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Evaluating the spatial heterogeneity of innovation drivers: a comparison between GWR and GWPR

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Abstract

In studies focusing on innovation activities, the potential spatial heterogeneity in the relationships between innovation and its triggering factors is an unexplored topic. On this ground, this paper aims to a twofold contribution. First, we verify the existence of spatial variability in the relationships. We evaluate the estimation gains due to local regressions, such as geographically weighted regression (GWR) and geographically weighted panel regression (GWPR), with respect to the classical global methods (e.g., OLS, Fixed Effects panel regression). Second, we compare the GWPR with GWR and global models to evaluate if the joint consideration of time and space dimensions allows for the rise of new insights. We resort to official data on 287 NUTS-2 European regions in 2014–2021. The results confirm that GWPR estimations significantly differ from GWR and global models, potentially producing new patterns and findings.

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Data availability statement

The data that support the findings of this study are available from the corresponding author, GM, upon reasonable request.

Notes

  1. The data can be found at the following URL:

    https://research-and-innovation.ec.europa.eu/statistics/performance-indicators/regional-innovation-scoreboard_en.

  2. As stated by European Commission [13] the data are normalised using the min–max procedure. The minimum score observed for all regions is first subtracted from the regional score. The result is then divided by the difference between the maximum and minimum scores observed for all regions. Formally, the procedure is the following: \(\frac{{X}_{r} - \mathrm{min}({\forall }_{r}{X}_{r})}{\mathrm{max}\left({\forall }_{r}{X}_{r}\right) - \mathrm{min}({\forall }_{r}{X}_{r})}\)

  3. Notably, for the five models (GWR 2014, 2017, 2019, and 2021, and GWPR) the optimal bandwidth procedure converges towards adaptative bi-square kernel but it highlights different nearest neighbours: 85 (GWR 2014), 58 (GWR 2017), 44 (GWR 2019), 62 (GWR 2021), and 93 (GWPR). This is not surprising since CV procedure is based on the value of dependent and independent variables. We adopt the larger bandwidth for sake of comparability between models. However, the estimations with different adaptative bi-square kernels show very similar patterns (respect to those reported in the paper). We do not report here for conciseness but are available upon request.

  4. We estimate the GWR and GWPR models through R software. Unfortunately, the Monte Carlo test has not implemented in GWPR routine yet. For this test, we only refer to GWR. The spatial variability of GWPR local parameters can be evaluated only through the F test (at least one coefficient is spatially varying) and the local t tests.

  5. In Fig. 4 we show the results of all GWR estimated (one for each year in the period 2014–2021) and GWPR since the graphical representation allows it. For the other figures, as already stated, it is not possible for sake of space.

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Authors and Affiliations

  1. Department of Management and Quantitative Studies, University of Naples “Parthenope”, Naples, Italy

    Gaetano Musella & Rosalia Castellano

  2. Department of Economic and Legal Studies, University of Naples “Parthenope”, Naples, Italy

    Emma Bruno

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  1. Gaetano Musella
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Musella, G., Castellano, R. & Bruno, E. Evaluating the spatial heterogeneity of innovation drivers: a comparison between GWR and GWPR. METRON 81, 343–365 (2023). https://doi.org/10.1007/s40300-023-00249-0

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