On stochastic aspects of impact modeling of the innovation incentive system and business internationalization: evidence from Portuguese SMEs

Figures & data

Figure 1. Model considered after the application of the CTA-PLS algorithm.

Table 1. Distribution of participating companies by sector of activity.

Sector of Activity	Absolute Frequency	%	Cum. %
Agriculture, animal production, forest, etc.	13	10.8	10.8
Artistic, show, sporting activities	2	1.7	12.5
Consulting, scientific and technical activities	3	2.5	15.0
Information and communication activities	1	0.8	15.8
Human health activities and social support	7	5.8	21.7
Financial and insurance activities	1	0.8	22.5
Real estate activities	4	3.3	25.8
Collection, treatment and distribution of water	8	6.7	32.5
Wholesale and retail trade	6	5.0	37.5
Construction	14	11.7	49.2
Education	2	1.7	50.8
Electricity, gas, steam	9	7.5	58.3
Food, canning and beverage industry	6	5.0	63.3
Manufacturing industry	5	4.2	67.5
Extractive industries	14	11.7	79.2
Manufacturing industries	16	13.3	92.5
Transport and storage	9	7.5	100.0
TOTAL	120	100.0

Table 2. Results obtained with the application of the CTA-PLS algorithm.

Construct	Indicators	Original Sample (O)	Sample Mean (M)	Standard Deviation (StDev)	T Statistics (O/StDev)	CI Low adj.	CI Up adj.
Working Conditions	1: WC1, WC2, WC3, WC4	0.723	0.699	0.262	2.758	0.159	1.335
	2: WC1, WC2, WC4, WC3	0.788	0.763	0.249	3.168	0.256	1.371
Organizational Innovation	1: WC4, OI1, OI2, OI3	−0.117	−0.114	0.155	0.755	−0.469	0.227
	2: WC4, OI1, OI3, OI2	0.19	0.181	0.223	0.852	−0.301	0.697
Marketing Innovation	1: MI1, MI2, MI3, PI3	0.084	0.078	0.183	0.457	−0.322	0.500
	2: MI1, MI2, PI3, MI3	0.047	0.043	0.2	0.234	−0.398	0.498
Product Innovation	1: OI2, PI1, PI2, PI3	−0.351	−0.343	0.267	1.314	−0.956	0.24
	2: OI2, PI1, PI3, PI2	−0.283	−0.275	0.231	1.221	−0.808	0.229
Inter. of Companies	1: Int2, Int3, Int4, Int5	−0.004	0	0.194	0.02	−0.508	0.493
	2: Int2, Int3, Int5, Int4	−0.232	−0.22	0.218	1.063	−0.806	0.319
	6: Int2, Int4, Int1, Int3	−0.578	−0.558	0.194	2.984	−1.098	−0.099
	10: Int2, Int4, Int5, Int1	−0.098	−0.096	0.207	0.472	−0.632	0.434

Figure 2. Estimated model obtained with PLSc (outer loadings, path coefficients and coefficients of determination).

Table 3. Outer loadings: mean, StDev, t-values and p-values.

Construct	Indicator	Original Sample (O)	Sample Mean (M)	Standard Deviation (StDev)	T Statistics (O/StDev)	p-value
Working Conditions	WC1	0.584	0.562	0.137	4.263	<0.001
	WC2	0.711	0.676	0.12	5.929	<0.001
	WC3	0.909	0.885	0.082	11.079	<0.001
	WC4	0.937	0.906	0.07	13.378	<0.001
Market Innovation	MI1	0.71	0.709	0.082	8.667	<0.001
	MI2	0.711	0.714	0.099	7.166	<0.001
	MI3	0.721	0.714	0.08	8.969	<0.001
Organizational Innovation	OI1	0.624	0.635	0.12	5.184	<0.001
	OI2	0.79	0.791	0.085	9.349	<0.001
	OI3	0.726	0.709	0.122	5.947	<0.001
Product Innovation	PI1	0.75	0.748	0.113	6.661	<0.001
	PI2	0.79	0.79	0.078	10.14	<0.001
	PI3	0.89	0.885	0.058	15.296	<0.001
Inter. of Companies	Int1	0.817	0.783	0.09	9.107	<0.001
	Int2	0.882	0.844	0.085	10.324	<0.001
	Int3	0.792	0.759	0.109	7.292	<0.001
	Int4	0.965	0.928	0.052	18.665	<0.001
	Int5	0.657	0.629	0.134	4.91	<0.001

Table 4. Internal consistence reliability: ρ_A, bias, 95% bootstrap BCa CI and p-values.

