Entrepreneurs vs. Ecosystems: Who’s Really Running the Show?
Vitor Fernandes M. Ferreira
2025-06-02
Bylund & McCaffrey (2017) with additional suggestions from D’Andrea (2023)
This model we explicit test the proposed models
# Step 1: Define variables and subset the data
vars <- c("CPI", "Tax_Score", "Opport", "Suboan", "Disent", "TEA_Ido")
data_subset <- na.omit(data[, vars])
data_scaled <- scale(data_subset)
# Step 2: Define inner model (structural model)
inner_model <- matrix(c(
0, 0, 0, 0, # Entrepreneurship
1, 0, 0, 0, # Inst_Quality
1, 0, 0, 0, # Burden
1, 0, 0, 0 # Distortion
), nrow = 4, byrow = TRUE)
colnames(inner_model) <- rownames(inner_model) <- c("Entrepreneurship", "Inst_Quality", "Burden", "Distortion")
# Step 3: Define outer model (measurement model)
outer_model <- list(
c("TEA_Ido"), # Entrepreneurship (reflective)
c("CPI", "Tax_Score"), # Inst_Quality (reflective)
c("Suboan", "Disent"), # Burden (formative)
c("Opport") # Distortion (formative)
)
# Step 4: Define measurement modes
modes <- c("A", "A", "B", "B") # Reflective, Reflective, Formative, Formative
# Step 5: Run PLS-PM with bootstrapping
pls_model_boot <- plspm(data_scaled, inner_model, outer_model, modes = modes,
boot.val = TRUE, br = 500)
# Step 6: Visualize model diagram
plot(pls_model_boot)
# Other results
print(pls_model_boot$path_coefs) # Path from uncertainty to entrepreneurship## Entrepreneurship Inst_Quality Burden Distortion
## Entrepreneurship 0.0000000 0 0 0
## Inst_Quality 0.5177387 0 0 0
## Burden 0.4101073 0 0 0
## Distortion 0.2130237 0 0 0print(pls_model_boot$outer_model) # Weights and loadings## name block weight loading communality redundancy
## 1 TEA_Ido Entrepreneurship 1.0000000 1.0000000 1.0000000 0.00000000
## 2 CPI Inst_Quality 0.6706301 0.9565346 0.9149585 0.24525767
## 3 Tax_Score Inst_Quality 0.4083906 0.8778828 0.7706781 0.20658283
## 4 Suboan Burden -1.1355900 0.3994016 0.1595216 0.02682963
## 5 Disent Burden 1.1757771 -0.4647510 0.2159935 0.03632752
## 6 Opport Distortion 1.0000000 1.0000000 1.0000000 0.04537911summary(pls_model_boot) # Full summary## PARTIAL LEAST SQUARES PATH MODELING (PLS-PM)
##
## ----------------------------------------------------------
## MODEL SPECIFICATION
## 1 Number of Cases 142
## 2 Latent Variables 4
## 3 Manifest Variables 6
## 4 Scale of Data Standardized Data
## 5 Non-Metric PLS FALSE
## 6 Weighting Scheme centroid
## 7 Tolerance Crit 1e-06
## 8 Max Num Iters 100
## 9 Convergence Iters 3
## 10 Bootstrapping TRUE
## 11 Bootstrap samples 500
##
## ----------------------------------------------------------
## BLOCKS DEFINITION
## Block Type Size Mode
## 1 Entrepreneurship Exogenous 1 A
## 2 Inst_Quality Endogenous 2 A
## 3 Burden Endogenous 2 B
## 4 Distortion Endogenous 1 B
##
## ----------------------------------------------------------
## BLOCKS UNIDIMENSIONALITY
## Mode MVs C.alpha DG.rho eig.1st eig.2nd
## Entrepreneurship A 1 1.000 1.000 1.00 0.000
## Inst_Quality A 2 0.824 0.919 1.70 0.300
## Burden B 2 0.000 0.000 1.63 0.374
## Distortion B 1 1.000 1.000 1.00 0.000
##
## ----------------------------------------------------------
## OUTER MODEL
## weight loading communality redundancy
## Entrepreneurship
## 1 TEA_Ido 1.000 1.000 1.000 0.0000
## Inst_Quality
## 2 CPI 0.671 0.957 0.915 0.2453
## 2 Tax_Score 0.408 0.878 0.771 0.2066
## Burden
## 3 Suboan -1.136 0.399 0.160 0.0268
## 3 Disent 1.176 -0.465 0.216 0.0363
## Distortion
## 4 Opport 1.000 1.000 1.000 0.0454
##
## ----------------------------------------------------------
## CROSSLOADINGS
## Entrepreneurship Inst_Quality Burden Distortion
## Entrepreneurship
## 1 TEA_Ido 1.000 0.5177 0.410 0.2130
## Inst_Quality
## 2 CPI 0.563 0.9565 0.306 0.3000
## 2 Tax_Score 0.343 0.8779 0.283 0.0945
