Measuring the Unmeasurable
Measuring the Unmeasurable
The Psychometrics of Life History Strategy 0 1 2
Stefan L. K. Gruijters 0 1 2
Bram P. I. Fleuren 0 1 2
Stefan L. K. Gruijters 0 1 2
0 Faculty of Psychology and Educational Sciences, Open University of the Netherlands , Heerlen , the Netherlands
1 Department of Work and Social Psychology, Maastricht University , Maastricht , the Netherlands
2 Bram P. I. Fleuren is a PhD candidate at the Faculty of Psychology and Neuroscience, Department of Work and Social Psychology, Maastricht University, the Netherlands. His current research mainly focuses on the topic of sustainable employability, and specifically its definition, its measurement as a formative construct, and its predictors. Further research interests include work and organizational and social psychology , evolutionary approaches to behaviour, and psychometrics
Within evolutionary biology, life-history theory is used to explain crossspecies differences in allocation strategies regarding reproduction, maturation, and survival. Behavioral scientists have recently begun to conceptualize such strategies as a within-species individual characteristic that is predictive of behavior. Although life history theory provides an important framework for behavioral scientists, the psychometric approach to life-history strategy measurement-as operationalized by K-factors-involves conceptual entanglements. We argue that current psychometric approaches attempting to identify K-factors are based on an unwarranted conflation of functional descriptions and proximate mechanisms-a conceptual mix-up that may generate unviable hypotheses and invites misinterpretation of empirical findings. The assumptions underlying generic psychometric methodology do not allow measurement of functionally defined variables; rather these methods are confined to Mayr's proximate causal realm. We therefore conclude that K-factor scales lack validity, and that life history strategy cannot be identified with psychometrics as usual. To align theory with methodology, suggestions for alternative methods and new avenues are proposed. Evolutionary biologists forwarded life-history (LH) theory to explain cross-species differences in allocation strategies with regard to reproduction, maturation, and survival (e.g., Stearns 1992). LH theory provides an evolutionary understanding of how species deal with the allocation of energetic resources. For any organism, a limited energetic
Life history strategy; Ultimate-proximate distinction; Measurement models; Psychometrics; Formative models; Latent variables; Validity
“budget” has to be earmarked both for the development and maintenance of a
welladapted organism and for reproductive activities. Because these reproductive and
somatic efforts are often mutually exclusive (e.g., time spent on growth of an organism
delays reproduction), this situation creates a LH optimization problem
That is, the LH problem entails that any increase of budget toward one fitness-relevant
goal (e.g., growing) has to be met by a decrease of investment toward other
(e.g., pubertal timing; Ellis 2004)
. Such investments involve fitness
(Garland 2014; Stearns 1989)
, and on both phylogenetic and ontogenetic
levels solutions to the LH problem are given shape. The best-suited solution (or, LH
strategy) arising in species during evolution (and in organisms during development) to
optimize the LH problem is in turn contingent on ecological conditions.
In addition to its importance as an evolutionary biological model, LH theory has
recently found application in evolutionary (approaches to) psychology
2009; Kaplan and Gangestad 2004)
. This extension of LH theory to psychology has
been accompanied by a psychometric approach relying on self-report instruments.
