Figure 1.
Intersecting scopes of reality delimited and described in the literature under the labels of institutional endowment (IE), institutional thickness (IT), and formal institutional environment (FIE)
Note: range sizes reflect, indicatively, the depth and breadth of the relevant literature
Source: own analysis
Figure 2.
Study area
Note: boundaries of the historical regions are reconstructed, based on Bartkowski's (2003) description, after Działek (2011)
Source of cartographic base: Państwowy Rejestr Granic at https://mapy.geoportal.gov.pl/ [accessed: May 2022]
Source: own analysis
Figure 3.
Schematic diagram of a composite-based SEM model for SRCPs
Source: own analysis
Figure 4.
Composite-based SEM model for SRCPs
Significant relationships (loadings and path coefficients) are marked *
Source: own analysis using R's cSEM package
Table 1.
Estimated path coefficients (resampling based on a bootstrap procedure)
| Effect | Estimate | Standard Error | t-value | P-value | effect size (Cohen's f2) |
|---|---|---|---|---|---|
| P3 → P1+P2 | 0.5543 | 0.0473 | 11.7219 | 0.0000 | 0.4266 |
| P4+P5 → P1+P2 | 0.0775 | 0.0495 | 1.5647 | 0.1173 | 0.0083 |
| R2=0.3376; adjusted R2=0.3336; RMSEA=0.0107; CFI=0.9988; GFI=0.9768; NFI=0.9707 | |||||
[i] Source: own analysis using R's cSEM package
Table 2.
Estimated path coefficients in a cross-section of the study regions
| Effect | Estimate | Standard Error | t-value | P-value |
|---|---|---|---|---|
| Kujawsko-Pomorskie Voivodship | ||||
| P3 → P1+P2 | 0.4931 | 0.1000 | 4.9318 | 0.0000 |
| P4+P5 → P1+P2 | 0.2160 | 0.1416 | 1.5247 | 0.1273 |
| Podkarpackie Voivodship | ||||
| P3 → P1+P2 | 0.5402 | 0.0956 | 5.6497 | 0.0000 |
| P4+P5 → P1+P2 | 0.1985 | 0.1053 | 1.8842 | 0.0595 |
| Świętokrzyskie Voivodship | ||||
| P3 → P1+P2 | 0.4855 | 0.1665 | 2.9166 | 0.0035 |
| P4+P5 → P1+P2 | −0.2290 | 0.3013 | −0.7601 | 0.4472 |
| Zachodniopomorskie Voivodship | ||||
| P3 → P1+P2 | 0.6538 | 0.0713 | 9.1679 | 0.0000 |
| P4+P5 → P1+P2 | 0.2011 | 0.0952 | 2.1132 | 0.0346 |
[i] Source: own analysis using R's cSEM package
Appendix 1.
The original outline of constructs and indicators
| Constructs (latent variables) | Indicators (explicit variables) |
|---|---|
| P1: the SRCPs in terms of its effectiveness | P1_1 I have the conviction that my company/institution has at some time been covered by regional support P1_2 I consider the level of development of the cluster initiative of which my company/institution is a member to be high P1_3 Participation in the cluster initiative has positively translated into the level of development of my company/institution |
| P2: the SRCPs in terms of its utility | P2_1 I believe that the regional support tools and instruments available so far, directed at the establishment, development or guiding of cluster initiatives, were well suited to the needs of the initiative of which my company/institution is a member P2_2 The regional tools and support instruments available so far directed to the establishment/development/animation of cluster initiatives were well suited to the needs of my company/institution P2_3 Regional activities to date dedicated to clusters or cluster members have, in practice, led to the realisation of an important need of my company/institution |
| P3: FIE | P3_1 From the point of view of my company/institution, the offer of public services managed by regional institutions has so far/since joining the EU been broad P3_2 I believe that the quality of public regional institutions so far/since joining the EU has been high P3_3 I believe that the voivodship has developed a well-functioning regional innovation system P3_4 So far/since joining the EU, there have been many interesting services for my company/institution in the offer of regional business environment institutions |
| P4: the normative dimension of SC | P4_1 I believe that giving bribes is wrong P4_2 I believe that people can be trusted P4_3 I believe that people primarily try to help others P4_4 I believe that it is necessary for a person who wants to be a good citizen to participate in elections |
| P5: The structural dimension of SC | P5_1 I think it is imperative for people to be actively involved in the community P5_2 I believe that people should be members of some organisations, associations, clubs, parties, councils or circles P5_3 I think it is imperative for people to have a very good relationship with their neighbours P5_4 I believe that people should actively engage in volunteering |
[i] Source: own analysis
Appendix 2.
