Estudio de la organización

The model that was proposed in this report, did not perform well when it came to predicting quantiles of the citation distribution for a group of articles from the same country or university. The model did predict the quantiles correctly when predicting for a group of articles from different countries and univer- sities. This means that the Impact Factor and the number of recent citations are insufficient to predict the quantiles for the separate countries or universities correctly. Apparently, some factor is missing in the model that captures the differences between countries and universities. To be able to predict the performance of publications from a certain university or country, a different model would be needed.

In this report, all publications from the scientific field of Physics were taken into account. This is a very broad field of science, with different subfields. Within those subfields, the citation behavior might be different. This is not taken into account in this report, and might need further research.

In the model which we presented in this report, two factors were taken into account to predict the quantiles: the Impact Factor and the number of citations in the first year after publishing. Of course it is possible to add more factors to this model, such as the number of pages that the article consists of or the number of references in the article. In further research, the effect of adding these factors to the model could be investigated. In particular, it would be interesting to see if adding one or more covariates solves the inaccuracy in the predictions for a set of papers from the same country or university.

Another possibility for further research lies in the fitness factor we used in the model. We assumed that the fitness factor was a product of the two covariates to a certain power. Other variants of the fitness factor could also be investigated.

Appendix A

Quantile Regression

min ξ X i ρj(yi−xiξ), (A.1) where ρj(z) =zj−z1z<0,

is minimized. To show that this quantile regression indeed fits the quantiles of the distribution, we look at the directional derivatives of equation (A.1) [14]. The values ofyi−xiξare just the residuals, which

we callri. The directional derivative of the function that is minimized along vectoruis:

d dt X i ρj(yi−xi(ξ+ut))|t=0 = −X i xiuρ0j(ri−xiut))|t=0 = −X i xiuφj(ri,−xiu), where φj(a, b) = ( j−1a<0 a6= 0 j−1b<0 a= 0.

The vectorξ minimizes equation (A.1), if the directional derivatives of the function are larger than or equal to zero in all directions, so if they satisfy:

−X

i

xiuφj(ri,−xiu)≥0, ∀u.

If we takeu| ₌

1 0 0

, then because of the definition ofX, xiu= 1for alli. Now the directional

derivative with respect to this vector should of course be larger than or equal to zero:

−X i φ(ri,−1) ≥ 0 − X i:ri=0 (j−1)− X i:ri>0 j− X i:ri<0 (j−1) ≥ 0 −Nz(j−1)−Npj−Nn(j−1) ≥ 0.

Here Nz, Np and Np are respectively the number of observations with residuals of value zero, the

foru=−1 0 0

,xiu=−1for alli, so:

−X i φ(ri,1) ≥ 0 X i:ri=0 j+ X i:ri>0 j+ X i:ri<0 (j−1) ≥ 0 Nzj+Npj+Nn(j−1) ≥ 0.

The total number of articles in the regression isn, wheren=Nz+Np+Nn. By rewriting the previous

two inequalities and combining them, the following inequalities can be obtained: Nn n ≤ j ≤ Nz+Nn n , Np n ≤ 1−j ≤ Nz+Np n .

This means that indeed by minimizing equation (A.1), the resulting model fits the quantiles exactly onto the empirical quantiles. A fraction ofjobservations has a value less than the predictedjthquantile.

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