Daily Archives: 07/02/2011

Publications, Statistics

The longer the better ?

4 Comments

No, this time it is not a post for Valentine’s day… It is simply that a few days ago, on Gaïa Universitas, Rachel mentioned a study on academic journals in astronomy. The study is online here, written by Krzysztof Zbigniew Stanek. « Naively, one would expect longer papers to have larger impact (i.e., to be cited more) – how long a paper should be to maximize its impact? Is it better to write several shorter papers or one longer paper? ». Actually, I did not expect that, and I was truly surprised to see that the number of citations was an increasing function of the number of pages. So I had a look at several academic in economics and mathematics. The first journal I looked at is the Journal of Finance. Here, the relationship between the number of pages and the number of citation is strong: a 40 page paper is – on average – two times more cited than a 20 page paper. Actually, the shape of the regression curve is rather close to the one obtained in Krzysztof’s paper,

The colors are due to the fact that some articles were published in 2010, and some in 1995. Obviously, the number of citations is a function of the year of publication (a longer post will be published soon on the dynamics of the citation process). I considered only articles published before 2005 to fit a regression model (here a spline regression, to see if the function is linear). And indeed, a longer paper has more chance to be cited.
Then, I looked at the Journal of Multivariate Analysis, which is a mathematical journal, where (theoretical) econometricians can publish.

Here the pattern is rather different: if we do not take into account short notes, the number of citations is independent of the size of the paper.
The more I look at those graphs, the more disturbing I find them…

  • on the one hand, I strongly believe that the size of the paper has nothing to do with the quality (or the importance) of the paper: so in some sense, I was expecting a flat regression, like the one we see above, with the Journal of Multivariate Analysis. It might come from the fact that in statistics (for instance) with empirical processes, e.g., proofs are extremely long and technical (and papers are long), while on stochastic orderings, proofs are extremely short (and papers rather short). But both can appear in the same journal…
  • on the other hand, researchers are more and more evaluated, and a common tool is to look at citation indexes (the called « publish or perish » paradigm). The more citations, the better the researcher, something like that… So sometimes, when we have a quite long paper, the question that naturally arises is: why not splitting the paper in two ? with flat regression, it is, indeed, optimal to split the paper (if possible) in two, since two papers with 20 page each might yield two times more citations than one. But with a curve like the one we see with the Journal of Finance, such a split is not an issue…

Anyway, I did really like the conclusion of Krzysztof’s paper « This paper will not be submitted to any journal, but please feel free to cite it as often as possible, or better yet cite my regular astronomical papers »….

Computer, Databases, Statistics

Open data might be a false good opportunity…

2 Comments

I am always surprised to see many people on Twitter tweeting about #opendata, e.g. @data4all, @usdatagov, @datapublicatwit, @ProPublica or @open3 among so many others… Initially, I was also very enthousiastic, but I have to admit thatopen data are rarely raw data. Which is what I am usually looking for, as a statistician…
Consider the following example: I was wondering (Valentine’s day is approaching)when will a man born in 1975 (say) get married – if he ever gets married ?More technically, I was looking for a distribution of the age of first marriage (given the year of birth), including the proportion of men that will never get married, for that specific cohort.

The only data I found on the internet is the following, on statistics.gov.uk/

Note that we can also focus on women (e.g. here). Is it possible to use that opendata to get an estimation of the distribution of first marriage for some specific cohort ? (and to answer the question I asked). Here, we have two dimensions: on line http://freakonometrics.free.fr/blog/latex/marriage01.gif, the year (of the marriage), and on column http://freakonometrics.free.fr/blog/latex/marriage02.gif, the age of the man when he gets married. Assume that those were rawdata, i.e. that we have the number of marriages of men of age http://freakonometrics.free.fr/blog/latex/marriage02.gif during the year http://freakonometrics.free.fr/blog/latex/marriage01.gif.

We are interested at a longitudinal lecture of the table, i.e. consider some man born year http://freakonometrics.free.fr/blog/latex/marriage03.gif, we want to estimate (or predict) the age he will get married, if he gets married. With raw data, we can do it… The first step is to build up triangles (to have a cohort vs. age lecture of the data), and then to consider a model, e.g.

http://freakonometrics.free.fr/blog/latex/marriage04.gif

where http://freakonometrics.free.fr/blog/latex/marriage05.gif is a year effect, and http://freakonometrics.free.fr/blog/latex/marriage06.gif is a cohort effect.

base=read.table("http://freakonometrics.free.fr/mariage-age-uk.csv",
sep=";",header=TRUE)
m=base[1:16,]
m=m[,3:10]
m=as.matrix(m)
triangle=matrix(NA,nrow(m),ncol(m))
n=ncol(m)
for(i in 1:16){
triangle[i,]=diag(m[i-1+(1:n),])
}
triangle[nrow(m),1]=m[nrow(m),1]
 
triangle
      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
 [1,]   12  104  222  247  198  132   51   34
 [2,]    8   89  228  257  202  102   75   49
 [3,]    4   80  209  247  168  129   92   50
 [4,]    4   73  196  236  181  140   88   45
 [5,]    3   78  242  206  161  114   68   47
 [6,]   11  150  223  199  157  105   73   39
 [7,]   12  117  194  183  136   96   61   36
 [8,]   11  118  202  175  122   92   62   40
 [9,]   15  147  218  162  127   98   72   48
[10,]   20  185  204  171  138  112   82   NA
[11,]   31  197  240  209  172  138   NA   NA
[12,]   34  196  233  202  169   NA   NA   NA
[13,]   35  166  210  199   NA   NA   NA   NA
[14,]   26  139  210   NA   NA   NA   NA   NA
[15,]   18  104   NA   NA   NA   NA   NA   NA
[16,]   10   NA   NA   NA   NA   NA   NA   NA
 
