Critical thinking
Article: Schmittmann, V, D., Cramer, A, O, J., W., Waldorp, L, J., Epskamp, S., Kievit, R, A., & Dorsboom, D (2011)
Deconstructing the construct: A network perspective on psychological phenomena

In psychological measurement, three interpretations of measurement systems have been developed:

• the reflective interpretation
  The measured attribute is conceptualized as the common cause of the observables
• Formative interpretation
  The measured attribute is seen as the common effect of the observables.
• Attributes are conceptualized as systems of causally coupled (observable) variables.

Reflective and formative models

In reflective models, observed indicators (item or subject scores) are modelled as a function of a common latent (unobserved) and item-specific error variance.
Commonly presented as ‘measurement models’.
In these models, a latent variable is introduced to account for the covariance between indicators.

• In reflective models, indicators are regarded as exchangeable save for measurement parameters.
• The observed correlations between the indicators are spurious in the reflective model.
  Observed indicators should correlate, but they only do so because they share a cause.

In formative models, possibly latent composite variables are modelled as a function of indicators.
Without residual variance on the composite, models like principal components analysis and clustering techniques serve to construct an optimal composite out of observed indicators.
But, one can turn the composite into a latent composite if one introduces residual variance on it.
This happens, for instance, if model parameters are chosen in a way that optimizes a criterion variable.

• In formative models, conditioning on the composite variable induces covariance among observables even if they were unconditionally independent.
  The composite variable functions analogously to a common effect.

Formative models differ from reflective models in many aspects

• indicators are not exchangeable because indicators are hypothesized to capture different aspects of the construct.
• contrary to reflective models, there is not a priori assumption about whether indicators of a formative construct should correlate positively, negatively or not at all.

Problems with the reflective and formative conceptualizations

The role of time

In most conceptions of causality, causes are required to precede their effects in time.
But, in psychometric models like the reflective and formative models, time is generally not explicitly represented.
The dynamics of the system are not explicated.

• it is therefore unclear whether the latent variables relate to the observables in whatever dynamical process generated the observations. It is unclear whether the latent variables in question would figure in a dynamic account at all.

This puts the causal interpretation of latent variable models in a difficult position.

Inability to articulate processes

The identification of causal relations is an essential ingredient of the scientific enterprise.
Typically, after a causal relation is discovered, it is broken down into constituent processes to illustrate the precise mechanism(s) that realize(s) that relation.
There is rarely a progressive research program that identifies how the found causality works.
A plausible cause of this problem is that most constructs in psychology are not empirically identifiable apart from the measurement system under validation.

Relations between observables

An important issue in both reflective and formative models is the neglect or subordinate treatment of causal relations between the observed indicators themselves.

• the reflective model relies on the assumption that no direct causal relation exist between observables
• in the formative model relations between observables that are not accounted for by the latent variables are typically treated as a nuisance.

But, casual relations between observables are likely to exist in many psychological construct.
Such causal relations between observables may be the reason why a phenomenon is perceived or interpreted as an entity.

The network perspective: constructs dynamical systems

Variables that are typically taken to be indicators of latent variables should be taken to be autonomous causal entities in a network of dynamical systems.
Instead of positing a latent variable, one assumes a network of directly related causal entities as a result of which one avoids the three problems above.

After constructing a network, one can use techniques from network analysis to visualize the system.
From a network perspective, a construct is seen as a network of variables. These variables are coupled in the sense that they have dependent developmental pathways, because a change in one variable causes a change in another.

Studying the construct means studying the network. Such investigation would naturally focus on

• network structure
• network dynamics

The relation between observables and the construct should not be interpreted as one of measurement, but as one of methodology: the observables do not measure the construct, but are part of it.

Dynamical systems

A general framework to formalize and study the behaviour of a network of interconnected variables over time is dynamical systems theory.
A dynamical system changes its state (which is represented by a set of interrelated variables) according to equations that describe how the previous state determines the present state (how the variables influence each other).
Given an initial state, the system will move through a trajectory of states over time.

Particularly relevant are attractor states of the system.
If the system is close to an attractor state, it will converge to it, and remain in there an equilibrium.
In dynamical systems, parameters in the state-transition function determine the number and type of equilibrium points.
If we allow these parameters to change, the system may show qualitative changes in its structure.

Causal inference

A problem with formal theories of dynamical system is that almost all of the known mathematical results concern deterministic systems.
In psychology, we typically deal with probabilistic systems and data characterized by high levels of noise. The difficulty then is to derive, from statistical pattern, that changes in A are structurally related to changes in B.
One way to arrive at a viable method for interring such relationships between variables is to adopt the assumption of linearity and normality.
These methods typically work through the detection of conditional independence relations.

Network analysis

Once the network structure has been inferred in one of the aforementioned ways, the network may be subject to further analysis.

Constructs and their interrelations

The ontological status of psychological constructs as well as the epistemic question of how to measure them has been the topic of considerable controversy in psychology.

In the network view, a construct label does not refer to a latent variable or inductive summary, but to a system.
Since there is no latent variable that requires causal relevance, no difficult questions concerning its reality arise.
Naturally, the components of the system have to be capable of causal action, but this is typically not much of a problem.

Validity

If the question of validity is constructed as whether a set of items “really measures” a given attribute, the answer to that question requires an account of item response processes in which that attribute plays a causal role.

The essence of a network construct is not a common cause; rather, it resides in the relations between its constituents.
These relations lead to a clustering of symptoms picked up both by formal methods to detect clustering and by people.

Relations with other constructs

Unless a network is completely isolated (an unlikely situation in psychology) construct labels denote an inherently fuzzy sense.
In particular, the distinction between different traits or disorders or abilities in itself is a matter of degree, depending on the extent to which the networks are separated.

• networks that are not well separated are likely to show entangled behaviour that may often cause researchers to wonder whether they are dealing with one or two constructs.

Causes and effects in a network structure

In a network perspective, causes do not work on a latent variable, and effects do not spring from it.
Since the individual observables are viewed as causally autonomous, they are responsible for incoming and outgoing causal action.
This motivates the study of such observables themselves as gateways of causal action, a perspective that has rarely been taken in psychometric thinking.

In some cases, consequences may be seen as a result of the overall state of the network.
In other cases, it is more plausible that only a few of the symptoms are responsible.
The network perspective offers a natural way to accommodate this, as in dynamical systems even simple interactions between variables may cause emergent phenomena to arise as a result of nonlinear interactions between components of the system.