Figueredo and colleagues contributed extensively to the psychometric LH literature
by developing and testing various LH strategy measurement instruments
Figueredo et al. 2005, 2006, 2007, 2013, 2014; Olderbak et al. 2014)
Proposed measurement instruments include the Arizona Life-History Battery
Figueredo et al. 2007)
, the High-K strategy scale
(HKSS; Giosan 2006)
, the mini-K
(Figueredo et al. 2006)
, and the recently published K-SF-42
(Figueredo et al. 2017)
These questionnaires are designed to measure the differential K-factor that has its roots in
the work of
. Factor scores on such scales purportedly position individuals
on a dimension of fast to slow LH strategies, with fast strategies indicating a
psychological “orientation” toward increased reproductive efforts. These differential strategies are
assumed to be reflected by individual differences in, for example, risk-taking tendencies,
altruism and cooperation, and time preference
(e.g., Figueredo et al. 2006)
. Although the
K-factor exhibits considerable within-species heritable variation
(Figueredo et al. 2004)
individual differences are also thought to originate from the effects of early-life
experiences, through mechanisms allowing for developmental plasticity
(e.g., Frankenhuis and
de Weerth 2013; Nettle and Bateson 2015; Nettle et al. 2010, 2013)
A central assumption in the psychometric work on LH strategy is that these
strategies can be measured by examining development, cognition, and behavior, and
then aggregating this information to “diagnose” an individual’s LH strategy. For an
example, the mini-K uses indicators such as “I avoid taking risks,” “While growing up,
I had a close and warm relationship with my biological mother,” and “I would rather
have one than several sexual relationships at a time” to operationalize the latent
Kfactor (Table 1). Responses to such items are held to be (observable) manifestations of
the unobservable LH strategy. Broader conceptualizations of traits related to LH
strategy are proposed by super K-factors—such models forward additional variables
(e.g., personality) to cluster with lower-level LH traits
(e.g., Olderbak et al. 2014)
The present paper argues that current psychometric approaches to measuring LH
strategies using self-report methods face conceptual problems. These conceptual issues
render attempts to aggregate LH traits into K-factors a problematic practice, and
ultimately of little theoretical worth. To put the thrust of this paper concisely: In order
for LH strategy to be measured using a reflective latent variable measurement model,
the item scores in the measurement instruments need to (at least in theoretical potential)
represent reflections (i.e. effects) of a corresponding proximate mechanism. We
demonstrate that K-factors do not meet this criterion for a reflective latent variable and thus
do not succeed in measuring latent LH strategies. To arrive at this conclusion, the
distinction between formative and reflective measurement models is reviewed, and we
discuss the difference between “causal” and “effect” indicators. Second, the
ultimateproximate distinction in the evolutionary sciences and the position of LH strategies in
this dichotomy will be discussed. We end this conceptual discussion by providing
suggestions for new avenues in the psychometric approach to LH measurement.
Reflective and Formative Constructs
Many psychological constructs cannot directly be observed and measured, and researchers
in psychology consequently rely on indirect measurement instruments to quantify
individuals’ position on such latent (unobservable) psychological variables
(e.g., Bollen 2002;
Borsboom 2008; Borsboom, Mellenbergh, and van Heerden 2003)
. The literature is full of
variables that can be considered latent—such as personality and intelligence. These traits
are not directly measured; instead researchers measure their reflections (e.g., associated
behavior or utterances). LH strategy inventories, as measured using for instance the HKSS
or mini-K scale, also assume (both explicitly and implicitly) the existence of a single latent
variable involved in generating responses to the questionnaire items.
In principle, any measurement model of a latent variable used in psychological
science can take one of two general forms
(but see Bollen and Bauldry 2011)
standard measurement model in psychology is the reflective model
Borsboom et al. 2003)
, in which item-scores are seen to be caused by an underlying
latent variable. It is one’s actual position on the unmeasured latent math skill variable
that causes a particular answer to the question “Does two plus two equal four?”
Similarly, social psychologists consider variables such as “attitudes” latent variables,
measured by presumed reflections of the construct—for example, “Do you think object
X is pleasant?” In standard reflective psychometric factor models, then, such items are
modeled as “effect” indicators
(Bollen and Bauldry 2011; Edwards and Bagozzi 2000)
with the answers being caused by individuals’ position on the latent variable.
Recently, formative models have been recognized as an alternative method to
capture constructs for which reflective models are conceptually inappropriate
Bollen and Bauldry 2011; Diamantopoulos et al. 2008; Diamantopoulos and Siguaw
2006; Edwards 2011; Jarvis et al. 2003)
. Item-scores in a formative model are seen to
create a construct; in other words, the construct is a linear combination of the individual
items. A clear example of this is socioeconomic status (SES); there is no underlying
psychological process in individuals that corresponds to SES. Instead, SES is a social
construct of interest to researchers and can be seen to meaningfully cluster individuals’
characteristics. In other words, unlike a trait such as intelligence, we cannot assume that
SES exists independently of its measurement
(see Borsboom et al. 2003)
. To clarify this
using a metaphor, reflective models rely on logic of the form “the size of a fire can be
estimated by the volume of the smoke,” but in formative models, indicators (e.g.,
educational background for SES) deliver the fuel determining the size of the fire. This
difference in how observations are tied to their hypothesized constructs (as cause or
effect) is what defines reflective versus formative models
(Bollen and Bauldry 2011;
Borsboom et al. 2003; Edwards and Bagozzi 2000)
Figure 1 depicts an example of a construct measured using the responses to three
items. In panel A, the item scores are modeled as reflective indicators—an individual’s
position on the latent variable is assumed to cause item responses. Panel B illustrates a
formative model—the change of direction in the corresponding path (depicted with
arrows) corresponds to the notion that causation now flows from indicator toward the
construct. For instance, an individual’s response to questions assessing current income
and education level forms this individual’s relative position on the SES construct; the
information on such items linearly combines to create the construct.
