4. Results and Main Findings
4.5. Diagnostic of the model
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4.5. Diagnostic of the model
Chen, Ender, Mitchell, and Wells (2013)explain: It is necessary to verify whether our model satisfies the assumptions of logistic regression because the results can be biased if the basic assumptions are not met.
First of all, it is necessary to specify what assumptions are needed to take into account.
Chen, Ender, Mitchell, and Wells (2013) made the next list of assumptions that our model needs to meet:
- The true conditional probabilities are a logistic function of the independent variables.
- No important variables are omitted.
- No extraneous variables are included.
- The independent variables are measured without error.
- The observations are independent.
- The independent variables are not linear combinations of each other.
4.5.1. Specification Error
According to Chen, Ender, Mitchell, and Wells (2013), building a logit or logistic model can be subject to two types of specification errors: First, the logit is not the correct function to use. Second, the model does not include relevant variables, the model includes variables that are not relevant and the combination of the predictors is not linear. However, the second specification error is the most important to solve, because the inclusion or exclusion of the correct variables become important in practice.
In order to do this, the research uses the test given by the software STATA on our third improved model.
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Table N° 24
Analysing the result given by the command linktest, it is possible to observe that the value of _hat is significant for the four outcomes (innovation in product, innovation in process, innovation in organization and innovation in commercialization). This result shows us that the research includes meaningful variables in the model. Second, it is possible to observe that the variable _hatsq is greater than 0.05, so _hatsq is not significant, so the linktest is not significant. This means that there is not statistical evidence that we omit relevant variables or the link function is not correctly specified.
4.5.2. Goodness-of-fit
The principal objective of this part is to see whether the model is statistically significant as a whole. In order to achieve this objective, the research will use the Hosmer and Lemeshow’s goodness-of-fit test and it will also compare some measures such AIC (Akaike Information Criterion) and BIC (Bayesian Information Criterion) between our final model and the second model developed in this work.
Table N° 25
Inn_Prod Inn_Proc Inn_Orga Inn_Comm
_hat 0.00 0.00 0.00 0.00
_hatsq 0.22 0.21 0.08 0.628
_cons 0.37 0.43 0.35 0.757
P-Values of the Link Test
Inn_Prod Inn_Proc Inn_Orga Inn_Comm
groups 10 10 10 10
Hosmer-Lemeshow chi2 4.21 8.91 10.15 7.75
Prob > chi2 0.8376 0.3503 0.2545 0.4584
Values of the Hosmer-Lemeshow Goodness-of-Fit Test
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outcomes, it is possible to see that our models fit the data.Comparing the Model 3 and Model 2 in the four outcomes, it is possible to observe that the AIC (Akaike Information Criterion) of model 3 is minor than the same value of the model 2 for the four outcomes. Under this result, the model 3 is the best model to use.
A similar result is found for the BIC (Bayesian Information Criterion), so the model 3 again is the best model to use.
4.5.3. Multicollinearity
According to Chen, Ender, Mitchell, and Wells (2013), “multicollinearity (or collinearity for short) occurs when two or more independent variables in the model are approximately determined by a linear combination of other independent variables in the model”.