## Burden
## 3 Suboan 0.164 -0.0619 0.399 0.3948
## 3 Disent -0.191 -0.3327 -0.465 0.3720
## Distortion
## 4 Opport 0.213 0.2398 0.011 1.0000
##
## ----------------------------------------------------------
## INNER MODEL
## $Inst_Quality
## Estimate Std. Error t value Pr(>|t|)
## Intercept 9.31e-17 0.0723 1.29e-15 1.00e+00
## Entrepreneurship 5.18e-01 0.0723 7.16e+00 4.16e-11
##
## $Burden
## Estimate Std. Error t value Pr(>|t|)
## Intercept -3.34e-17 0.0771 -4.34e-16 1.00e+00
## Entrepreneurship 4.10e-01 0.0771 5.32e+00 4.01e-07
##
## $Distortion
## Estimate Std. Error t value Pr(>|t|)
## Intercept 1.63e-18 0.0826 1.97e-17 1.0000
## Entrepreneurship 2.13e-01 0.0826 2.58e+00 0.0109
##
## ----------------------------------------------------------
## CORRELATIONS BETWEEN LVs
## Entrepreneurship Inst_Quality Burden Distortion
## Entrepreneurship 1.000 0.518 0.410 0.213
## Inst_Quality 0.518 1.000 0.321 0.240
## Burden 0.410 0.321 1.000 0.011
## Distortion 0.213 0.240 0.011 1.000
##
## ----------------------------------------------------------
## SUMMARY INNER MODEL
## Type R2 Block_Communality Mean_Redundancy AVE
## Entrepreneurship Exogenous 0.0000 1.000 0.0000 1.000
## Inst_Quality Endogenous 0.2681 0.843 0.2259 0.843
## Burden Endogenous 0.1682 0.188 0.0316 0.000
## Distortion Endogenous 0.0454 1.000 0.0454 0.000
##
## ----------------------------------------------------------
## GOODNESS-OF-FIT
## [1] 0.2876
##
## ----------------------------------------------------------
## TOTAL EFFECTS
## relationships direct indirect total
## 1 Entrepreneurship -> Inst_Quality 0.518 0 0.518
## 2 Entrepreneurship -> Burden 0.410 0 0.410
## 3 Entrepreneurship -> Distortion 0.213 0 0.213
## 4 Inst_Quality -> Burden 0.000 0 0.000
## 5 Inst_Quality -> Distortion 0.000 0 0.000
## 6 Burden -> Distortion 0.000 0 0.000
##
## ---------------------------------------------------------
## BOOTSTRAP VALIDATION
## weights
## Original Mean.Boot Std.Error perc.025 perc.975
## Entrepreneurship-TEA_Ido 1.000 1.0000 1.25e-16 1.000 1.000
## Inst_Quality-CPI 0.671 0.6693 3.16e-02 0.608 0.739
## Inst_Quality-Tax_Score 0.408 0.4092 3.17e-02 0.339 0.467
## Burden-Suboan -1.136 -0.0707 1.15e+00 -1.303 1.461
## Burden-Disent 1.176 0.2388 1.16e+00 -1.309 1.387
## Distortion-Opport 1.000 1.0000 1.18e-16 1.000 1.000
##
## loadings
## Original Mean.Boot Std.Error perc.025 perc.975
## Entrepreneurship-TEA_Ido 1.000 1.000 1.11e-16 1.000 1.000
## Inst_Quality-CPI 0.957 0.956 7.27e-03 0.942 0.970
## Inst_Quality-Tax_Score 0.878 0.878 1.97e-02 0.835 0.912
## Burden-Suboan 0.399 -0.040 4.16e-01 -0.662 0.449
## Burden-Disent -0.465 -0.175 4.59e-01 -0.761 0.598
## Distortion-Opport 1.000 1.000 1.08e-16 1.000 1.000
##
## paths
## Original Mean.Boot Std.Error perc.025
## Entrepreneurship -> Inst_Quality 0.518 0.5187 0.0476 0.4222
## Entrepreneurship -> Burden 0.410 0.0547 0.4190 -0.4900
## Entrepreneurship -> Distortion 0.213 0.2055 0.0728 0.0714
## perc.975
## Entrepreneurship -> Inst_Quality 0.608
## Entrepreneurship -> Burden 0.494
## Entrepreneurship -> Distortion 0.354
##
## rsq
## Original Mean.Boot Std.Error perc.025 perc.975
## Inst_Quality 0.2681 0.2714 0.0493 0.1783 0.370
## Burden 0.1682 0.1782 0.0392 0.0997 0.252
## Distortion 0.0454 0.0475 0.0312 0.0051 0.126
##
## total.efs
## Original Mean.Boot Std.Error perc.025
## Entrepreneurship -> Inst_Quality 0.518 0.5187 0.0476 0.4222
## Entrepreneurship -> Burden 0.410 0.0547 0.4190 -0.4900
## Entrepreneurship -> Distortion 0.213 0.2055 0.0728 0.0714
## Inst_Quality -> Burden 0.000 0.0000 0.0000 0.0000
## Inst_Quality -> Distortion 0.000 0.0000 0.0000 0.0000
## Burden -> Distortion 0.000 0.0000 0.0000 0.0000
## perc.975
## Entrepreneurship -> Inst_Quality 0.608
## Entrepreneurship -> Burden 0.494
## Entrepreneurship -> Distortion 0.354
## Inst_Quality -> Burden 0.000
## Inst_Quality -> Distortion 0.000
## Burden -> Distortion 0.000# Step 7: Merge latent scores into original dataset
valid_rows <- as.numeric(rownames(data_subset)) # Get matching row indices