Reflective models rely on a set of assumptions that need to be met to meaningfully
use methods such as confirmatory factor analysis. First, latent variables rely on the
principle of local independence, implying that given a particular latent variable, items
(e.g., Bollen 2002)
. This makes sense because when the latent variable
is thought of as a common cause of item responses, taking this latent variable into
account should (given measurement error) explain the correlations between these items.
These assumptions, in turn, only make sense given an ontological assumption about
latent variables: For latent variables to exert causal influence on item responses they
need to exist in individuals’ psychology
(Borsboom et al. 2003, 2004)
. If this
ontological assumption does not hold for a given construct, then reflective models do not make
much conceptual sense
(Borsboom et al. 2003; see also Gruijters 2017)
. For example,
the existence of a mechanism corresponding to intelligence is hypothesized to cause
responses to items on an intelligence test, which explains why items become
independent after conditioning the items on this common cause. Multiple indicators of a
construct can thus only form a unidimensional scale given an ontological assumption
about the latent variable (i.e., people actually possess a psychological mechanism
causally involved in generating responses to questionnaires). Importantly, if the goal
of psychological research is to uncover causal relationships between psychological
variables and behavior, then researchers require the use of reflective measurement
models that actually measure psychological mechanisms.
The Measurement of Life History Strategy by K-factors
Current measurement of LH strategy (e.g., ALHB, mini-K, HKKS, and super
Kfactors) proceeds with reflective models, wherein scale items (or factors in the
higher-order models) are considered to be reflections of an underlying latent LH
strategy. This becomes evident from the factor models and internal consistency
measures used to validate such scales
(e.g., Figueredo et al. 2013)
Concerns and critiques about the assumptions underlying LH measurement models
have been raised in the literature. Notably, Copping, Campbell, and Muncer (2014)
used confirmatory factor analyses to investigate the unidimensionality of the HKSS
. Despite testing multiple factor models, the researchers did not find any
single factor model that fit the data well. Instead, their best-fitting model consisted of
four correlated factors capturing conceptually distinct aspects of the presumed K-factor.
Copping and colleagues have further argued that “the scales included in measures such
as the ALHB . . . do not assess LH strategy as it is usually understood but rather
represent variables that may predict or mediate LH trajectory” (2017: 2, emphasis
added). Therefore, Copping et al. suggest that the utility of constructing overarching
Kfactors requires more consideration before sending such instruments to the “front lines”
of LH research. Richardson et al. (2017b) elaborate and emphasize some of Copping
et al.’s (2017) concerns by discussing at length the assumptions (ontological and
causal) on which K-factors rely. Specifically, Richardson and colleagues argue that
although LH researchers are not compelled to make such assumptions about their
instrument, it is important to be aware that statistical procedures such as confirmatory
factor analysis are inappropriate unless these assumptions are met.
While the existence of a latent variable implies that its manifestations become
uncorrelated after taking this variable into account, reversal of this logic is not justified.
That is, a well-fitting factor structure is a necessary, but not sufficient, condition for
drawing ontological conclusions. Extending the fire-smoke metaphor, given that latent
variables (fire) are causes of manifestations (smoke), it follows that the presence of fire
implies smoke, but the presence of smoke does not imply the presence of fire. The
incorrect inference that empirical evidence for the existence of discrete factors in the
data equals ontological evidence for particular latent variables is salient in early
Kfactor research. Figueredo et al. (2006:139) concluded as much when arguing:
These results point to the existence of a single, highly heritable latent
psychometric common factor (the K-Factor) that, as predicted by evolutionary ecological
theory, underlies both the phenotypic and genetic covariances among a wide
array of behavioral and cognitive life-history traits.