Table N° 26
Model 3 Model 2 Difference Model 3 Model 2 Difference Model 3 Model 2 Difference Model 3 Model 2 Difference
Model: logit logit logit logit logit logit logit logit
N: 1442.00 1442.00 0.00 1442.00 1442.00 0.00 1442.00 1442.00 0.00 1442.00 1442.00 0.00
Log-Lik Intercept Only: -997.07 -997.07 0.00 -971.37 -971.37 0.00 -972.94 -972.94 0.00 -986.43 -986.43 0.00 Log-Lik Full Model: -778.45 -777.52 -0.93 -864.12 -861.88 -2.24 -861.88 -855.06 -6.83 -877.19 -875.64 -1.54
Prob > LR: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
McFadden's R2: 0.22 0.22 0.00 0.11 0.11 0.00 0.11 0.12 -0.01 0.11 0.11 0.00
McFadden's Adj R2: 0.20 0.19 0.01 0.09 0.09 0.01 0.10 0.09 0.00 0.09 0.09 0.01
Maximum Likelihood R2: 0.26 0.26 0.00 0.14 0.14 0.00 0.14 0.15 -0.01 0.14 0.14 0.00
Cragg & Uhler's R2: 0.35 0.35 0.00 0.19 0.19 0.00 0.19 0.20 -0.01 0.19 0.19 0.00
Efron's R2: 0.28 0.28 0.00 0.14 0.15 0.00 0.15 0.16 -0.01 0.15 0.15 0.00
Variance of y*: 5.03 5.04 -0.01 3.99 4.01 -0.02 4.03 4.09 -0.07 4.01 4.02 -0.01
Variance of error: 3.29 3.29 0.00 3.29 3.29 0.00 3.29 3.29 0.00 3.29 3.29 0.00
Count R2: 0.74 0.74 0.00 0.68 0.68 0.01 0.68 0.68 0.00 0.68 0.68 0.00
Adj Count R2: 0.45 0.44 0.00 0.21 0.20 0.02 0.21 0.21 0.00 0.26 0.26 0.00
AIC: 1.11 1.11 -0.01 1.22 1.23 -0.01 1.22 1.22 0.00 1.24 1.25 -0.01
AIC*n: 1592.90 1607.03 -14.13 1764.24 1775.77 -11.52 1759.77 1762.12 -2.35 1790.37 1803.28 -12.91
BIC: -8800.97 -8744.65 -56.32 -8629.63 -8575.92 -53.71 -8634.10 -8589.57 -44.54 -8603.50 -8548.40 -55.10
BIC': -335.41 -293.63 -41.78 -112.66 -73.50 -39.17 -120.28 -90.29 -29.99 -116.65 -76.10 -40.56
Innovation in Product Innovation in Process Innovation in Organization Innovation in Organization
Other Criterias of Goodness-of-Fit Test
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possible to conclude that all the variables are close to being orthogonal to each other, in this sense, there is no multicollinearity. Another important way of realizing the presence of multicollinearity is the correlation between variables. As it is possible to observe the value of the correlations between different variables don’t surpass the value of 0.4, so there is not a strong correlation between variables.4.5.4. Influential Observations
Also, it is important to analyse whether the observations can impact in our model. In order to do this, the research will use the Pearson residual, the deviance residual, the leverage and the cook distance. An interesting aspect, in general, is that according to
Table N° 27
RD_I adnet_know adnet_Prod adnet_cust abs_capa year size industry
RD_I 1.00
adnet_know 0.21 1.00
adnet_Prod 0.15 0.22 1.00
adnet_cust 0.13 0.15 0.48 1.00
abs_capa 0.26 0.10 0.10 0.06 1.00
year 0.14 0.07 0.05 -0.01 0.21 1.00
size 0.09 0.08 0.03 -0.02 0.37 0.28 1.00
industry 0.11 0.02 0.05 0.06 0.00 0.11 -0.08 1.00
Matrix of Correlation
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Figure N° 01
cut off points of leverage and cook distance there is not an influential observation in the model.
However, the number of cases that surpass the cut off for Pearson Residual and deviance residual are high. In this sense, there is a covariance pattern that is not covered by the model. Analysing the graphs of the influential points for the model of innovation in product, it is possible to observe that there are points that highlight over the rest of observations such as the following observations: 1172, 1528, 743, 605, 1368, 553, 32, and 134.
Table N° 29
Diagnostic of Influential Observation for the Model of Innovation in Product
Inn_Prod Inn_Proc Inn_Orga Inn_Comm
abs(Pearson Residual) >2 69 30 41 40
abs(Deviance Residual) >2 34 12 13 17
Leverage (hat value) > 2 0 0 0 0
Leverage (hat value) > 3 0 0 0 0
Cook Distance >1 0 0 0 0
Number of observations according to the cut points that determine the existence of influence of the observation
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However, analysing the change in the log likelihood after the exclusion of this points, it is possible to see that there is no significant change in the model. In this sense, despite the existence of outliers, they do not have enough influence in the model
Making a similar analysis of the graphs of the influential points for the model of innovation in process, the most outstanding observations are 743, 1339, 312, 1429, 1656, and 1178.