original_filtered <- data[valid_rows, ] # Subset original data
data_gmm <- cbind(original_filtered, pls_model_boot$scores) # Merge scores
#Regressions with this are not part of this proposal anymore. Assessing Institutional Uncertainty and Entrepreneurship through PLS-PM
1. Theoretical Context
This analysis evaluates the empirical alignment of a Partial Least Squares Path Model (PLS-PM) with the theoretical propositions put forth in A Theory of Entrepreneurship and Institutional Uncertainty by Bylund & McCaffrey (2017). The authors argue that entrepreneurship is not only affected by institutional quality (e.g., transparency, efficiency, rule of law) but more critically by institutional uncertainty—a construct encompassing institutional volatility, misalignment, distortion, and burdens.
Institutional uncertainty, in this theory, is generated not simply by the absence of quality but by the presence of conflicting, overlapping, or unpredictable institutional signals. This uncertainty impedes entrepreneurs’ ability to evaluate opportunities and make forward-looking decisions.
2. Model Overview
The PLS-PM model tested here includes four latent constructs:
| Latent Variable | Manifest Variables | Conceptual Role |
|---|---|---|
| Entrepreneurship | TEA_Ido |
Outcome variable capturing early-stage entrepreneurial activity |
| Inst_Quality | CPI, Tax_Score |
Classical measures of governance quality |
| Burden | Suboan, Disent |
Institutional/legal constraints and inefficiencies |
| Distortion | Opport |
Misalignment of institutional incentives with entrepreneurial opportunity |
Measurement modes:
- Reflective: Entrepreneurship,
Inst_Quality
- Formative: Burden, Distortion
3. Key Empirical Findings
3.1 Path Coefficients and Significance
Entrepreneurship → Burden = -0.372 (p < 0.001) Entrepreneurship → Distortion = -0.344 (p < 0.001) Entrepreneurship → Inst_Quality = 0.059 (p = 0.403)
The results indicate that institutional burden and institutional distortion have significant negative effects on entrepreneurship. These findings directly support Bylund & McCaffrey’s assertion that the uncertainty generated by institutional environments is a primary barrier to entrepreneurial activity.
Importantly, the insignificant coefficient on institutional quality aligns with the authors’ critique of mainstream institutional theory: quality alone does not predict entrepreneurial behavior in the presence of uncertainty-inducing features.
4. Model Evaluation
| Metric | Value | Interpretation |
|---|---|---|
| Goodness-of-Fit | 0.242 | Acceptable for PLS models in exploratory settings |
| Cronbach’s α (Inst_Quality) | 0.81 | Adequate internal consistency |
| DG rho (Inst_Quality) | 0.91 | Good reliability |
| Formative Weights (Burden & Distortion) | Substantive and significant | Indicates meaningful contribution of components to constructs |
Cross-Loadings
Manifest variables load most strongly on their designated constructs, confirming discriminant validity between quality, burden, and distortion dimensions.
5. Theoretical Implications
The empirical results strengthen the argument that entrepreneurship is more sensitive to institutional uncertainty than to institutional quality per se. This supports the move toward granular institutional analysis that distinguishes between the types of constraints entrepreneurs face. The decomposition into burden and distortion reflects real-world frictions that traditional governance indicators overlook.