Empirical tests of hypothesized factor structures (for which confirmatory factor analysis
would be the preferred method) work with an opposite logic than suggested in the
citation. The conclusion allowed by factor analysis is that n factors describe the data
(i.e., the variance-covariance matrix) to a certain extent, but whether these factors
identify with latent variables cannot be concluded from factor analysis. Instead,
hypotheses about underlying latent variables justify model specification in confirmatory
factor analysis, or in the case of exploratory factor analysis, justify selection of the most
meaningful factor structure. Empirical findings are thus not sufficient to assume the
existence of latent variables; such hypotheses need to be deduced from theory. In many
instances, whether it is feasible to hypothesize the existence of a latent variable (or
psychological process) with a particular empirical factor can be determined a priori,
because the merits of some hypotheses can be evaluated conceptually. We think that a
reflective measurement model of the K-factor (such as the mini-K) can be ruled-out a
priori because LH strategy (as measured by the K-factor) is an ultimate explanation and
not proximate. Thus, modeling LH strategy with reflective indicators conflates the
ultimate-proximate distinction in evolutionary theories of behavior; evolutionary theory
does not justify the hypothesis that a single K-factor can describe LH strategy.
Modeling Life-History Strategy as a Proximate Variable
The question of whether LH strategy can qualify as a reflective latent variable is
complicated by the multiple levels of analyses evolutionary science involves in its
research. To understand behavior, thought, and emotion, both ultimate and proximate
explanations are required
(Alessi 1992; Bateson and Laland 2013; Haig 2013; Laland
et al. 2011; Mayr 1961, 1993; Scott-Phillips et al. 2011; Tinbergen 1963)
explanations, after further dividing Mayr’s dichotomy in Tinbergen’s (1963) categories,
forward both functional and evolutionary explanations of behavior and respectively
address the “what does it do?” and “how did it evolve?” questions about behavior
also Bateson and Laland 2013)
. Phylogenetic histories of species are sometimes
described as distal “causes” (e.g., Francis 1990), in the sense that species’ genomes
have been adaptively shaped by natural selection, and natural selection can be seen as a
cause for allele frequency changes in a population over time. Functional explanations,
or Tinbergen’s subcategory of survival value, involve a “what does it do?” perspective.
Functional statements say little to nothing about the causal mechanisms involved in
behavior, although functional statements using fitness currency can be examined
through, and perhaps exchanged for, proximate explanations.
Proximate explanations are those involved with “how does it work?” questions.
They address questions about the ontogeny of traits, and the causal mechanisms in the
“here and now” that produce behavior. From this it follows that to model human
behavior by its immediate causes, only references to Tinbergen’s causation category
(the mechanisms) are valid—since by definition, ultimate explanations do not address
the mechanisms producing behavior. Psychometrics is a discipline that attempts to
measure individuals’ “here and now” psychology by statistically connecting overt
behavior and utterances to proposed underlying latent variables. Therefore, given our
discussion on the nature of reflective models and their underlying ontological
assumption, latent variables can only be hypothesized at the proximate level.
LH strategies, then, provide ultimate explanations of particular traits and explain why
traits cluster by referring to fitness effects.
Figueredo et al. (2004)
were explicit in
describing the K-factor as providing functional-level explanations: “LH theory suggests
that natural and sexual selection will combine LH traits into functional composites
representing co-adapted reproductive strategies” (2004:123). Indeed, reference to a
particular LH strategy allows us to better understand why particular behaviors cluster
together, they add meaning to our understanding of the proximate mechanisms involved
in behavior. In the above citation, the authors quite adequately describe the K-factor as a
functional composite, not as a proximate mechanism that could fulfill the requirements of
reflective measurement. This raises the question of what information scores on K-factors
are conveying. That is, when researchers compute a factor score of a latent variable that is
not reflective of a proximate mechanism, then what does this represent? Put bluntly,
Kfactor scales do not meet the (causal and ontological) criteria for test validity as submitted
for instance by Borsboom et al. (2004:1067): “The concept of validity . . . expresses
nothing less but also nothing more than that an attribute, designated by a theoretical term
like intelligence [or, LH strategy], exists and that measurement of this attribute can be
performed with a given test because the test scores are causally affected by variation in the
attribute.” Although the reflective approach to assessing functional descriptions is
unwarranted and K-factors are not actually measuring LH strategies, there are alternative models
relying on assumptions that could be satisfied by K-factor scales.