ρA	Original Sample (O)	Sample Mean (M)	Standard Deviation (StDev)	T Statistics (|O/StDev|)	Bias	2.5%	97.5%	p-values
Marketing I.	0.758	0.766	0.05	15.138	0.008	0.625	0.834	<0.001
Organizational I.	0.767	0.784	0.051	14.966	0.017	0.614	0.836	<0.001
Product I.	0.859	0.868	0.106	8.138	0.009	0.708	0.895	<0.001

Table 5. Convergent validity: Average Variance Extracted (AVE), Bias, 95% bootstrap BCa CI and p-values.

AVE	Original Sample (O)	Sample Mean (M)	Standard Deviation (StDev)	T Statistics (|O/StDev|)	Bias	2.5%	97.5%	p-values
Marketing I.	0.51	0.515	0.067	7.579	0.005	0.37	0.631	<0.001
Organizational I.	0.514	0.523	0.062	8.236	0.009	0.373	0.617	<0.001
Product I.	0.66	0.663	0.059	11.127	0.003	0.549	0.749	<0.001

Table 6. Discriminant validity: Heterotrait-Monotrait ratio (HTMT), bias, 95% bootstrap BCa CI.

Relationship	Original Sample (O)	Sample Mean (M)	Bias	2.5%	97.5%
Organizational I.→Marketing I.	0.259	0.290	0.030	0.100	0.471
Product I.→Marketing I.	0.594	0.593	0.000	0.399	0.764
Product I.→Organizational I.	0.430	0.434	0.003	0.195	0.645

Table 7. Collinearity analysis in outer model: Variance Inflation Factor (VIF).

$$	Indicator	VIF
Inter. of Companies	Int1	2.766
	Int2	3.900
	Int3	3.101
	Int4	3.301
	Int5	2.027
Market Innovation	MI1	1.500
	MI2	1.665
	MI3	1.475
Organizational Innovation	OI1	1.802
	OI2	2.120
	OI3	1.343
Product Innovation	PI1	1.675
	PI2	2.549
	PI3	2.778
Working Conditions	WC1	2.984
	WC2	2.927
	WC3	2.926
	WC4	3.009

Table 8. Outer weights: mean, StDev, t-values and p-values.

Construct	Indicator	Original Sample (O)	Sample Mean (M)	Standard Deviation (StDev)	T Statistics (O/StDev)	p-value
Working Conditions	WC1	−0.357	−0.333	0.22	1.621	0.105
	WC2	0.269	0.241	0.204	1.318	0.188
	WC3	0.500	0.488	0.264	1.893	0.058
	WC4	0.601	0.584	0.275	2.187	0.029
Market Innovation	MI1	0.404	0.404	0.040	10.047	<0.001
	MI2	0.405	0.407	0.052	7.734	<0.001
	MI3	0.410	0.407	0.042	9.815	<0.001
Organizational Innovation	OI1	0.355	0.359	0.059	5.971	<0.001
	OI2	0.449	0.449	0.047	9.604	<0.001
	OI3	0.413	0.403	0.071	5.797	<0.001
Product Innovation	PI1	0.351	0.351	0.050	7.068	<0.001
	PI2	0.370	0.371	0.035	10.653	<0.001
	PI3	0.417	0.416	0.029	14.347	<0.001
Inter. of Companies	Int1	0.156	0.144	0.224	0.697	0.486
	Int2	0.315	0.313	0.232	1.359	0.174
	Int3	−0.053	−0.062	0.273	0.194	0.846
	Int4	0.699	0.675	0.226	3.097	0.002
	Int5	−0.056	−0.050	0.212	0.265	0.791

Table 9. Fit summary of the saturated and estimated models.

Discrepancy	Model	Original Sample (O)	Sample Mean (M)	95%	99%
SMR	Saturated	0.056	0.051	0.063	0.070
	Estimated	0.078	0.064	0.085	0.098
dULS	Saturated	0.539	0.452	0.687	0.844
	Estimated	1.04	0.719	1.225	1.655
dG	Saturated	0.277	0.245	0.35	0.419
	Estimated	0.304	n/a	0.369	0.437

Table 10. Collinearity analysis in inner model: Variance Inflation Factor (VIF).

Inner VIF	Inter. Of Companies	Marketing Innovation	Organizational Innovation	Product Innovation	Working Conditions
Inter. of Companies
Marketing Innovation	1.026
Organizational Innovation				1.000	1.000
Product Innovation		1.000
Working Conditions	1.026

Table 11. Variance explained: Coefficient of determination (R${}^2$), Bias, 95% bootstrap BCa CI and p-values.