Figure N° 02 Table N° 30
Observation Original loglikehood
Corrected
loglikehood Diference
1172 -777.52 -775.80 -1.71
1528 -777.52 -775.42 -2.10
743 -777.52 -777.15 -0.36
605 -777.52 -777.13 -0.39
1368 -777.52 -775.94 -1.58
553 -777.52 -776.13 -1.39
32 -777.52 -774.93 -2.58
134 -777.52 -774.63 -2.89
Comparison of the Innovation in Product model after the exclusion of the influencial points
Diagnostic of Influential Observation for the Model of Innovation in Process
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Despite the presence of outliers, it is possible to observe that there is not a significant change in the log likelihood after the exclusion of these points; in other words, there is not a real influential point that can affect the model and the estimation made by the research of the Innovation in Process and its determinants.
After a similar analysis, the graphs of the influential points for the model of innovation in organization highlight the observations with differing of the rest of observations:
743, 1339, 812, 1429, 664, and 1010.
Figure N° 03 Table N° 31
Observation Original loglikehood
Corrected
loglikehood Diference
743 -861.88 -860.72 -1.16
1339 -861.88 -860.83 -1.05
312 -861.88 -860.81 -1.08
1429 -861.88 -861.23 -0.66
1656 -861.88 -860.09 -1.79
1178 -861.88 -860.09 -1.79
Comparison of the Innovation in Process model after the exclusion of the influencial points
Diagnostic of Influential Observation for the Model of Innovation in Organization
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There is not a significant change in the log likelihood after the exclusion of the most outstanding points of the previous graphs, so at least there is no evidence that a real influential point can affect the model and the estimation of this model.
Finally, the research made the analysis of graphs of the influential points for the model of innovation in commercialization. The analysis shows the existence of some points that highlight over the rest of observation such as605, 199, 743, 879, 1623 and 296.
Table N° 32
Figure N° 04 Observation Original
loglikehood
Corrected
loglikehood Diference
743 -855.06 -853.64 -1.42
1339 -855.06 -854.12 -0.94
812 -855.06 -854.24 -0.82
1429 -855.06 -854.34 -0.71
664 -855.06 -854.52 -0.54
1010 -855.06 -853.84 -1.22
Comparison of the Innovation in Organization model after the exclusion of the influencial points
Diagnostic of Influential Observation for the Model of Innovation in Commercialization
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Comparison of the Innovation in Commercialization model after the exclusion of the influencial points
After the analysis of the impact of these points in the model of Innovation in commercialization, it is possible to observe that there is not a significant change in the log likelihood after the exclusion of the most outstanding points. Thus, despite the presence of outliers, there is not a real influential observation in the model.
4.5.5. Heteroscedasticity
Another important aspect to analyse is the presence of heteroscedasticity in our model.
According to Giles (2011), the heteroscedasticity problem can be much more serious than what is generally commented, since, in the presence of heteroscedasticity, the MLEs of the parameters of these models are inconsistent.
Because in practice the difference between the choice of the logit and probit model is very small, a very practical way to analyse the presence of heteroscedasticity can be done using the hetprob command provided by the Stata statistical package that will provide us with a chi-square test on the null hypothesis of homoscedasticity. For this the analysis will be carried out in the groups concerning the technological intensity (industry) and size of the company (size).
Table N° 33
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Analysing the values of the heteroscedasticity test from the hetprob command, we can corroborate that at 5% significance for each innovation outcome, there is no statistical evidence that rejects the null hypothesis of homoscedasticity between groups for the variable of technological intensity and the variable size of the companies. In this sense it is possible to say that the models do not present a problem of heteroscedasticity and therefore the coefficients obtained by the method of Maximum Likelihood are not biased.
