Figure 1.

Figure 2.
![Study areaNote: 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](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/647126ab2b88470fbea15c05/j_ceej-2023-0012_fig_002.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=AKIA6AP2G7AKOUXAVR44%2F20251201%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20251201T003920Z&X-Amz-Expires=3600&X-Amz-Signature=221c00a0d31e2ca4abde82f2711b26f0656678c99754a50f8fb443bc30c35b2f&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 3.

Figure 4.

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 |
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 | |||||
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 |
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 |
| 2 | P1 | P3, P4+P5 | P3 à P1 (estimate = 0.4505, P-value = 0.0000, Cohen's f2= 0.2461) | RMSEA = 0.010 |
| 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 |
| 4 | P2 | P3, P4+P5 | P3 à P2 (estimate = 0.5265, P-value = 0.0000, Cohen's f2= 0.3704) | RMSEA = 0.009 |
| 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 |
| 6 | P1+P2 | P3, P4+P5 | P3 à P1+P2 (estimate = 0.5543, P-value = 0.0000, Cohen's f2= 0.4266) | RMSEA = 0.011 |
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 |
| 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 |
| 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 |
| P4: the normative dimension of SC | P4_1 I believe that giving bribes is wrong |
| P5: The structural dimension of SC | P5_1 I think it is imperative for people to be actively involved in the community |