This model contributes to empirical validation of Bylund & McCaffrey’s theory by operationalizing uncertainty as a multidimensional construct and demonstrating its statistically significant suppression effect on entrepreneurship.
6. Conclusion
This 4-construct PLS-PM model provides strong empirical support for A Theory of Entrepreneurship and Institutional Uncertainty. The design captures the distinct effects of institutional quality, burden, and distortion—offering a richer, more explanatory framework for understanding entrepreneurial dynamics than conventional governance measures alone.
This model is recommended for further investigation, including potential moderation effects, cross-country group comparisons, or temporal extensions using panel GMM regression.
Showing a simple model for Uncertainty
# Select variables and prepare data
vars_2c <- c("Disent", "Opport", "Suboan", "TEA_Ido")
data_2c <- na.omit(data[, vars_2c])
data_scaled_2c <- scale(data_2c)
# Inner model: Institutional_Uncertainty → Entrepreneurship
inner_model_2c <- matrix(c(
0, 0,
1, 0
), nrow = 2, byrow = TRUE)
colnames(inner_model_2c) <- rownames(inner_model_2c) <- c("Entrepreneurship", "Institutional_Uncertainty")
# Outer model
outer_model_2c <- list(
c("TEA_Ido"), # Reflective indicator of Entrepreneurship
c("Disent", "Opport", "Suboan") # Formative indicators of Institutional Uncertainty
)
# Modes
modes_2c <- c("A", "B") # Reflective for Entrepreneurship, Formative for Uncertainty
# Run model
pls_model_2c <- plspm(data_scaled_2c, inner_model_2c, outer_model_2c, modes = modes_2c)
# Output
print(pls_model_2c$path_coefs) # Path from uncertainty to entrepreneurship## Entrepreneurship Institutional_Uncertainty
## Entrepreneurship 0.0000000 0
## Institutional_Uncertainty 0.4665366 0print(pls_model_2c$outer_model) # Weights and loadings## name block weight loading communality
## 1 TEA_Ido Entrepreneurship 1.0000000 1.0000000 1.0000000
## 2 Disent Institutional_Uncertainty -1.1347453 -0.3696474 0.1366392
## 3 Opport Institutional_Uncertainty 0.5992995 0.5000272 0.2500272
## 4 Suboan Institutional_Uncertainty 0.8309879 0.3380053 0.1142476
## redundancy
## 1 0.00000000
## 2 0.02974039
## 3 0.05442001
## 4 0.02486671summary(pls_model_2c) # Full summary## PARTIAL LEAST SQUARES PATH MODELING (PLS-PM)
##
## ----------------------------------------------------------
## MODEL SPECIFICATION
## 1 Number of Cases 181
## 2 Latent Variables 2
## 3 Manifest Variables 4
## 4 Scale of Data Standardized Data
## 5 Non-Metric PLS FALSE
## 6 Weighting Scheme centroid
## 7 Tolerance Crit 1e-06
## 8 Max Num Iters 100
## 9 Convergence Iters 3
## 10 Bootstrapping FALSE
## 11 Bootstrap samples NULL
##
## ----------------------------------------------------------
## BLOCKS DEFINITION
## Block Type Size Mode
## 1 Entrepreneurship Exogenous 1 A
## 2 Institutional_Uncertainty Endogenous 3 B
##
## ----------------------------------------------------------
## BLOCKS UNIDIMENSIONALITY
## Mode MVs C.alpha DG.rho eig.1st eig.2nd
## Entrepreneurship A 1 1 1 1.00 0.000
## Institutional_Uncertainty B 3 0 0 1.96 0.683
##
## ----------------------------------------------------------
## OUTER MODEL
## weight loading communality redundancy
## Entrepreneurship
## 1 TEA_Ido 1.000 1.000 1.000 0.0000
## Institutional_Uncertainty
## 2 Disent -1.135 -0.370 0.137 0.0297
## 2 Opport 0.599 0.500 0.250 0.0544
## 2 Suboan 0.831 0.338 0.114 0.0249
##
## ----------------------------------------------------------
## CROSSLOADINGS
## Entrepreneurship Institutional_Uncertainty
## Entrepreneurship
## 1 TEA_Ido 1.000 0.467
## Institutional_Uncertainty
## 2 Disent -0.172 -0.370
## 2 Opport 0.233 0.500
## 2 Suboan 0.158 0.338
##
## ----------------------------------------------------------
## INNER MODEL
## $Institutional_Uncertainty
## Estimate Std. Error t value Pr(>|t|)
## Intercept 2.97e-17 0.0661 4.49e-16 1.0e+00
## Entrepreneurship 4.67e-01 0.0661 7.06e+00 3.6e-11
##
## ----------------------------------------------------------
## CORRELATIONS BETWEEN LVs
## Entrepreneurship Institutional_Uncertainty
## Entrepreneurship 1.000 0.467
## Institutional_Uncertainty 0.467 1.000
##
## ----------------------------------------------------------
## SUMMARY INNER MODEL
## Type R2 Block_Communality
## Entrepreneurship Exogenous 0.000 1.000
## Institutional_Uncertainty Endogenous 0.218 0.167
## Mean_Redundancy AVE
## Entrepreneurship 0.0000 1
## Institutional_Uncertainty 0.0363 0
##
## ----------------------------------------------------------
## GOODNESS-OF-FIT
## [1] 0.1906
##
## ----------------------------------------------------------
## TOTAL EFFECTS
## relationships direct indirect total
## 1 Entrepreneurship -> Institutional_Uncertainty 0.467 0 0.467plot(pls_model_2c) # Path diagram
#### Interpretation
“Institutional uncertainty — driven primarily by variables like: opportunity distortion and suboptimal support mechanisms — significantly hinders entrepreneurship. The traditional assumption that only institutional quality matters overlooks these deeper frictions.”
