about what this research team have shown, and what else might now be done as a possible extension of that work.”
Jageshwar Sungkur
Hi Paul,
Often
in science
we are
called upon
to make
grand pronouncements
about our
objects of study.
What is
the nature
of this
phenomenon to
which we
have become
so attached,
which we
have labored over, and tended to in loving detail?
Standard practice is to put forth a grand unified theory, or GUT. A GUT hews to the scientific ideal of parsimony by describing a phenomenon in terms of necessary and sufficient conditions, often with a single rule. When a grand unified theory fails, it is assumed that we have simply articulated the wrong one. But what if our failure is not imperfect knowledge of our pet phenomenon, but a misapprehension that a good theory will be able to shoehorn everything into a fundamental law?
An impediment to would-be grand unified theories is that many natural phenomena—particularly those within the psychological sciences—do not have well-defined boundaries or a clear center of gravity. Call these psychological nebulae: rather than rigid, self-contained modules, they are an indistinct cluster of partially overlapping clouds, with foggy tendrils expanding into many domains. Nebulae are ill-suited to apprehension by grand unified theories. Such one-dimensional models leave off so much explanatory desiderata that they are doomed to be completely, comedically inadequate.
The fetishization of parsimony means that unwieldy theories are often dismissed on these grounds alone. But it is the theories which are unafraid of chaos that are best able to handle nebulae. Messy theories should not only be tolerant of penumbral fuzz around the edges, but receptive to the possibility that the nebula contains no central, essential core. No doubt there is something less satisfying about settling for inelegance, but the best theories won’t always feel right. Elegance is not a suitable heuristic for veracity. Good theory-making retains all important details, no matter how awkwardly they cleave to the rest of the phenomenon.This process is still capable, though, of judiciously slicing away the flimsiest proposals. Good theories are just parsimonious enough.
Since nebulae crop up across multiple disciplines, they benefit from scholastic opportunism. Meaningful contributions can be made by conceptual analysis, informal observation, introspection, and phenomenological methods more generally. But it is crucial to separate what this sort of evidence can provide and what it cannot. The chief value of these perspectives is idea generation, and a check against the ever-narrowing focus encouraged by the grand unified theory tradition. Phenomenology can resonate with us, it can lend a patina of understanding, but it is not equivalent to an empirical claim. If our goal is to get at truth and not just truthiness, we must defer to data
Under ideal circumstances, a theory carves nature at its joints. But this is only possible when nature is jointed. In selecting what type of theory to build, we should consider the properties of the phenomenon we are trying to grasp. Complex phenomena require more convoluted, nuanced explanations than have traditionally been marshaled for this task. Given their heterogeneity and unboundedness, it is possible that some nebulae can never be fully captured by any theory, no matter how inclusive. The goal of nebular theories may be less about definitive truths than postulating relationships between entangled systems and creating novel testable hypotheses. Their virtue lies not in their finality, but their ability to slouch us towards an incrementally better understanding of a sprawling, deeply intricate spectacle.
Strohminger, N. (2014). The Meaning of Disgust: A Refutation. Emotion Review, 6(3), 214-216. Doi 10.1177/1754073914523072
Sent: Thursday, 10 December 2015 9:56 a.m.
To: talking-m...@googlegroups.com
Subject: RE: [talking-measurement] What happened to this group?
Paul Barrett
Thanks Jag .. that is a very nice article, it resonates well with my perspectives. Another one for the database‼
Regards .. Paul
Chief Research Scientist
Cognadev.com
__________________________________________________________________________________
Garett Howardson
Would you disagree that the distinction between continuous and class-based evidence is itself a class-based form of reasoning? If so, such perspective pre-supposes that at the highest, most abstract level of scientific conceptualization achievable (classes or continua) exists a class. Speaking formally in mathematics, we can also think of a class as a set of mathematical objects.