Indicators removed from the model - summary of results
| Indicators | Significance of weight (p-value) | Value of loading | Significance of loading (p-value) | Decision |
|---|---|---|---|---|
| P1_1 | 0.3807 | 0.5171 | 0.0000 | OK |
| P1_2 | 0.0182 | OK | ||
| P1_3 | 0.9602 | 0.6607 | 0.0000 | OK |
| P2_1 | 0.9370 | 0.6800 | 0.0000 | OK |
| P2_2 | 0.0000 | OK | ||
| P2_3 | 0.0783 | 0.8094 | 0.0000 | OK |
| P3_1 | 0.0666 | 0.7244 | 0.0000 | OK |
| P3_2 | 0.0357 | OK | ||
| P3_3 | 0.0001 | OK | ||
| P3_4 | 0.0001 | OK | ||
| P4_1 | 0.8627 | 0.0217 | 0.8803 | indicator removed |
| P4_2 | 0.1001 | 0.6266 | 0.0002 | OK |
| P4_3 | 0.0098 | OK | ||
| P4_4 | 0.2676 | 0.2514 | 0.1839 | indicator removed |
| P5_1 | 0.1621 | 0.1126 | 0.5619 | indicator removed |
| P5_2 | 0.5443 | 0.1148 | 0.5895 | indicator removed |
| P5_3 | 0.7647 | 0.1604 | 0.4151 | indicator removed |
| P5_4 | 0.0030 | OK |
[i] Source: own analysis using R's cSEM package
Appendix 3.
Summary of the trials of model building
| Model | Endogenous construct | Exogenous constructs | Remarks | Model fit |
|---|---|---|---|---|
| 1 | P1 | P3, P4, P5 | Due to the significance of weights and values of loading there is a need to remove indicators: P4_1, P4_4, P5_1 | RMSEA = 0.050 R2 = 0.2370 adjusted R2 = 0.2301 |
| 2 | P1 | P3, P4+P5 | P3 à P1 (estimate = 0.4505, P-value = 0.0000, Cohen's f2= 0.2461) P4+P5 à P1 (estimate = 0.0910, P-value = 0.0761, Cohen's f2= 0.0100) Due to the significance of weights and values of loading there is a need to remove indicator: P5_2 | RMSEA = 0.010 R2 = 0.2329 adjusted R2 = 0.2283 |
| 3 | P2 | P3, P4, P5 | Due to the significance of weights and values of loading there is a need to remove indicators: P4_1, P4_4, P5_1, P5_2, P5_3 | RMSEA = 0.056 R2 = 0.3126 adjusted R2 = 0.3064 |
| 4 | P2 | P3, P4+P5 | P3 à P2 (estimate = 0.5265, P-value = 0.0000, Cohen's f2= 0.3704) P4+P5 à P2 (estimate = 0.0822, P-value = 0.1002, Cohen's f2= 0.0090) | RMSEA = 0.009 R2 = 0.3076 adjusted R2 = 0.3034 |
| 5 | P1+P2 | P3, P4, P5 | Due to the significance of weights and values of loading there is a need to remove indicators: P4_1, P4_4, P5_1, P5_2, P5_3 | RMSEA = 0.045 R2 = 0.3406 adjusted R2 = 0.3346 |
| 6 | P1+P2 | P3, P4+P5 | P3 à P1+P2 (estimate = 0.5543, P-value = 0.0000, Cohen's f2= 0.4266) P4+P5 à P1+P2 (estimate = 0.0775, P-value = 0.1173, Cohen's f2= 0.0086) | RMSEA = 0.011 R2 = 0.3376 adjusted R2 = 0.3336 |
[i] Source: own analysis using R's cSEM package