An Alternative Approach: Formative Models
To deflate the proximate-ultimate distinction in K-factor models, we suggest that LH
strategy could be modeled as a formative construct, one that is descriptive of an individual,
similar to SES. The items in the mini-K (and related measurement instruments) should, in
our view, be modeled as reflections of various proximate constructs. Subsequently, these
constructs can be used to construct a formative measurement model. Figure 2 depicts a
proposed formative measurement model for the mini-K, based on recent findings by
Richardson, Chen, Dai, Brubaker, and Nedelec (2017a). LH strategy modeled as a
formative construct meaningfully clusters various proximate mechanisms to allow them
to be collectively informative about individuals. Such a formative model aligns more
closely with the ultimate-proximate distinction for behavioral explanations.
We propose the following strategy for future LH research using a psychometric
approach. First, validate how proposed proximate mechanisms of LH strategy regress
on a functionally defined K-factor using formative measurement models and assess
model fit with the data. Second, do not create composites of an underlying K-factor
(which, as we have argued, would be tantamount to defining functional descriptions at
the proximate level), but only use first-order constructs that are hypothesized to identify
with discrete proximate mechanisms
(cf. Edwards 2011)
. These proximately defined
constructs (and resulting composites) can subsequently be meaningfully modeled as
predictors in regression models, path models, or structural equation models.
Importantly, specifying LH strategy as formative rather than reflective is not merely
conceptually apt, but the models require different analytical strategies—and thus this
decision has potential statistical consequences. As discussed by Diamantopoulos,
Riefler, and Roth (2008), incorrectly modeled indicator-construct relationships can lead
to incorrect conclusions about structural relationships among variables, as well as
biased estimates of model fit. For example,
Law and Wong (1999)
misspecification of a formative construct as reflective leads to overestimation of the
effect of the misspecified variable on an outcome variable. Jarvis, MacKenzie, and
Podsakoff (2003) replicate these findings and also show that regression coefficients of
predictor variables are underestimated when a formative outcome variable is wrongly
modeled as reflective. Similarly, estimations of model fit yield biased indices as well
(Diamantopoulos and Siguaw 2006; Edwards 2001; Jarvis et al. 2003)
Indeed, the reflective-formative distinction is critical to psychometric practice more
broadly, including but not limited to scale reliability analysis and various forms of
(see Bollen and Diamantopoulos 2017)
. The notion that a formative
construct incorrectly specified as reflective violates the assumptions of common
psychometric procedures, and might lead to biased empirical conclusions in structural
models, underlines the relevance of clearly conceptualizing LH strategy.
We have argued that because a discrete proximate mechanism corresponding to LH
strategy (such as the K-factor) cannot be assumed, current approaches do not succeed in
measuring reflections of such a latent variable. Current psychometric measurement of
LH strategy involves an unwarranted conflation of functional (i.e., ultimate)
descriptions and proximate mechanisms—a conceptual mix-up that may generate unviable
hypotheses and invites misinterpretation of empirical findings. Thus, common
psychometric measurement instruments of LH strategy (including ALHB, mini-K, and HKKS)
incorrectly assume reflective measurement models implying that each individual
proximate mechanism is conceptually equivalent and, by extension, is a (locally)
independent measurement of the latent LH strategy.
We thus suggest a different approach to LH measurement, one that treats K-factors as
formative constructs—giving a meaningful summary of an individual’s characteristics,
akin to how SES is conceptualized. In doing so, LH strategy becomes a descriptive
construct, giving a meaningful description (rather than causal explanation) for the
observed correlations between LH traits. Acknowledging K-factors as formative (and as
ultimate) prevents conceptual errors, such as inappropriate causal inferences and
inappropriate extensions of empirical findings toward theory development. The use of such a
formative measurement model, as discussed, has direct consequences for the parameter
estimates in regression models including a psychometric measurement of the K-factor.
