# How to present a model which is based on the result not yet discussed?

I am facing the following problem while writing a paper. I have a model which contains a function whose explicit form I derived empirically from the data presented in the paper itself.

However, I would like to present the model during the introduction and thus before the result. However, to justify the shape of that function, I have no other way than to anticipate the result (saying something like: “Since in the result of the experiment we found X, we empirically assumed X in the model“). I am not completely happy with this, because I would like to present the result directly in the result session, not earlier.

A solution would be to move the explanation of the model after the results. I do not like this either because I want to fit the real data with the model itself, and I don’t think it is wise to start fitting something without explaining it first.

So, what it your advice in this matter? What would you do?

Also, any papers with example of something similar are welcome.

• Two questions: 1) Are you sure that you do not apply circular reasoning? 2) What’s wrong with using a placeholder for that function? – Wrzlprmft Aug 22 '14 at 12:29
• 1) Quite sure. I use the experimental result to get an idea about the shape of the function (for example, its dependency on experimental conditions). This does not imply that the model (which function is only a part of it) will absolutely fit my data. I don't think it is so uncommon to build a model based on empirical findings. 2) I don't feel I can explain the model satisfying if I do not give an explicit version of the function. Plus, in fitting my data, I use the explicit version, so I need to present it before the fitting. – Vaaal Aug 22 '14 at 12:36
• Side note: reminds me of en.wikipedia.org/wiki/Empirical_Bayes_method – Memming Aug 22 '14 at 13:22
• Memming: thank you for the interesting point. I have been advised to present the basic part of the model (the one that does not rely on the result) in the introduction, and to introduce and explain the empirical function after the result, fitting the data again. What do you think about this solution? – Vaaal Aug 22 '14 at 13:45

You have data S, and a model M={H, f(H), g(H)}, where H are the set of assumptions of the model, and {f(H), g(H)} are components of the model that of course depend on the assumptions in some way.

Using the data, you estimate a functional form for f(H), for lack of mathjax denote it empf(S,H)

Then you apply your model to the data and obtain a measure of fit, expressed here in abstract as a distance measure between model and data

{M,S}->d(M,S)* or **{[H, empf(S,H), g(H)], S}->d([H, empf(S,H), g(H)],S)

One (not all) components of your model had a chance to "fit with the data" prior to applying the whole model, and so it has increased the chances of your model as a whole to fit the data.

So the "distance" is not purely between model and data -it is a distance between a model that has already come "closer to the data", through empf(S,H), and the data.

In a rather known dialect, "you trained (partly) your model, using the same data set on which you are going to test it". I would not consider this as scientifically acceptable.

The way out of course, is to estimate f by using a different data set, a data set that should, according to your theory, be able also to be represented by the same model. And this also guides you as to how you could go about writing your paper.

• Thank you for your answer. I think that the validity of this line of reasoning depends on the particular formulation of empf. In my case, empf has a really low power to fit the data without the rest of the model, but the models does need an explicit form. It seems reasonable to base this explicit form on empirical findings. I don't see any scientific problem in this. Any model which aims to describe reality is based on empirical evidence. Of course the model needs to be tested on more than one dataset to be valid. If there is any mistake in my reasoning please feel free to let me know. – Vaaal Aug 24 '14 at 21:50
• What I pointed out is that you need to use a different data set for obtaining empf, than the one that you will use to fit the whole model -not that you should not use empirical findings. This has nothing to do with "testing the model on more data sets". Here you are using a data set to form the model (partially), it is not sound practice to then use the same data set to see "whether the model fits well to the data". – Alecos Papadopoulos Aug 24 '14 at 22:02
• I think this depends on how I actually used the data to form the model. One think would be, as you said, to train a model with the dataset and test it with the same dataset. Another thing would be to use the dataset as an indication that, for example, one function of the model need to be concave, as the data shows. Yes, using the model based on the real data increased the chance of fitting the data, but it is possible and reasonable to argue in some cases that most of the "fitting" is done by the part of the model not based on the data itself. – Vaaal Aug 24 '14 at 22:11
• ...meaning, for example, that the function in question might have been specified as convex, and nothing visible will change in the results? I understand your view of the matter, but if you cannot somehow quantify "how much of the fitting" is due to the "rest" of the model, I believe your research will be open to easy criticism on this point, perhaps unjustly compared to the overall achievement, but not unjustifiably, nevertheless. – Alecos Papadopoulos Aug 24 '14 at 23:24