Mathematical Modeling & Statistical Computing

Parameter	Academic Credentials & Competencies
Formal Education	STAI Al-Bahjah, Bachelor of Education (S.Pd.), Mathematics Education
Academic Rigor	140 Credits Completed, GPA 3.71
Advanced Statistics	Final Score: 89.8 (Grade A-)
Pillar	4. Data Analysis

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1. Applied Mathematical Foundations

Commercial business intelligence and scholarly research initiatives frequently suffer from generalization failures because practitioners ignore fundamental assumption testing. Analysts routinely rush into multiple linear regressions or ANOVA without first verifying mathematical prerequisites:

1. Normality of residual distributions (Shapiro-Wilk / Kolmogorov-Smirnov).
2. Homogeneity of variances across groups (Levene’s Test).
3. Absence of severe multicollinearity (Variance Inflation Factor VIF < 5.0 and Tolerance > 0.10).
4. Absence of residual autocorrelation (Durbin-Watson d-statistic bounds).

Our background in pure and applied mathematics ensures principled data sanitization: executing Box-Cox power transformations, Winsorizing extreme outliers, or transitioning to non-parametric analogs (Mann-Whitney U, Kruskal-Wallis) without falsifying underlying empirical signals.

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2. Structural Equation Modeling (SEM-PLS)

For complex latent variable architectures with multi-item indicators, we construct Partial Least Squares Structural Equation Modeling pipelines (SmartPLS / WarpPLS / semopy):

• Measurement Model Evaluation (Outer Model): Convergent validity (Outer Loadings > 0.70, AVE > 0.50), Discriminant validity (Fornell-Larcker criterion and HTMT ratios < 0.85/0.90), and Composite Reliability (> 0.80).
• Structural Model Evaluation (Inner Model): Coefficients of determination ($R^2$), effect sizes ($f^2$), predictive relevance ($Q^2$), and path significance evaluated via 5,000-iteration non-parametric bootstrapping.

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3. Deterministic Python Statistical Verification

import numpy as np
import scipy.stats as stats

def evaluate_classical_assumptions(residuals: np.ndarray) -> dict:
    """Evaluate normality of regression residuals via Shapiro-Wilk test."""
    stat, p_val = stats.shapiro(residuals)
    return {
        "shapiro_statistic": float(stat),
        "p_value": float(p_val),
        "is_normal": bool(p_val > 0.05)
    }

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4. Contact Applied Mathematician

• Email Direct: devapenseo@gmail.com
• Consultation Portal: Available via the homepage project initiation form.