Y=as.vector(triangle)
YEARS=seq(1918,1993,by=5)
AGES=seq(22,57,by=5)
X1=rep(YEARS,length(AGES))
X2=rep(AGES,each=length(YEARS))
reg=glm(Y~as.factor(X1)+as.factor(X2),family="poisson")
summary(reg)
 
Call:
glm(formula = Y ~ as.factor(X1) + as.factor(X2), family = "poisson")
 
Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-5.4502  -1.1611  -0.0603   1.0471   4.6214  
 
Coefficients:
                    Estimate Std. Error z value Pr(>|z|)    
(Intercept)        2.8300461  0.0712160  39.739  < 2e-16 ***
as.factor(X1)1923  0.0099503  0.0446105   0.223 0.823497    
as.factor(X1)1928 -0.0212236  0.0449605  -0.472 0.636891    
as.factor(X1)1933 -0.0377019  0.0451489  -0.835 0.403686    
as.factor(X1)1938 -0.0844692  0.0456962  -1.848 0.064531 .  
as.factor(X1)1943 -0.0439519  0.0452209  -0.972 0.331082    
as.factor(X1)1948 -0.1803236  0.0468786  -3.847 0.000120 ***
as.factor(X1)1953 -0.1960149  0.0470802  -4.163 3.14e-05 ***
as.factor(X1)1958 -0.1199103  0.0461237  -2.600 0.009329 ** 
as.factor(X1)1963 -0.0446620  0.0458508  -0.974 0.330020    
as.factor(X1)1968  0.1192561  0.0450437   2.648 0.008107 ** 
as.factor(X1)1973  0.0985671  0.0472460   2.086 0.036956 *  
as.factor(X1)1978  0.0356199  0.0520094   0.685 0.493423    
as.factor(X1)1983  0.0004365  0.0617191   0.007 0.994357    
as.factor(X1)1988 -0.2191428  0.0981189  -2.233 0.025520 *  
as.factor(X1)1993 -0.5274610  0.3241477  -1.627 0.103689    
as.factor(X2)27    2.0748202  0.0679193  30.548  < 2e-16 ***
as.factor(X2)32    2.5768802  0.0667480  38.606  < 2e-16 ***
as.factor(X2)37    2.5350787  0.0671736  37.739  < 2e-16 ***
as.factor(X2)42    2.2883203  0.0683441  33.482  < 2e-16 ***
as.factor(X2)47    1.9601540  0.0704276  27.832  < 2e-16 ***
as.factor(X2)52    1.5216903  0.0745623  20.408  < 2e-16 ***
as.factor(X2)57    1.0060665  0.0822708  12.229  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
 
(Dispersion parameter for poisson family taken to be 1)
 
    Null deviance: 5299.30  on 99  degrees of freedom
Residual deviance:  375.53  on 77  degrees of freedom
  (28 observations deleted due to missingness)
AIC: 1052.1
 
Number of Fisher Scoring iterations: 5

Here, we have been able to derive http://freakonometrics.free.fr/blog/latex/marriage12.gif and http://freakonometrics.free.fr/blog/latex/marriage13.gif, where now http://freakonometrics.free.fr/blog/latex/marriage14.gifdenotes the cohort.
We can now predict the number of marriages per year, and per cohort

http://freakonometrics.free.fr/blog/latex/marriage15.gif

Here, given the cohort http://freakonometrics.free.fr/blog/latex/marriage03.gif, the shape of http://freakonometrics.free.fr/blog/latex/marriage16.gif is the following

Yp=predict(reg,type="response")
tYp=matrix(Yp,nrow(m),ncol(m))
tYp[16,]
tYp[16,]
[1]  10.00000 222.94525 209.32773 159.87855 115.06971  42.59102
[7]  18.70168 148.92360
The errors (Pearson error) look like that
Ep=residuals(reg,type="pearson")
 

(where the darker the blue, the smaller the residuals, and the darker the red, the higher the residuals). Obviously, we are missing something here, like a diagonal effect. But this is not the main problem here…

I guess that study here is not valid. The problem is that we deal with open data, and numbers of marriages are not given here: what is given is a he proportion of marriage of men of age http://freakonometrics.free.fr/blog/latex/marriage02.gif during the year http://freakonometrics.free.fr/blog/latex/marriage01.gif, with a yearly normalization. There is a constraint on lines, i.e. we observe

http://freakonometrics.free.fr/blog/latex/marriage08.gif

so that

http://freakonometrics.free.fr/blog/latex/marriage09.gif

This is mentioned in the title

It is still possible to consider a Poisson regression on the http://freakonometrics.free.fr/blog/latex/marriage10.gif, but unfortunately, I do not think any interpretation is valid (unless demography did not change last century). For instance, the following sum

http://freakonometrics.free.fr/blog/latex/marriage17.gif

looks like that

apply(tYp,1,sum)
 [1] 919.948 838.762 846.301 816.552 943.559 930.280 857.871 896.113
 [9] 905.086 948.087 895.862 853.738 826.003 816.192 813.974 927.437

i.e. if we look at the graph

But I do not think we can interpret that sum as the probability (if we divide by 1,000) that a man in that cohort gets married…. And more basically, I cannot do anything with that dataset…

So open data might be interesting. The problem is that most of the time, the data are somehow normalized (or aggregated). And then, it becomes difficult to use them…

So I will have to work further to be able to write something (mathematically valid) on marriage strategy before Valentine’s day…. to be continued.