MODELING RELATIONSHIPS BETWEEN VARIABLES

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    There are many different kinds of relationships between variables. This page attempts to list ALL the possible relationships in a parsimonious, 3-variable model. Much of this information is taken from the theory of Elaboration Analysis, and the specific names of particular relationships have been established by convention in the research literature. Don't worry if you have trouble with the more complex relationships because even the most experienced theorist-researchers have problems.

LEGEND:

X = INDEPENDENT VARIABLE (CAUSE)
Y = DEPENDENT VARIABLE (EFFECT)
Z = OTHER FACTOR (3rd VARIABLE)

==> (single arrow) indicates CAUSAL PATHWAY
<==> (double arrow) indicates FEEDBACK RELATION*

* a "feedback" relation is another word for "interaction" between variables. It is usually reserved for cases of two-way causal influence; i.e., it cannot be determined which variable has the greater causal influence.

THE SIMPLE RELATIONSHIPS:

In a CAUSAL RELATIONSHIP (upper left hand corner), there is no Z factor because the rules of causality require that we have eliminated any possible 3rd factor in the explanation. As a reminder, the three rules of causality are:

In real life, casual relationships are hard to find. In addition, it is almost always possible to think of Z factors that might be related to any relationship.

Therefore, a CONTINGENT RELATIONSHIP (upper right hand corner) is always possible. A theorist may have established a causal relation between X and Y, but simply did not go far enough in thinking of a Z factor down the road. This occurs quite frequently when the theorist has no interest in behavioral outcomes, and is only interested in connecting mental processes that "prepare" one for action. In these cases, we say the researcher has only succeeded in specifying contingencies or a contingent relationship.

Another possibility is the INTERVENING RELATIONSHIP (lower left corner). In this case, the theorist has implied that a Z factor needs to be inserted into the X-Y causal chain to make it complete; that is, Z must "intervene" in the relationship between X and Y. This occurs quite frequently when the theorist must deal with concepts that are dualities or dichotomies (external or internal; left-wing or right-wing; either-or, etc.). The Z factor may represent some attitude or worldview that is necessary to make the X-Y relationship a causal one. In sociology, the Z factor may simply represent the requirement that other people be around for a group influence. In these cases, we say the researcher has specified an intervening relationship.

An ANTECEDENT RELATIONSHIP (lower right corner) is also known as a conditional relationship, although some people also refer to contingent relationships as conditional. In this case, the Z factor must "precede" or come before the X-Y causal chain. It is a necessary precondition or event that must take place. This occurs most frequently when the theorist is dealing with a developmental model where something like abuse, previous victimization, or prior contact with law enforcement is assumed to shape attitudes and in turn, behavior. In these cases, we say the researcher has specified an antecedent relationship.

NOTE: "specifying" a relationship usually means that the theorist-researcher is aware of the Z factor, and explicitly or implicitly makes note of it. "Elaborating" a relationship is where you, the reader, have thought up the Z factor. Elaboration will become more apparent with the complex examples that follow.

THE COMPLEX RELATIONSHIPS

These two cases are usually considered the worst things that can happen. In the case of MULTICOLLINEARITY (which can also be established by looking at correlation tables for inter-item coefficients of .80 or greater), the theorist has a strong Z factor which is influencing both X and Y so greatly that Z might be a cause of both X and Y. Note that there still is a causal connection between X and Y; that is, the primary causal pathway stands on its own. But there is a serious problem because Z has not been "controlled", "partialed" or "factored out" in its influence. This occurs most frequently when certain concepts like intelligence or ability are being measured. In these cases, we say that the research suffers from multicollinearity.

A SPURIOUS RELATIONSHIP violates the rules of causality. It occurs when a strong Z factor is a probable cause of X and Y, and in fact, overshadows the X-Y causal chain so much that the X-Y link disappears once we think about it. These cases usually occur when there might be some underlying medical or mental condition, but they are readily apparent in any simplistic statement such as "Poverty causes crime" because there might be some Z factor which causes both poverty and crime. Lack of opportunities, for example, might be a better explanation of both variables. In these cases, we say that examination of the spurious relationship reveals an important, 3rd factor.

Both of these cases involve words you don't often see in everyday vocabulary. In fact, you are unlikely to run into anyone using these words. But in the case of an EXTRANEOUS RELATIONSHIP, the theorist has usually "borrowed" a concept or idea from another theorist, and has tied it into his or her own theory. Think of it as a type of theoretical integration, if you will. It occurs when the original theory is weak, and the X-Y causal chain disappears. You might ask why this is not called an intervening relationship, and the answer is that the theorist, for one reason or another, keeps pushing the X variable as important or primary. This occurs most frequently with untestable concepts, such as subconscious guilt or Freudian defense mechanisms. An option to saying the relationship is extraneous is to say the theory represents a "new", "revised", or "neo-" version of an old theory, as in "neoFreudian".

