# What do we call the “middle” variables in a complex research model?

Basic theory building goes like this: you create a theory which has an independent variable and a dependent variable. I have also been taught to use "explanatory variable" as synonym for "independent variable" and "goal variable" and "response variable" as synonyms for "dependent variable". Then you do empirical research and measure the connection strength, or find out that there is no connection after all :(

As this is rarely complex enough for theories in disciplines where humans are involved, there is also the option to create a multivariate model, where many independent variables will explain a dependent (or goal) variable. There, the terminology is still unambiguous.

But many models from recent publications are more complex than this. Consider this path model:

Continuance intention seems to be the goal variable, because it doesn't lead to any other variables. Interaction and User value are certainly independent variables in this model, because they don't depend on others. But what are Satisfaction and Flow experience? They depend on lots of other variables, but they are not our goal variable, because this model is about Continuance intention, not about Satisfaction or Flow experience.

So, what is the proper terminology for such variables stuck in the middle of a multi-level model?

Citation for the picture: Examining users′ intention to continue using social network games: A flow experience perspective Chiao-Chen Chang (2013) Telematics and Informatics 30 (4) p. 311-321

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• Is the "language" you request specific to the research model you are developing? Is this a research model or a model that you are researching? – drN Mar 18 '14 at 21:35
• I still think that Academia is the best place for it, as it is about research methodology, completely independent from any discipline or of statistical methods. See my question where I argue about this, and the community seems to agree with me. meta.academia.stackexchange.com/questions/779/… – rumtscho Mar 19 '14 at 11:24
• I find your argument about the independence from statistical methods fascinating but somewhat unconvincing. I see a lot of statistical terms in your question (or at least terms that I see most often in statistical contexts), I find Ana's answer on-point in referencing another primarily statistical term, and I find the whole question reminiscent of topics on Cross Validated. We discuss models all the time over there, we have a terminology tag for just such questions as these, and we wouldn't require you to actually plan to fit this model to some data...but then what's the point of it otherwise? – Nick Stauner Mar 19 '14 at 12:50

I've always found it difficult to pack up real-world data into the neat boxes of methodology textbooks, but if you really need a label for these, I'd go with mediator variable.

From a famous article on these variables:

Specifically, we differentiate between two often-confused functions of third variables: (a) the moderator function of third variables, which partitions a focal independent variable into subgroups that establish its domains of maximal effectiveness in regard to a given dependent variable, and (b) the mediator function of a third variable, which represents the generative mechanism through which the focal independent variable is able to influence the dependent variable of interest.

Reference:

Baron, R. M., & Kenny, D. A. (1986). The moderator–mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of personality and social psychology, 51(6), 1173.

@Ana is correct. Satisfaction and Flow Experience are mediator variables in this path analytic model linking Interaction and User Value to Continuance Intention to Use Social Network Games. I don't see any indication that this is a multilevel model; I think you might be mistaken about that, or at least might be excluding any information that would make this relevant. There could be a second level fit to Interaction and User Value directly rather than to the two variables contained in each of those boxes, but I don't see any paths leading from those outer boxes, so I assume there is no second level...and again, "mediator variables" would still work as the term you probably want. In this model, the middle variables completely mediate the relationship of the leftmost variables to the rightmost, but Flow Experience only partially mediates the relationship of Satisfaction to the rightmost, because Satisfaction also has a direct pathway depicted. The coefficient of this pathway indicates any independent relationship those two variables have when controlling Flow Experience.

Another distinction can be made between the variables on the left with no inbound arrows and all others that do have inbound arrows: they are "exogenous" and "endogenous", respectively. That is, even though the mediator variables have both inbound and outbound arrows, they are endogenous. Only the leftmost four variables in this path diagram are exogenous. Exogenous variables are strictly independent, but only the rightmost variable is strictly dependent. All endogenous variables are at least dependent on some other variables, but in this path model, Satisfaction and Flow Experience may be treated as independent variables when estimating their paths to the final outcome variable on the right. They have dual status as in/dependent variables in this model, at least if it is estimated piece-by-piece. It might be misleading to call the mediator variables independent if the whole model is fit simultaneously via SEM.

To repeat what's been said, @Ana's answer is correct, to a point. I think a more powerful way to look the kind of data you're talking about is using structural equation modelling. In SEM terminology, your middle variables could either be manifest (if you're measuring them directly), or latent (if they're inferred from other variables). The terminology is explained quite well here.

It definitely does not have anything to do with neural networks, although they could at a stretch be used to model the same phenomenon.

Edit: I meant to also say that the language and analysis framework you use is often dependent on the specific field you're coming from. Mediation and moderation analyses are most common in social psychology, but to the best of my knowledge unheard of in cognitive psychology. SEM is more common in psychometrics, and for researchers looking at things like anxiety and OCD (I can't reference this, as I'm mostly going by who I know in my own university).

• The depiction of these variables as rectangular boxes is conventionally the notation for manifest variables, whereas ellipsoids would denote latent variables. Since the figure was published very recently, it seems likely the authors would've been conscious of this and either intended their design to indicate manifest variables or not to indicate a SEM at all. If they've referred to it as a path analysis, this is further indication that the variables are manifest, not latent. Path analyses are SEMs with no latent variables. SEM, mediation, and moderation analyses are used very widely. – Nick Stauner Mar 19 '14 at 19:27
• You're right on all counts, and in this case, satisfaction and flow experience are more than likely directly measured, although it would do the OP no harm at all to look into both SEM, and mediation/moderation, and their respective terminologies. – Eoin Mar 20 '14 at 10:55
• I agree in spirit, but in my own experience with SEM...it's got a pretty intimidating learning curve! :) – Nick Stauner Mar 20 '14 at 14:43