Research, Structural Models and Publishing

This article discusses basics of developing structural models as well as research and getting published in journals.

There are a number of cheap, dirty secrets that many in academia are reserved to admit, if they will admit at all. Some are related to research, structural models and publishing.

Research is a process which is normally conducted in order to solve a research question. A research question, in turn, the usual explanation goes, should have at least 2 characteristics:

1. A research question should be solvable.
2. A research question should be interesting.

Being solvable is often related to the need to be empirically falsifiable/verifiable and operationalize-able/measureable in both the technical and the practical sense. If a question can be shown to be unanswerable it would not qualify as a research question. If a question could be answered through access to some data, it is at least theoretically solvable. If, however, that data is illegal to obtain or prohibitively expensive to obtain, it could still be considered unfeasible. Some questions may not be feasible today but may become so tomorrow.

The "interesting" thing is the reason that academia as a social institution sucks. "Interesting," they will tell you, means something which significantly ads to some body of knowledge. "Significant" then becomes the trick.

In theory, an interesting question is one which is in the interest of someone or some group to ask or have answered. In practice, an interesting question is one which is in the interest of the editors of the respected journals and so on to have asked or answered. At the end of the day it comes down to subjectivity and money. Don't get me wrong - I think money driving research is fine - I just don't like the fact that the current academic system systematically propagates bad information (ie, lies), people are ignorant of and even proudly deny those problems and the fact that the current system is completely inefficient from a financial ROI standpoint.

<span style="line-height: 1.5em;">The real answer is that "interesting" and "significant" are subjective and arbitrary valuations made by individuals. If you want to be published, you must be "interesting" according to the editor of the journal in which you seek to be published.

Funding is also a major constituent of what determines which research is "significant" or "interesting." That would be whichever research the funders want done. As most who have a clue about these sorts of things know, the editors of the papers often run in the same circles as the preferred researchers and the funders. "Academia" or "the scientific/academic consensus" turns out to be nearly as much an old boys club as some political party - and they are hardly a disinterested group, although they will claim it to the end. Getting published, then, is about meeting the expectations of these editors.

Structural models are quite a different topic, but they are related in two ways. Academics love them and make them way more complicated then they need to be. Structural models are simply mathematically structured models used to describe relationships, although they are often described in much more convoluted ways. A = B + C could be an example of a structural model. X = Y(B) could be a structural model. Economists are sometimes even so lazy they won't specify what's called functional form (I'll get to that later) so they might say that Y = f(L) without even specify what the f(x) they are talking about....is per se.

Structural models are models "based in theory," they will tell you. What this seems to indicate, or some will even tell you, is that a person has no justification for creating a theory without having read mounds and mounds of academic literature. While reading the literature and discovering models that other people have used and the reasons for that are often good ideas, they are by no means necessary. The irony is to ask, "Where did the theory come from?" Why it came from observation, induction, hypothesis and testing to verify - the classic scientific method! Massive lit reviews are not requisite. Here is the real process, which almost no one will outright tell you, for how to create a structural model:

1. Observe stuff
2. Wonder/hypothesize whether some stuff is related.
3. Test whether stuff is related.
4. After determining that stuff is related, try to establish a more exact form of that relationship. This boils down to 2 real questions: A) What does the functional form look like? B) Can we establish some kind of causality or not?
5. Here is the really hilarious part that no one will admit....Functional form is largely a guess and check game with process of elimination!

Functional form is the mathematical form of the equation used to define the relationship between variables. A+B=C is one functional form. AB=C is another, A^B=C is another, A/B=C, A-B=C and so on. In all of these cases C=f(A,B) which means, \"C is a function of A and B.\" In each of these cases we know that there is a relationship between A, B and C, but in each case the way we describe that relationship/the kind of relationship/the way the relationship works/the functional form is different.

Functional form begins as a hypothesis. It is guess and check. There may be logical reasons you might posit one form or another, but in general no form is sure until it is tested. This is in strong contravention of the common thread idea that there are right or wrong functional forms. In some cases there may be, but in fact many times the correct functional form is a hypothesis to be confirmed or denied by comparing to other forms and comparing explanatory power or predictive power.

Let's use an example. I am chillin one day and I think I might have noticed a pattern. I have driven by a hot dog stand on two different Mondays, a Friday and a Tuesday. On both Mondays there was a discount on the hot dogs. "Is it just a coincidence, or could it be that Mondays and discounts are related?" I hypothesize that they are related and set to check it out with statistical testing for association.

I take an SRS (simple random sample) of days over a sufficiently large number of repititions (n>= 30, preferred >=100.) Because in this case different observations means different points in time, I note that my analysis does not account for time effects. I could accept that weakness as a possible confounding factor, or I could argue that it is fit to be ignored or assumed away.

Let's say I determine that there is some statistical association between day of the week and whether or not there is a sale. Now I try to figure out the functional form. How do I go about this? I simply try a variety of regressions and, unless I have some logical reasons to hold to one or the other, I prefer the functional form with the highest explanatory and predictive power. Even if logical, or apparently logical, reasons to support one model exist, trying many models is often a good idea because reality can be counter-intuitive or even downright confusing. Don't limit reality to theory! Instead, build theory from reality.

For my hot dog relationship I could try any number of forms. I could try a linear regression, logarithmic regressions, exponential or others. One cool trick would be to use a <a href="http://en.wikipedia.org/w/index.php?title=Taylor_series&oldid=594230260">Taylor Series, since these can be used to arbitrarily approximate any function. I may even prefer a discontinuous function.

In conclusion, don't be intimidated from conducting your own research, even if it is looked down upon by academia. At the same time, beware of overly trusting academic research. They have plenty of methodological, cultural, bias and other problems of their own.