A COJOINT RELATIONSHIP is the case of when two, separate variables, X and Z, which are not related to one another in any way, act together at the same time to influence Y in a causal manner. It can occur when the theorist tries to bridge the micro-macro gap, but most often occurs when there is reference to ratios, dilemmas, ironies, certain syndromes, or quotients, as in a "community tolerance quotient" being necessary along with repeated acts of deviance to trigger a formal social control response. Cojoint relationships are often attempts to have things both ways, as in "it could be a little of this and a little of that" when it is obvious that the two things are mutually exclusive. Other names for cojoint relationships are "two pronged models", "twin theories", or forced integrations.

A CONTAMINATING RELATIONSHIP, more properly referred to as a contaminating variable, involves the case of X leading to a Z factor as well as its intended target, Y. It occurs when an X is selected that is so strong as to be a cause of just about anything. Various types of criminalization theories which claim that the existence of law is the cause of crime may represent a contaminated relationship because law may lead to obedience as well as disobedience. When no concern or connection is made with the alternative explanation (a Z-Y link), the relationship is said to be contaminated.

A SUPPRESSED RELATIONSHIP, more properly referred to as a suppressor variable, usually (and I say usually because there is some disagreement over exactly what a "suppressed" relationship means) involves the case of a contaminated relationship where there is some concern or connection made with alternative explanations (Z-Y links). Informal social control by those who obey the law, for example, may "suppress" or shape the effect of the law's influence on disobedience, but we do not really know if the Z-Y link is direct or inverse. It may be that the disobedient become less disobedient thru learning by example, or it may be that the disobedient become more disobedient thru reaction formation. In any case, we refer to the relationship as containing a suppressor variable.

A DISTORTED RELATIONSHIP, sometimes called a distorter variable (terminology varies), usually involves the case of contaminated relationship with the addition of feedback, or two-way interaction between an X and Z variable. The theorist will usually say, or imply, that there is a feedback or interactive relationship at work. But again, there is no concern or connection with a Z-Y link. This leaves the reader to imagine why there is no connection. This model appears with some frequency in attempts to explain the operation of the criminal justice system. Prison bedspace capacity, for example, is implied as involved in a reciprocal loop with law enforcement discretion, but only law enforcement activities are stated as a cause of crime. One is left wondering if criminal activity is really affected by bedspace capacity or not. In such cases, we say the relationship is distorted.

A POTENTIATING RELATIONSHIP is usually depicted (although different depictions exist) as an improved form of the distorted relationship. The theorist has specified, or the reader has elaborated, a Z-Y link. Unfortunately, without any facts to go on, the best that the theorist can do is say that there is a "potential" for Z to increase Y. The influence is direct, rather than inverse, in most cases involving a potentiating relationship, although control theories are notorious for some potentiating, inverse logic. Often, when an theory involving inverse logic (when something goes up, the other goes down) is translated into more positive, direct terms, you automatically have a potentiating model.

A MODERATED RELATIONSHIP can be quite complicated, but is usually depicted as one in which there is simultaneous influence going on between X and Z, but the overall relationship is more like an intervening situation where the most important causal link is between Z and Y. The model would be drawn with Z above X in this diagram if Z were the primary variable, but it is instead treated as a "moderating" factor or variable. Often, this is the explicit language used by the theorist, but it is obvious that Z does more than simply "moderate". It drives the whole theory. There are numerous examples of this relationship in the criminal justice and criminological literature.

A CONFOUNDED RELATIONSHIP can be quite complicated, but usually involves two feedback loops added to a simple X-Y causal chain. If crime is the outcome, the cause of it interacts with some 3rd factor, and crime itself interacts with this 3rd factor. Any examples here would tend to get a bit tricky, and this language usually involves remarks by imaginative readers.

The CONTEXTUAL RELATIONSHIP is (or should be, in my opinion) the proper form of an "everything causes everything else" model.  However, differences of opinion can be found. Note that at least one pathway (X-Y) is left open. For the truly "everything causes everything" model, the proper diagram is at right.  As far as I know, nobody has used this ECLECTIC RELATIONSHIP model in years. Contextual relationships are starting to appear in the contemporary literature, and are most often found in community studies and neighborhood watch evaluations where the intent is to capture a different meaning of "context" as a neighborhood factor or the like.  However, the basic idea behind a truly eclectic relationship is that there are no causal chains, only reciprocal feedback loops. Hence, the theorist might sometimes resort to explanations involving metaphors, like "spirals" or "circles."

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Last updated: July 12, 2006
Not an official webpage of APSU, copyright restrictions apply, see Megalinks in Criminal Justice
O'Connor, T.  (Date of Last Update at bottom of page). In Part of web cited (Windows name for file at top of browser), MegaLinks in Criminal Justice. Retrieved from http://www.apsu.edu/oconnort/rest of URL accessed on today's date.