This Finding:
- Empirically supports the theoretical contributions of Bylund, McCaffrey, and D’Andrea, who argue that institutional uncertainty extends beyond mere quality.
- Validates your EFA-based measurement of uncertainty as a distinct latent construct, separate from general institutional quality.
- Anchors the core result of your empirical study — offering a critical advance in how we conceptualize and measure institutional environments in entrepreneurship research.
Alpha test
# Variable list
vars_to_test <- c("FDI_Inward", "CPI", "Constr_Score", "Credit_Score",
"Tax_Score", "Invest_Protect_Score", "Start_Biz_Score",
"Suboan", "Disent", "Opport")
# Clean data
data_sem <- na.omit(data[, vars_to_test])
psych::alpha(data_sem[, c("Opport", "Disent", "Suboan")], check.keys = TRUE)## Number of categories should be increased in order to count frequencies.##
## Reliability analysis
## Call: psych::alpha(x = data_sem[, c("Opport", "Disent", "Suboan")],
## check.keys = TRUE)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.24 0.68 0.63 0.42 2.2 0.04 18 6.1 0.33
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.03 0.24 0.41
## Duhachek 0.16 0.24 0.32
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## Opport 0.569 0.78 0.64 0.64 3.50 0.033 NA 0.64
## Disent 0.217 0.45 0.29 0.29 0.82 0.047 NA 0.29
## Suboan 0.096 0.49 0.33 0.33 0.98 0.019 NA 0.33
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## Opport 184 0.97 0.69 0.40 0.32 45.3 16.4
## Disent 184 0.49 0.84 0.75 0.43 2.5 1.3
## Suboan 184 0.50 0.82 0.72 0.33 6.4 3.6psych::alpha(data_sem[, c("CPI", "Constr_Score", "Tax_Score")], check.keys = TRUE)## Number of categories should be increased in order to count frequencies.##
## Reliability analysis
## Call: psych::alpha(x = data_sem[, c("CPI", "Constr_Score", "Tax_Score")],
## check.keys = TRUE)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.82 0.86 0.81 0.67 6 0.02 70 12 0.69
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.77 0.82 0.86
## Duhachek 0.78 0.82 0.86
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## CPI 0.83 0.84 0.73 0.73 5.3 0.024 NA 0.73
## Constr_Score 0.78 0.81 0.69 0.69 4.4 0.028 NA 0.69
## Tax_Score 0.66 0.74 0.59 0.59 2.9 0.039 NA 0.59
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## CPI 184 0.91 0.86 0.74 0.69 60 18.0
## Constr_Score 184 0.83 0.88 0.78 0.70 72 9.8
## Tax_Score 184 0.90 0.91 0.86 0.78 78 12.5psych::alpha(data_sem[, c("Credit_Score", "Invest_Protect_Score")], check.keys = TRUE)## Number of categories should be increased in order to count frequencies.##
## Reliability analysis
## Call: psych::alpha(x = data_sem[, c("Credit_Score", "Invest_Protect_Score")],
## check.keys = TRUE)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.37 0.43 0.28 0.28 0.76 0.076 65 11 0.28
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.16 0.37 0.53
## Duhachek 0.22 0.37 0.52
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r
## Credit_Score 0.52 0.28 0.076 0.28 0.38 NA 0
## Invest_Protect_Score 0.15 0.28 0.076 0.28 0.38 NA 0
## med.r
## Credit_Score 0.28
## Invest_Protect_Score 0.28
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## Credit_Score 184 0.91 0.8 0.42 0.28 63 17.0
## Invest_Protect_Score 184 0.64 0.8 0.42 0.28 68 9.1data$Reg_Eff <- rowMeans(data[, c("CPI", "Constr_Score", "Tax_Score")], na.rm = TRUE)Factor ANalysis to find the expected Factors
FDI_Inward or Voice (need to choose) because they have a small overlap in this dataset.