So in other words, your argument seems to state that the most abstract conceptualization of scientific psychology possible is a set (let's call it aleph-naught) containing at least two objects: sub-classes/sub-orders and a continua. This still brings us back to the problem how we can know that aleph-naught is itself not a member of an even higher-yet order set/class, which is the classic problem of Russell's paradox and Gödel's, Turing's and Church's work showing that we cannot know what the highest level of abstraction is, we can only use human judgement and logic to figure that out, which I don't think disagrees with your stance.
Probably! All I’m saying is that without evidence to date showing that a psychological attribute varies as a continuous quantity, or any theory that claims (with some kind of formal justification) that an attribute should vary in this manner, I’m reduced to exploration of phenomena which starts from a more ‘gentle’ position where I can at least provide some kind of reasoned justification for looking at classes or orders. The ‘ideal’ goal within this perspective is to provide a body of work that begins to inform us just how an attribute varies, what is causal for it, and whether or not something more precise than a broad classification can be imposed on the observed variations. I don’t have any more ambition than that right now.
- One should at a minimum have a reasoned set of self-consistent statements to justify the stated nature of the phenomenon.
- Ideally, one should also have observable evidence supporting the validity of conclusions drawn from these statements.
- Without adequate evidence supporting the superiority of one set of self-consistent statements over another, one should choose the more parsimonious and logically defensible set of statements.
- Applying this line of reason to psychological measurement suggests that we should prefer class- and order-based sets of statements over set of statements derived from assuming a continuum because the class- and order-based perspective is more parsimonious and logically defensible.
Paul Barrett
Hello Garett
In response to my:
“All I’m saying is that without evidence to date showing that a psychological attribute varies as a continuous quantity, or any theory that claims (with some kind of formal justification) that an attribute should vary in this manner, I’m reduced to exploration of phenomena which starts from a more ‘gentle’ position where I can at least provide some kind of reasoned justification for looking at classes or orders.”
You ask:
Is it really logically defensible to claim that class- and order-based perspectives are more parsimonious than continuum-based perspectives? Perhaps this is the case if every single observation fits neatly into one class/order but not others. I do, however, think it is perfectly defensible and logically consistent to think about psychological and behavioral observations that veridically belong to multiple classes/orders of 'things.'
Let’s take two concrete examples:
1. Psychopathy. It is easy to distinguish real, nasty psychopaths - the kind that end up in high security forensic psychiatric hospitals from those who behave quite differently .. we can even develop a checklist of psychological attributes and behaviours, index offence magnitude, type, and frequency which can be completed by a trained interviewer or from offender/patient records. But, are we dealing with a continuum of psychopathy or a class-category difference? Legally and as far as the public are mainly concerned, we are dealing with a class-category based upon perceptions of the most famous psychopaths who make public news - whether children or adult. They are few and far between relatively speaking. But many psychologists now choose to view psychopathy as a linearly measurable, additive-unit metric continuum, with no evidence at all that the attribute (which is remains loosely defined) does indeed vary as a continuum.
Me, I can only say my impression after having seen the offender/patient records of some very high scorers on the PCL-R (in my stint as Chief Scientist at two of the UK’s High Security Forensic Psychiatric Hospitals) - they seem qualitatively different from those who score in a mid-range. The “score” is simply a sum of discrete ‘events/checklist items’ associated with observations of their behaviours). However, that’s just my impression. But, without any means of showing that a unit increase in a score equates to something observable, why should I think I’m justified in assuming I’m dealing with a continuum at all?
Perhaps I could order people .. but again, is the absence of an observation indicative of anything? i.e. a low ‘scorer’ might have no criminal record, no index offence, no obvious aggressive tendencies etc., never experienced trouble at school ..
In a continuum view, what exactly is ‘no psychopathy or a tiny amount of’ compared to saying a person either is or is not a psychopath? That class-category judgment can be made pretty well, and has identifiable real-world consequences (in terms of risk of violence and recidivism). One can even work like this with ordered categories on a violent recidivism risk assessment which incorporates the PCL-R score as a series of ordered categories - where the highest category Violence Risk Assessment score (9) is associated with 100% certainty of recidivist risk.