4.5.6. Robustness Test
Finally, it is important to review the robustness of the coefficients of our variables of interest. In the linear regression model, through the addition or elimination of variables, the coefficients of the regression are maintained with the same behaviour and remain relatively unchanged. However, as pointed out by Holm, Karlson & Breen (2012), "the common practice of comparing the coefficients of a given variable through differently specified models adjusted to the same sample does not guarantee the same interpretation in logits and probits as in linear regression". Due to this, Holm, Karlson &
Breenproposed a different method that takes into account the problems that the previous method brings to prove the robustness. This method is known as the KHB method6, and separates the direct effect of the key variables (incorporating the rest of the variables)
Table N° 34
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and the corresponding indirect effect (the difference between the reduced model and the complete model).
According to the KHB confounding summary, the most robust coefficient of the model related to innovation in product is the coefficient related with the existence of network between a firm and other firm for the purpose of education, thus the total effect is 1.07 times larger than the direct effect, and 9.7% of the total effect is due to R&D and absorptive capacity.The less robust coefficient of this model is the coefficient related with the existence of network between a firm and knowledge organization (university, institutes, laboratories, etc) for the purpose to request financing, thus the total effect is 0.0598 than the direct effect, and -1572.97% of the total effect is due to R&D and absorptive capacity.
For the model related to innovation in process, the most robust coefficient in this model is the coefficient related with the existence of network between a firm and other firm for the purpose of working together in innovation activities, thus the total effect is 1.14than the direct effect, and 12.38% of the total effect is due to R&D and absorptive capacity. The less robust coefficient of this model is the coefficient related with the
1.adnet_know 0.0598 -1572.9700 0.5124 -95.1600 0.54602084 -83.14 7.7078987 87.03
2.adnet_know 1.3569 26.3000 1.3277 24.6800 1.1800987 15.26 1.1051251 9.51
3.adnet_know -0.2408 515.3300 1.4494 31.0100 1.4244191 29.8 1.5413222 35.12
4.adnet_know 2.4390 59.0000 1.8603 46.2500 1.8808374 46.83 1.7578292 43.11
0b.adnet_Prod . . . . . . . .
1.adnet_Prod 0.8445 -18.4100 0.9504 -5.2200 0.91783268 -8.95 0.92536202 -8.07
2.adnet_Prod 0.7907 -26.4700 0.8653 -15.5700 0.87201042 -14.68 0.70381173 -42.08
3.adnet_Prod 1.1075 9.7100 1.1509 13.1100 1.0944981 8.63 1.1309534 11.58
4.adnet_Prod 1.3186 24.1600 1.1413 12.3800 1.2295116 18.67 1.263225 20.84
0b.adnet_cust . . . . . . . .
1.adnet_cust 2.9490 66.0900 0.7907 -26.4700 0.86574629 -15.51 2.6250109 61.9
2.adnet_cust 1.8391 45.6300 1.6666 40.0000 2.5162798 60.26 3.4166047 70.73
3.adnet_cust 2.7751 63.9700 1.4628 31.6400 1.4667517 31.82 2.6525764 62.3
4.adnet_cust 1.5207 34.2400 -12.3635 108.0900 1.3578987 26.36 1.0905684 8.3
Innovation in Product Innovation in Process Innovation in Organization Innovation in Commercialization KHB Confounding Summary of the Innovation models
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existence of network between a firm and customers for the purpose of working together in innovation activities, thus the total effect is -12.51than the direct effect, and 108.09%
of the total effect is due to R&D and absorptive capacity.
For the model related to innovation in organization, the most robust coefficient is the same of the innovation in product. The total effect is 1.09 than the direct effect, and 8.63% of the total effect is due to R&D and absorptive capacity. The less robust coefficient of this model is the coefficient related with the existence of network between a firm and knowledge organization (university, institutes, laboratories, etc) for the purpose to request financing, thus the total effect is 0.54 than the direct effect, and -83.14% of the total effect is due to R&D and absorptive capacity.
For the model related to innovation in commercialization, the most robust coefficient in this model is the coefficient related with the existence of network between a firm and customer for the purpose of work together in innovation activities, thus the total effect is 1.09 higher than the direct effect, and 8.30% of the total effect is due to R&D and absorptive capacity.
