In chapter 3 and in the appendix we concluded that, given the characteristics of the dependent variable, the Zero-Inflated Negative Binomial Model was the preferred model to study the determinants of team output in Colombia. Given the relatively complexity of this model, a brief explanation of the ways its coefficients should be interpreted is worth doing before we discuss the findings.
As Long and Freese (2001) acknowledge, when interpreting zero inflated models, it is easy to be confused by the direction of the coefficients. The first portion of the Stata output, which in this study is reported in the first four columns, contains coefficients for those in the Not Always-0 Group. This group comprises those teams who have the opportunity to report bibliographic products during the period of observation. The
coefficients can be interpreted in the same way as coefficients from the OLS, the PRM or the NBRM models. The second portion of the Stata output, which in this study is reported in the latter three columns, contains coefficients for the log-odds of being in the Always-0 Group of teams compared to the Not Always-0 Group. As explained earlier, a team is in the Always-0 group if it is not allowed to report bibliographic products due to structural constraints (it works for industry on cutting edge technologies or works for a government agency on issues not to be made public, etc.) or due to conjunctural reasons (it did not
have the chance to report bibliographic products for a given reason). These coefficients can be interpreted just as the coefficients for a binary logit model. When the same variables are included in both equations (because they are judged to be important for explaining team output as well as for explaining the impossibility of teams to report bibliographic products, or due to the lack of theory like in the case of this study), the signs of the corresponding coefficients from the binary equation are often in the opposite
direction of the coefficients for the count equation. Hence, while the first columns help to predict number of bibliographic products so that a negative coefficient would indicate lower productivity, the latter columns helps to predict membership in the group of teams that always has zero counts so a positive coefficient implies lower productivity.
Thus, using a Zero-Inflated Negative Binomial model to account for the effects of research collaboration on team output in Colombia, we find that teams that collaborate internationally, that are large in size, that have many PhDs, and that report many projects active tend to be more productive than comparable teams that do not collaborate
internationally, that are of a small size, that have few or no PhD members, and that report few projects active. Teams working in the humanities are less productive than comparable teams working in the natural sciences. Teams affiliated with small institutions are less productive than comparable teams affiliated with big institutions (see Table 12).
Collaborating internationally or having many research projects active reduces the odds of reporting no bibliographic products. In contrast, larger teams, older teams, teams working in the medical sciences, and teams affiliated with the business or the government sector, are more likely than comparable teams of smaller size, younger teams, teams
working in the natural sciences, and teams affiliated with the academic sector to be in the always-0 group of non-productive teams.
Table 12: Factors Affecting Team Output: ZINB
Tot. Bib. Prods. 2003-5 Always0
Coef. z P>|z| Coef. z P>|z|
Internat. Res. Coll. 0.305 4.38 0.000 -0.824 -3.13 0.002
Team size in 2003 0.024 2.71 0.007 0.052 2.49 0.013 Team Age in 2003 0.011 1.74 0.082 0.041 2.22 0.027 Total PhDs in 2003 0.075 3.27 0.001 -0.075 -1.29 0.197 Tot. Proj. in 2003 0.044 7.54 0.000 -0.064 -2.11 0.035 Agrosciences -0.098 -0.55 0.584 0.786 1.78 0.075 Medical Sciences 0.028 0.26 0.794 0.822 2.20 0.028 Social Sciences 0.003 0.03 0.975 0.559 1.37 0.170 Humanities -0.181 -1.98 0.047 0.288 0.74 0.459 Engineering 0.017 0.16 0.871 0.216 0.53 0.598 Other Sciences -0.169 -1.09 0.274 0.178 0.32 0.750 Business Sector -0.383 -1.71 0.088 1.198 2.33 0.020 Government 0.205 1.22 0.222 1.256 3.07 0.002 Other Sector 0.300 1.70 0.090 0.579 0.92 0.355
Mid. Home Inst. 0.036 0.51 0.609 -0.373 -1.52 0.129
Small Home Inst. -0.268 -2.37 0.018 -0.328 -0.82 0.415
Small City 0.131 0.60 0.549 0.521 0.79 0.432 Midsize City -0.139 -1.77 0.077 -0.363 -1.20 0.230 Constant 1.521 14.14 0.000 -1.957 -4.83 0.000 /lnalpha -0.020 -0.33 0.744 alpha 0.980 Observations: 1889
International research collaboration is the explanatory variable with the greatest impact on team productivity right after the number of R&D projects active and the number of PhDs a team has. In fact, a one standard deviation increase (not shown in the table) in international collaboration increases team’s expected productivity count by 16%, holding the other variables constant (the effects of number of projects active and of members with PhDs are 34% and 18% respectively). The expected count of bibliographic
products of collaborating teams is 36% higher than that of non-collaborating teams, and their odds of being in the always zero group of unproductive teams are 56% lower than comparable teams that do not collaborate internationally. Measured in terms of discrete changes, and holding all other variables constant at their means, collaborating
internationally increases expected productivity count by 3.14 bibliographic products. On the other hand, regarding the control variables, team size increases the
expected team’s rate of bibliographic products, but curiously, an additional team member increases team’s odds of being in the always zero group. This contradictory result may suggest the presence of quadratic effects of team size, that is, it might be the case that team size increases productivity but at a decreasing rate. This hypothesis is explored later.