R${}^2$	Original Sample (O)	Sample Mean (M)	Standard Deviation (StDev)	T Statistics (|O/StDev|)	Bias	2.5%	97.5%	p-values
Inter. of Companies	0.421	0.458	0.066	6.358	0.037	0.236	0.512	<0.001
Marketing I.	0.348	0.354	0.113	3.075	0.006	0.145	0.583	0.002
Product I.	0.182	0.197	0.102	1.78	0.015	0.028	0.406	0.075
Working Cond.	0.179	0.199	0.093	1.924	0.021	0.027	0.37	0.054

Table 12. Predictive relevance Q${}^2.$

Construct	SSO	SSE	$Q^2(=1-\mathit{SSE}/\mathit{SSO})$
Inter. of Companies	600,000	445,443	0.258
Marketing I.	360,000	307,525	0.146
Organizational I.	360,000	360,000	0.000
Product I.	360,000	328,544	0.087
Working Cond.	480,000	446,987	0.069

Table 13. Predictive performance of the PLS model vs. benchmark LM, considering the full dataset.

Construct	Indicator	$Q_{\mathit{predict}}^2$		PLS predict		LM predict		LM - PLS${}^1$
		PLS	LM	RMSE	MAE	RMSE	MAE	RMSE	MAE
Working Conditions	WC1	0.018	0.001	1.529	1.320	1.542	1.335	0.013	0.016
	WC2	0.039	0.022	1.427	1.209	1.440	1.217	0.013	0.009
	WC3	0.087	0.082	1.338	1.134	1.341	1.132	0.003	−0.001
	WC4	0.094	0.068	1.293	1.074	1.312	1.092	0.019	0.018
Market Innovation	MI1	0.001	−0.014	1.380	1.178	1.390	1.179	0.010	0.001
	MI2	0.037	0.000	1.423	1.234	1.450	1.242	0.027	0.008
	MI3	0.019	−0.024	1.425	1.229	1.456	1.261	0.031	0.032
Product Innovation	PI1	0.030	−0.003	1.453	1.247	1.477	1.279	0.024	0.032
	PI2	0.102	0.085	1.480	1.290	1.494	1.295	0.014	0.005
	PI3	0.100	0.075	1.420	1.222	1.440	1.237	0.020	0.015
Inter. of Companies	Int1	0.025	−0.022	1.540	1.384	1.576	1.408	0.037	0.024
	Int2	0.007	−0.017	1.398	1.225	1.415	1.228	0.017	0.003
	Int3	−0.001	−0.028	1.433	1.249	1.452	1.248	0.019	−0.001
	Int4	0.026	−0.002	1.379	1.183	1.399	1.183	0.020	0.000
	Int5	0.018	−0.015	1.432	1.264	1.455	1.274	0.024	0.010

¹ Negative values shows indicators for which there is no improvement in predictive power of the PLS model over the LM benchmark.

Table 14. Path coefficients with the 95% bootstrap BCa CI and p-values.

$$	Path coefficient					95% bootstrap BCa CI		$$
Relationship	Original Sample (O)	Sample Mean (M)	Standard Deviation (StDev)	T Statistics (|O/StDev|)	Bias	2.5%	97.5%	p-values
Marketing I. →Inter. of Companies	0.306	0.308	0.095	3.234	0.002	0.119	0.489	0.001
Organizational I. →Product I.	0.426	0.428	0.12	3.559	0.001	0.168	0.638	<0.001
Organizational I. →Working Conditions	−0.423	−0.433	0.109	3.868	−0.01	−0.61	−0.169	<0.001
Product I. →Marketing I.	0.59	0.587	0.098	5.997	−0.003	0.381	0.764	<0.001
Working Conditions →Inter. of Companies	0.525	0.543	0.079	6.666	0.018	0.308	0.646	<0.001

Table 15. Predictive relevance Q${}^2.$

Endogenous construc	BIC (Bayesian Information Criteria)
Inter. of Companies	−52,161
Marketing I.	−42,744
Product I.	−15,511
Working Cond.	−15,029

Figure 3. The minimum A value for which each of the Indicators violates conditions (2) in left panel and condition (3) in right panel. Unbounded intervals beginning in each of these minimum values for A at given lag h (x-axis) which violate positive definiteness of each Indicator (y-axis) autocovariance.