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CONCLUSIONS
Innovation is an important factor in the economic development of a country; in fact, it is the only factor that supports a growing economy in the long run. Due to this, it is important to study the causes of innovation performance. For a long time, innovation studies considered innovation as a product of various firms' efforts in Research and Development activities. However, the evolutionary economy offered a better understanding through the insertion of the national innovation system framework. This framework makes an emphasis on the importance of this system in the diffusion and facilitation of innovation attempts. The main idea is that innovation is not operating in isolation but it is done through collaboration with the other elements of the system. The networks between organizations become a relevant aspect in order to make tangible the wide range of relationship between a firm and the different components.
However, the vision of an innovation system is not limited to the national level, but it is also extended to the regional level when the networks play an important role in the configuration of a region, especially in those regions that follow a bottom-up process of integration known as regionalization. This is the case of the Asia Pacific region where the economy interaction between non-state actors became the foundation of the region. With these considerations, the research proposes to study the impact of the networks in the innovation of Peruvian manufacture companies considering the role of those in the national and regional (Asia Pacific) networks.
The study shows that innovation in Peru is not an uncommon phenomenon. At least 40% of Peruvian companies innovate in some way (product, process, marketing and commercialization). In spite of this, innovation is still a practice that is carried out
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informally, since many companies do not register innovation through patents or other types of intellectual properties.
On the other hand, the situation of the networks between the Peruvian manufacturers and the other elements of the innovation system (national or transnational) is diverse.
Meanwhile, 60% of manufacturers have had links with some other firm; the situation is very different for the link between manufacturing and educational institutions where only 27% of companies have been linked to an educational institution.
With this panorama, the study provides interesting information. Thus, the study shows that networks are significant variables in the propensity to innovate, especially the production network that is relevant in all levels of analysis and it has a positive impact in all the dimensions of innovation. However, a fact that may be more useful is the impact of the network of manufactures and knowledge organizations (universities, private laboratories, public laboratories, etc). Thus, it was determined that the relationship between the company and the educational institution that aims to carry out innovation, tend to succeed in innovating in any of the forms of innovation present.
Although it seems an obvious result, this fact is encouraging since many of the companies do not work side by side with educational institutes and there is a great margin to work on policies that encourage the collaboration between both in search of a business renewal.
In the case of Asia Pacific networks, the network seems to have a positive impact in innovation, but its effect is not dominant over the impact of the national network and other regional networks. We observed two case studies that show how the relationship of Peruvian companies with organizations in Asia Pacific can generate innovation in the company and allow it to achieve various benefits.
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Thus, the first case analysed was the relationship between the economic group Intercop and the multinational IDEO, a company that is located in various cities in the Asia-Pacific region. After a joint effort, both institutions revolutionized Peruvian banking through the implementation of a commercial innovation with the name of “Interbank Explora”. The initial objective of this innovation was to improve the user experience by reducing queues, better care and a more welcoming environment. This would not have been possible without using the “design thinking” methodology and determining that the client needs to value their time and provide them with a better service.
The second case study shows a different relationship. The relationship of this case is between a parent company and a subsidiary company. The companies in question are Ajinomoto Corp. Inc. and Ajinomoto Peru. The influence of the Ajinomoto economic group served as the basis for Ajinomoto Peru to innovate in product and create Ajinomen. Ajinomen is a product made in Peru that mixes instant ramen soup and different ingredients preferred by Peruvian homes. This product is very successful, controlling 90% of the Peruvian market in this industry. Currently, it is exported to countries such as Chile, Colombia, Bolivia and Panama.
In general, the study covers a broad topic. A first point to consider in future studies would be the study of a particular type of network being the knowledge connections of national interest that could be supported with governmental intervention. One aspect that this study lacks and that can be taken into account in future research would be the impact of national or regional institutions that affect innovation. Another aspect that would be important in the future is the role of APEC (if it had one) on the innovation of member economies that are in development, especially of its Latin American members such as Mexico, Chile and Peru. This last aspect would imply a completely different but useful research area in the field of innovation and regionalism.
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