2. Conscientiousness. Here we can distinguish between people who show a variety of behaviours we would all agree - more or less - as being indicative of showing/being conscientious. But, it is ‘more or less, good-enough’; it is not precise because we have no precise definition of what “Conscientious” actually means. We have what Mike Maraun has termed “a common-or-garden’ understanding of the meaning.
Many psychologists play number games with this attribute, slicing and dicing semantics, scales, items, whatever to arrive at a real-valued continuum variable via latent variable analysis of one form or another. Yet, because the meaning of Conscientiousness is fuzzy (see the white paper I created with J.P. Rolland http://www.pbarrett.net/stratpapers/metacorr.pdf - which showed the conflicting situation that exists with population-estimate meta-analyses), how can anyone seriously propose Conscientiousness varies as a quantity? At best it would seem a few simple orders are all we can claim right now, until we can establish how we would ever detect the difference between a few ordered classes, then show empirically we can do so.
And, I don’t want to get precious here - in many cases I’ll use simple sum-score test scores and quantitative forms of analysis out of sheer convenience - but I’m always aware of the illusory precision afforded by such methods, and balance any interpretation or use of such results with that knowledge.
But I’m curious - where does this line of argument enter into any of the issues above?
The benefit in using continuum-based views over discrete views is that the continuous probability distributions have been long researched in mathematics and many of the functions are well behaving, well-understood, and supported both deductively and analytically. Conversely, the understanding of probability for discrete states is in its relative infancy (e.g., Quantum Theory, Complexity Theory).
Whether or not particular functions are well-described in mathematics or probability theory is irrelevant (in my mind) to the two questions that I ask myself:
1. Can I even define beyond “good enough/more or less’ what it is I claim to be ‘measuring/classifying’? If not, why should I assume something with such a definition should vary continuously? Everything I’m doing and dealing with is ‘fuzzy/good enough for now/more or less’. I don’t have a single theory to work with which stands more than idle scrutiny - such is the poverty of technically-specified explanatory theory in psychology.
2. Even if I wanted to assume a ‘continuum’ for an attribute - how will I be able to distinguish between my proposed units of the attribute within that continuum, external to the numerical difference? That is, if I assign someone a latent score of 2.35 and 2.46 on Engagement, what does that 0.11 unit difference actually mean (in what way can I observe that difference beyond the numerical arithmetic)? When I can answer that question, I agree that making the assumption of a continuum becomes a realistic proposition, which can now be tested empirically.
As a closing example, an infinite number of discrete physical states can be described using Cartesian space to simplify physical reality and distill down the phenomenon from infinity to four continuous dimensions of length, width, height, and displacement/time (i.e., General Relativity)*.
Would you agree that four is more parsimonious than the infinite?
Of course. But look at the properties of those four dimensions - extensive variables with simple ways of understanding/demonstrating the additive variation of each.
Now do the same for Leadership. Where do you even begin - and with what? As someone has said - we all recognize Leadership when we see it, but we can’t define it in such a way that it is ‘normative’ and specified ‘technically’. In short, multiple definitions exist for something that we speak of day-to-day in terms of a few simple orders; without a clue what a continuum of ‘leadership’ would even look like, far less what unit-differences might indicate.
I hope I’m explaining more coherently why I’m choosing to work with fuzzy orders and classes - where the kind of meaning-related ‘errors’ I’m dealing with swamp any mathematical representation. That may change over time, as more evidence might accrue about how an attribute does actually vary.
I wouldn’t even call my approach parsimonious - more like ‘what else can I do without making even more assumptions that I’m making now”?
And as to: I hope you don't think that anything I said above is too abrasive (I'll absolutely own the wordiness though!). Not an issue at all. The more direct/clear we are, the better we (and anyone else reading anything we say!) can understand each others’ position/lines of argument (or my rather pitiful-sounding ‘what else can I do without making even more assumptions that I’m making now”?‼).
Visit this group at https://groups.google.com/group/talking-measurement.