The data does not support the claim found in the literature that team age increases team productivity (Harrison, Price et al. 2002; Rey-Rocha, Martin-Sempere et al. 2002), such effects are not confirmed by the data. As claimed by Cohen 1991, team age is not associated with team productivity. Instead, in the Colombian case, a one unit increase of team age increases team’s odds of being in the non-productive group of teams, once we hold the other variables constant.
The number of doctorates increases team’s expected bibliographic production, but it does not affect the odds of being in the always-0 group of teams. As one would have thought, the number of R&D projects active increases team’s expected rate of
bibliographic products and decreases its odds of being in the always-0 group. Teams working in medical sciences have similar expected rate of production of comparable teams working in the natural sciences, but they are more likely of being in the
contrary to what one would expect, teams working in the engineering are not less productive or more likely of being in the Always-0 group than teams of comparable characteristics working in the natural sciences.
As expected, teams affiliated with the business sector are less productive and are more likely of not having the opportunity to report bibliographic products than similar teams affiliated with the academic sector. Teams affiliated with the government sector, as compared to teams affiliated with institutions working in the academic sector, do not have different expected rate of production, however, and as expected, these teams are more likely than comparable teams affiliated with the education sector of not having the opportunity to report bibliographic products. As one would think, teams affiliated with small institutions are less productive than teams affiliated with big institutions, but these teams are not more likely than comparable teams affiliated with big institutions to report zero bibliographic products.
Finally, contrary to extant literature (see literature review), the size of the urban agglomerate where the team is located does not seem to affect its production nor its likelihood of reporting zero counts once we hold the other variables constant. In fact, a Wald Test performed on the joint effects of the variables associated with team location on team productivity shows that, holding all other variables constant, there is a 26%
probability that the observed results could have occurred by chance (Prob > chi2 = 0.2649). Therefore we conclude that location is not associated with team output. Furthermore, the measures of fit shown in Table 13 below, allows us to confidently conclude that the model without these location variables (called ‘current’ model in the
table) is much better than the full model with all the variables considered. The difference of 24.191 in BIC' provides very strong support for the ‘restricted’ model.
Table 13: Measures of Fit to Compare Models With and Without the Location Variables
Current Saved Difference Model: zinb zinb
N: 1889 1889 0 Log-Lik Intercept Only -5889.003 -5889.003 0.000 Log-Lik Full Model -5631.601 -5628.609 -2.992 D 11263.202(1854) 11257.218(1850) 5.984(4) LR 514.803(32) 520.787(36) 5.984(4) Prob > LR 0.000 0.000 0.200 McFadden's R2 0.044 0.044 -0.001 McFadden's Adj R2 0.038 0.038 0.000 ML (Cox-Snell) R2 0.239 0.241 -0.002 Cragg-Uhler(Nagelkerke) R2 0.239 0.241 -0.002 AIC 6.000 6.001 -0.001 AIC*n 11333.202 11335.218 -2.016 BIC -2723.008 -2698.817 -24.191 BIC' -273.401 -249.210 -24.191 BIC used by Stata 11527.235 11551.427 -24.191 AIC used by Stata 11333.202 11335.218 -2.016 Difference of 24.191 in BIC' provides very strong support for current model.
The agglomeration effects extensively claimed in the literature seem therefore not to be confirmed by the data in the Colombian case. Further investigation is necessary. We will come back to this point later.
To explore if there are curvilinear effects (Lewis 2002) of team size, team age, number of PhDs, and number of projects active, four quadratic variables are added to the model without the location variables. According to the regression, team size, team age, and number of projects active increase the expected number of bibliographic products but at a decreasing rate. In fact, holding all other variables constant, every additional team member increases expected team productivity, but once the team reaches a size greater
than 16 members, team output begins to decrease at an increasing rate with every additional team member. This finding is consistent with that suggested by Qurashi 1991 and Qurashi 1993 who also found curvilinear effects of team size in the US, UK, Pakistan, Bangladesh, and Greece with peaks between 6 and 46 members.
Interestingly, once the team reaches 20 years old, its output begins to fall at an increasing rate with every additional year of team age, holding the other variables constant. Finally, as the number of projects active rises, team productivity increases but once the team reaches a top of 46 projects active, the number of bibliographic products decreases at an increasing rate with every additional project, holding the other variables constant. All these top values are within the data range. Therefore, we conclude that there are curvilinear effects of team size, team age and number of projects active but not of number of doctorates a team has.
The comparison of the models with and without the quadratic variables through an LR Chi2 test shows that the model with the quadratic variables is preferred over the model without them. For this reason, we report the results obtained using the model with the quadratic variables in the study of the effects of different types of collaboration activities and of partners. Before we do that, let’s first analyze the overall effects of international research collaboration on research team output using control groups.
5.2 Overall Impact of International Research Collaboration on Team Output in