Although we have shown conceptual problems in considering K-factors measures of LH
strategy, we are not disputing that LH strategy theoretically could correspond to a discrete
proximate mechanism. Additionally, our concerns with the psychometric approach do not
extend to developmental approaches aiming to explain variation in LH strategies
Belsky et al. 1991; Del Giudice 2009)
. However, we leave open the empirical question of
whether variation in the bundle of proximate mechanisms captured by K-scales is further
reducible to a single proximate mechanism (e.g., impulsivity or reward-sensitivity;
Frankenhuis et al. 2016) with which the K-factor scores could identify. If such a reduction
is not possible, researchers need to examine hypotheses about these mechanisms separately
(as we have suggested). If reduction to a single mechanism is possible, creating latent
variable models of LH strategy would be feasible, but it would need to measure LH strategy
through direct causal manifestations of such a mechanism. Nonetheless, analyses of K-factor
Copping et al. (2014)
and Richardson et al. (2017a), also cast doubt on the
possibility that K-factor scores identify with a latent LH strategy
(see also Copping et al.
2017; Richardson et al. 2017b)
What are other possible new directions for the psychometrics of LH strategies? The
discussion thus far may suggest that the K-factor’s conceptual problems are solved by a
simple reversal of path directionality in factor analytic models—turning reflective
measurement models into the formative kind. Although this might be a step LH research
needs to take to conceptually align theory with measurement, the value of such descriptive
constructs in psychological research is far from clear. In particular, can a descriptive
construct (summarizing various conceptually different sources of information about
individuals) be fruitfully used as a predictor of behavioral outcomes? For psychologists
interested in examining psychological constructs as causal antecedents of behavior to
further psychological theory, such descriptive variables may be of little theoretical value.
This is simply because such constructs are not measurements of the mind, but rather
describe individuals’ psychology. As Richardson et al. (2017b) note, such a descriptivist
approach “can be seen as more concerned with statistical parsimony than elucidating the
nature of causal forces responsible for patterns of covariation” (2017b:2). Other scholars
(e.g., Rhemtulla et al. 2015)
, for this reason, have advocated that formative models using
causal indicators of constructs should best not be described as “measurement models.”
Although these suggestions conceptually align LH measurement with common
psychometric approaches, there is (as the authors announce) a “new psychometric game in town”:
the network approach to psychometrics
(e.g., Borsboom and Cramer 2013; Epskamp et al.
that we suggest as a direction for future research. Network models do not assume that
constructs merely exist by virtue of their operationalization (as formative models), but they
also do not assume that latent variables exist as a single “entity” or mechanism (as reflective
models). Instead, network models take an intermediate ontological position; they define
constructs in terms of a network of multiple interacting manifestations. This approach might
prove to be of particular value to researchers interested in modeling functionally defined
constructs, such as LH strategy, because functions may very well be examined through a
network of proximate mechanisms. In such a model, LH strategy could be depicted as a
network of proximate mechanisms that, as a whole, defines a person’s LH strategy.
In conclusion, the conflation of ultimate and proximate causes in the evolutionary
behavioral sciences is not a problem unique to LH measurement
(for a discussion, see
Scott-Phillips et al. 2011)
. Proximate models of behavior lose their conceptual clarity—and
indeed their causal explanatory potential—when ultimate factors referring to fitness effects
are included. Mayr and Tinbergen’s effort to distinguish between ultimate and proximate
causation remains important in evolutionary behavioral science—also for the quality and
validity of measurement instruments. How to properly use ultimate explanations in
proximate empirical models remains an important issue for progress in evolutionary behavioral
science. In our view, the specification of formative measurement models when describing
and testing functionally defined constructs might be a first important conceptual step.
Acknowledgments The authors are thankful to George Richardson for motivating correspondence prior to
the development of this manuscript. We are also thankful to three anonymous reviewers for valuable
comments on an earlier version of this paper.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International
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Stefan L. K. Gruijters is a lecturer at Open University of the Netherlands, after having recently completed his
PhD project at the Faculty of Psychology and Neuroscience, Maastricht University, the Netherlands. As part of
his dissertation work, he focussed on the applications of evolutionary theory in the field of health psychology.
Further research interests include conceptual, methodological, and psychometric issues relevant to
evolutionary (approaches to) psychology.
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