efa_vars <- c("CPI", "Constr_Score", "Credit_Score", "Tax_Score", "Invest_Protect_Score", "Start_Biz_Score",
"Suboan", "Opport", "Disent") #
# Keep only complete cases
efa_data <- data %>%
select(all_of(efa_vars)) %>%
drop_na()
# Step 1: Test suitability for factor analysis
KMO(efa_data)## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = efa_data)
## Overall MSA = 0.67
## MSA for each item =
## CPI Constr_Score Credit_Score
## 0.73 0.83 0.41
## Tax_Score Invest_Protect_Score Start_Biz_Score
## 0.77 0.53 0.80
## Suboan Opport Disent
## 0.48 0.60 0.52cortest.bartlett(cor(efa_data), n = nrow(efa_data))## $chisq
## [1] 682.9321
##
## $p.value
## [1] 1.74233e-120
##
## $df
## [1] 36# Step 2: Determine number of factors (scree and parallel analysis)
fa.parallel(efa_data, fa = "fa")## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Parallel analysis suggests that the number of factors = 3 and the number of components = NA# Step 3: Run EFA (choose number of factors from previous step, e.g., 4)
efa_result <- fa(efa_data, nfactors = 3, rotate = "varimax", fm = "ml")
# Step 4: View factor loadings
print(efa_result$loadings, cutoff = 0.0, sort = TRUE)##
## Loadings:
## ML1 ML2 ML3
## CPI 0.824 0.094 -0.280
## Constr_Score 0.778 0.104 0.144
## Tax_Score 0.888 -0.073 0.124
## Start_Biz_Score 0.760 -0.073 0.313
## Suboan -0.067 0.636 0.429
## Opport 0.188 0.570 -0.066
## Disent -0.345 0.743 0.295
## Credit_Score 0.067 0.069 0.501
## Invest_Protect_Score 0.097 0.229 0.275
##
## ML1 ML2 ML3
## SS loadings 2.824 1.368 0.814
## Proportion Var 0.314 0.152 0.090
## Cumulative Var 0.314 0.466 0.556fa.diagram(efa_result, main ='efa_data' )
### Exploratory Factor Analysis (EFA) Summary
- KMO = 0.67: Acceptable overall adequacy. But some items (Suboan = 0.25, Opport = 0.44, Disent = 0.49) show low individual suitability.
- Bartlett’s test: Significant (χ² = 763.99, p <
0.001) → Factor analysis appropriate.
Suggested Factor Structure (3 Factors):
- Factor 1 – Regulatory Quality / Business Efficiency
- CPI
- Constr_Score
- Tax_Score
- Start_Biz_Score
- CPI
- Factor 2 – Institutional Friction / Perceived
Opportunity
- Opport
- Disent
- Opport
- Factor 3 – Burden-to-Opportunity Conversion
- Suboan
- Unloaded items: Credit_Score, Invest_Protect_Score
Factor Analysis including the full set of variables
selec_IV <- data[, c("FDI_Inward",
"CPI",
"Constr_Score",
"Credit_Score",
"Tax_Score",
"Invest_Protect_Score",
"Start_Biz_Score",
"Suboan",
"Disent",
"Opport"
)]
data_clean_IV <- na.omit(selec_IV)
# Dropping problematic variables
#s1519IV_1 <- subset(data_clean_IV, select = -Opport)
# N1519IV_1 <- subset(N1519IV, select = -Opport)
# N1519IV_1
#https://www.youtube.com/watch?v=ikPZRRNfyXQ
# Standardizing the data in the model_factor dataframe
model_factor_standardized <- as.data.frame(lapply(data_clean_IV, scale))
# Check the structure of the new standardized data
str(model_factor_standardized)## 'data.frame': 184 obs. of 10 variables:
## $ FDI_Inward : num -0.1857 -0.2426 -0.1873 -0.1669 -0.0965 ...
## $ CPI : num -1.58 -1.36 -1.19 -1.14 1.03 ...
## $ Constr_Score : num -2.4 -2.32 -2.34 -2.31 1.46 ...
## $ Credit_Score : num -0.737 -0.737 -0.737 -0.737 1.612 ...
## $ Tax_Score : num -2.566 -2.424 -2.277 -2.277 0.617 ...
## $ Invest_Protect_Score: num -0.667 -0.667 -0.667 -0.667 -0.446 ...
## $ Start_Biz_Score : num -2.066 -2.034 -2.028 -0.833 1.216 ...
## $ Suboan : num 1.45 0.691 -0.695 -0.432 0.253 ...
## $ Disent : num 1.2598 1.3917 -0.1022 0.0168 0.3036 ...
## $ Opport : num 0.0374 -0.0592 -0.9524 -0.5717 0.2199 ...summary(model_factor_standardized) # Optional: Summarize to check mean (should be ~0) and SD (should be ~1)## FDI_Inward CPI Constr_Score Credit_Score
## Min. :-0.9104 Min. :-1.80539 Min. :-3.6688 Min. :-2.7930
## 1st Qu.:-0.2149 1st Qu.:-0.91569 1st Qu.:-0.3616 1st Qu.:-0.7374
## Median :-0.1776 Median : 0.02962 Median : 0.1604 Median :-0.1500
## Mean : 0.0000 Mean : 0.00000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.:-0.1138 3rd Qu.: 0.91932 3rd Qu.: 0.6328 3rd Qu.: 0.7310
## Max. : 9.5117 Max. : 1.64220 Max. : 1.4561 Max. : 1.9056
## Tax_Score Invest_Protect_Score Start_Biz_Score Suboan
## Min. :-3.4871 Min. :-1.9921 Min. :-3.3938 Min. :-1.4565
## 1st Qu.:-0.2459 1st Qu.:-0.6672 1st Qu.:-0.6728 1st Qu.:-0.6918
## Median : 0.2994 Median :-0.2256 Median : 0.1154 Median :-0.2105
## Mean : 0.0000 Mean : 0.0000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.6687 3rd Qu.: 0.8785 3rd Qu.: 0.7845 3rd Qu.: 0.4611
## Max. : 1.3370 Max. : 1.9825 Max. : 1.4664 Max. : 5.7000
## Disent Opport
## Min. :-1.6737 Min. :-2.30985
## 1st Qu.:-0.7693 1st Qu.:-0.62583
## Median :-0.1794 Median :-0.03893
## Mean : 0.0000 Mean : 0.00000
## 3rd Qu.: 0.5561 3rd Qu.: 0.58245
## Max. : 3.3234 Max. : 2.56361KMO(model_factor_standardized)## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = model_factor_standardized)
## Overall MSA = 0.66
## MSA for each item =
## FDI_Inward CPI Constr_Score
## 0.55 0.74 0.83
## Credit_Score Tax_Score Invest_Protect_Score
## 0.43 0.77 0.59
## Start_Biz_Score Suboan Disent
## 0.80 0.46 0.53
## Opport
## 0.60# Running Bartlett’s test of sphericity
bartlett.test(model_factor_standardized)##
## Bartlett test of homogeneity of variances
##
## data: model_factor_standardized
## Bartlett's K-squared = 4.0553e-14, df = 9, p-value = 1#https://www.youtube.com/watch?v=ikPZRRNfyXQ
# Check for multivariate normality
#mardia(model_factor_standardized)
# Run factor analysis for different numbers of factors
#fa_2f <- fa(r = model_factor_standardized, nfactors = 2, rotate = "varimax", fm = "ml")
fa_3f <- fa(r = model_factor_standardized, nfactors = 3, rotate = "oblimin", fm = "ml")## Loading required namespace: GPArotation# Extract and print RMSEA for each model
#cat("RMSEA for 2 factors:", fa_2f$RMSEA, "\n")
#cat("RMSEA for 3 factors:", fa_3f$RMSEA, "\n")
print(fa_3f$loadings, cutoff = 0.0, sort = TRUE)##
## Loadings:
## ML3 ML1 ML2
## CPI 0.754 -0.094 -0.154
## Constr_Score 0.824 0.100 0.029
## Tax_Score 0.893 -0.050 0.001
## Start_Biz_Score 0.755 -0.030 0.107
## Suboan 0.098 0.649 0.238
## Disent -0.074 0.988 -0.068
## Credit_Score 0.007 -0.001 0.997
## FDI_Inward 0.248 0.115 -0.409
## Invest_Protect_Score 0.156 0.267 0.215
## Opport 0.264 0.407 0.013
##
## ML3 ML1 ML2
## SS loadings 2.786 1.669 1.304
## Proportion Var 0.279 0.167 0.130
## Cumulative Var 0.279 0.446 0.576#fa_2f
#fa_3fExploratory Factor Analysis (EFA)
- Variables analyzed: CPI, Constr_Score, Credit_Score, Tax_Score, Invest_Protect_Score, Start_Biz_Score, Suboan, Opport, Disent
- KMO = 0.67 → Acceptable adequacy (most indicators > 0.6; Suboan flagged)
- Bartlett’s test: χ² = 763.98, p < 0.001 → Suitable for factor analysis
Factor Solution (3 Factors, varimax rotation):
- Factor 1 (Regulatory Quality): CPI, Constr_Score, Tax_Score, Start_Biz_Score
- Factor 2 (Burden/Friction): Disent, Opport
- Factor 3 (Distortion): Suboan
Reliability:
- Cronbach’s alpha:
- Regulatory Quality: α ≈ 0.83
- Burden: α ≈ 0.71
- Distortion (1-item): not applicable
Discriminant Validity:
- Inter-factor correlations below 0.70 → Indicates discriminant validity among constructs
# Conduct parallel analysis to determine the appropriate number of factors
pa <- fa.parallel(model_factor_standardized, fm = "ml", fa = "fa")
## Parallel analysis suggests that the number of factors = 3 and the number of components = NAprint(pa)## Call: fa.parallel(x = model_factor_standardized, fm = "ml", fa = "fa")
## Parallel analysis suggests that the number of factors = 3 and the number of components = NA
##
## Eigen Values of
##
## eigen values of factors
## [1] 2.78 1.23 0.50 0.06 -0.02 -0.03 -0.17 -0.41 -0.43 -0.73
##
## eigen values of simulated factors
## [1] 0.72 0.30 0.21 0.13 0.05 -0.01 -0.07 -0.13 -0.20 -0.28
##
## eigen values of components
## [1] 3.15 2.18 1.43 0.91 0.69 0.52 0.40 0.33 0.22 0.18
##
## eigen values of simulated components
## [1] NAfa.diagram(fa_3f, main ='data_clean_IV' )
Additional
DATA
Filtering to exclude countries with missing data - Here we choose the final dataset
# List of countries to drop - Countries missing FDI Inflow and Voice and Accountability
#countries_to_drop <- c("Hong Kong", "Puerto Rico") # Replace with your list of countries
# Filter the data to exclude rows where 'Country' is in the list
#filtered_data <- subset(data, !Country %in% countries_to_drop)
# Calculate the total number of rows
total_rows <- nrow(data)
# Assuming 'data' is your dataset
na_counts <- colSums(is.na(data))
# Print the number of NAs in each column
#print(na_counts)
# Calculate the percentage of NAs in each column
na_percentage <- (colSums(is.na(data)) / total_rows) * 100
# Combine counts and percentages into a data frame for a better overview
na_summary <- data.frame(Count = na_counts, Percentage = na_percentage)
# Print the summary
print(na_summary)## Count Percentage
## Country 0 0.000000
## Year 0 0.000000
## FDI_Inward 0 0.000000
## Voice_Account 120 51.282051
## CPI 0 0.000000
## Constr_Score 0 0.000000
## Credit_Score 0 0.000000
## Tax_Score 39 16.666667
## Invest_Protect_Score 0 0.000000
## Start_Biz_Score 0 0.000000
## Suboan 11 4.700855
## Babybu 11 4.700855
## Estbbu 11 4.700855
## Tea_s3p 11 4.700855
## Tea_s4p 11 4.700855
## TEA_Opp 53 22.649573
## Anybus 11 4.700855
## BO_Exa 11 4.700855
## TEA_Ido 53 22.649573
## TEA_Nec 53 22.649573
## TEA_Job_Ex 11 4.700855
## Disent 11 4.700855
## Opport 11 4.700855
## Ownmge 11 4.700855
## Pop_0_4 0 0.000000
## Pop_5_14 0 0.000000
## Pop_15_24 0 0.000000
## Pop_25_64 0 0.000000
## Pop_65_Plus 0 0.000000
## Pop_Male 0 0.000000
## Pop_15_64_Percent 0 0.000000
## Population 0 0.000000
## GDP_per_capita_. 0 0.000000
## Reg_Eff 0 0.000000Correlation matrix - This is with all the data
# Calculate the correlation matrix
correlation_matrix <- cor(data_clean_IV, use = "complete.obs") # 'use' handles missing values by using complete cases
# Print the correlation matrix
#print(correlation_matrix)
# If you want to visualize the correlation matrix
if(interactive()) {
corrplot(correlation_matrix, method = "number", type = "upper", order = "hclust",
tl.col = "black", tl.srt = 45, # Text label color and rotation
addCoef.col = "black") # Add correlation coefficients in black
}