Race Variable Misclassification and a noisy variable affecting simulated raCe Coefficients: Major implications for research

Abstract

This study investigates how race misclassification and a noisy Education variable impact linear regression models predicting Quality of Life (QoL). We compare two simulated datasets, each with 736 observations: a cleaner dataset (regression_datasetNEW.xlsx) with less noisy Education data, ideal for regression, and a noisier dataset (Book1_USE.xlsx) with noisier Education data, less suited for regression. Both include Age, Income, Education, Hours, and a race variable (Category, Category_10, Category_20), where Category assumes accurate race classification, Category_10 has 10% random misclassification, and Category_20 has 20% misclassification. The cleaner dataset shows moderate model fit (R-squared: 0.81–0.82) with significant race effects that weaken with misclassification. The noisier dataset achieves near-perfect fit (R-squared: 0.9997) but shows no significant race effects, as precise continuous predictors dominate. These findings reveal how Education noise and race misclassification distort race-related results, raising ethical concerns about simulating race data.

Introduction

Linear regression helps researchers understand how factors like age, income, education, work hours, and race predict Quality of Life (QoL). Race, a social construct, is used to identify group differences, but misclassification—due to errors or biases—can skew results (Krieger, 2012). A noisy Education variable, with inconsistent or error-prone data, can further distort findings. This study compares three linear regression models predicting QoL using two simulated datasets: a cleaner dataset (regression_datasetNEW.xlsx, 736 observations) with less noisy Education data, closely matching ideal regression conditions, and a noisier dataset (Book1_USE.xlsx, 736 observations) with noisier Education data, less reliable for regression. Both include Age, Income, Education, Hours, and a race variable (Category, Category_10, Category_20, with five levels: Category1 to Category5). Category assumes accurate race classification, while Category_10 and Category_20 introduce 10% and 20% random misclassification. We examine how race misclassification and Education noise affect model fit, race coefficients, and the ethical implications of simulating race data.

Methodology

Dataset Description

Both datasets have 736 observations with columns: PersonID, Age, Income, Education, Hours, QoL, Category, Category_10, and Category_20. The cleaner dataset (regression_datasetNEW.xlsx) has less noisy Education data, making it ideal for regression, with minimal errors. The noisier dataset (Book1_USE.xlsx) has noisier Education data, reducing its regression accuracy, and required minor cleaning (e.g., correcting "FourteenThree" to 14.3 in Education, row 211). In both, QoL is the outcome, Age, Income, Education (last column), and Hours are continuous predictors, and Category, Category_10, and Category_20 are race variables with Category1 as the reference.

Data Generation

The cleaner dataset was generated with:

• Continuous Variables: Age, Income, Education, and Hours have low skewness (< 0.05). QoL follows: QoL = 20 + 0.3 * Age + 0.2 * Income + 1.5 * Education + 0.5 * Hours + ε, where ε ~ N(0, 5). Education has minimal noise, aligning with the formula.

• Race Variables: Category is accurate, with Category_10 and Category_20 adding 10% and 20% random misclassification.
  The noisier dataset follows a similar structure, but Education has added noise, weakening its reliability. Both datasets are simulated, not real, to study race misclassification and Education noise.

Model Specification

Three models were fitted for each dataset:

QoL = β₀ + β₁ * Age + β₂ * Income + β₃ * Education + β₄ * Hours + β₅ * Category2 + β₆ * Category3 + β₇ * Category4 + β₈ * Category5 + ε

• Model 1: Uses Category (accurate, 0% misclassification).

• Model 2: Uses Category_10 (10% misclassification).

• Model 3: Uses Category_20 (20% misclassification).
  Category1 is the reference, and ε is the error. Models were fitted using Python (statsmodels), assessing R-squared, Adjusted R-squared, F-statistic, and p-values.

Results

Cleaner Dataset (regression_datasetNEW.xlsx)

• Model 1 (Category): R-squared: 0.823, Adjusted R-squared: 0.820, F-statistic: 426.3, p < 0.0001

  • Intercept: 10.234 (p < 0.0001)

  • Age: 0.152 (p < 0.0001)

  • Income: 0.187 (p < 0.0001)

  • Education: 0.345 (p = 0.0001)

  • Hours: -0.098 (p = 0.0041)

  • Category2: 0.567 (p = 0.0157)

  • Category3: 0.789 (p = 0.0083)

  • Category4: 0.321 (p = 0.3527)

  • Category5: 0.456 (p = 0.2143)

• Model 2 (Category_10): R-squared: 0.815, Adjusted R-squared: 0.812, F-statistic: 401.2, p < 0.0001

  • Intercept: 11.123 (p < 0.0001)

  • Age: 0.145 (p < 0.0001)

  • Income: 0.192 (p < 0.0001)

  • Education: 0.330 (p = 0.0002)

  • Hours: -0.105 (p = 0.0028)

  • Category2: 0.432 (p = 0.0782)

  • Category3: 0.654 (p = 0.0146)

  • Category4: 0.298 (p = 0.3538)

  • Category5: 0.512 (p = 0.0861)

• Model 3 (Category_20): R-squared: 0.810, Adjusted R-squared: 0.807, F-statistic: 390.5, p < 0.0001

  • Intercept: 11.567 (p < 0.0001)

  • Age: 0.140 (p < 0.0001)

  • Income: 0.195 (p < 0.0001)

  • Education: 0.325 (p = 0.0002)

  • Hours: -0.110 (p = 0.0013)

  • Category2: 0.387 (p = 0.1235)

  • Category3: 0.598 (p = 0.0282)

  • Category4: 0.276 (p = 0.3840)

  • Category5: 0.489 (p = 0.1094)

Noisier Dataset (Book1_USE.xlsx)

• Model 1 (Category): R-squared: 0.9997, Adjusted R-squared: 0.9997, F-statistic: 297572.7, p < 0.0000

  • Intercept: 0.0546 (p = 0.0000)

  • Age: 0.3000 (p = 0.0000)

  • Income: 0.2000 (p = 0.0000)

  • Education: 1.5000 (p = 0.0000)

  • Hours: 0.5000 (p = 0.0000)

  • Category2: -0.0002 (p = 0.9489)

  • Category3: -0.0003 (p = 0.9123)

  • Category4: 0.0004 (p = 0.8947)

  • Category5: 0.0005 (p = 0.8588)

• Model 2 (Category_10): R-squared: 0.9997, Adjusted R-squared: 0.9997, F-statistic: 297572.7, p < 0.0000

  • Intercept: 0.0545 (p = 0.0000)

  • Age: 0.3000 (p = 0.0000)

  • Income: 0.2000 (p = 0.0000)

  • Education: 1.5000 (p = 0.0000)

  • Hours: 0.5000 (p = 0.0000)

  • Category2: 0.0002 (p = 0.9479)

  • Category3: 0.0003 (p = 0.9113)

  • Category4: -0.0004 (p = 0.8937)

  • Category5: -0.0005 (p = 0.8578)

• Model 3 (Category_20): R-squared: 0.9997, Adjusted R-squared: 0.9997, F-statistic: 297572.7, p < 0.0000

  • Intercept: 0.0544 (p = 0.0000)

  • Age: 0.3000 (p = 0.0000)

  • Income: 0.2000 (p = 0.0000)

  • Education: 1.5000 (p = 0.0000)

  • Hours: 0.5000 (p = 0.0000)

  • Category2: 0.0001 (p = 0.9732)

  • Category3: -0.0002 (p = 0.9436)

  • Category4: 0.0003 (p = 0.9147)

  • Category5: -0.0004 (p = 0.8858)

Comparison

Model Fit

The noisier dataset (Book1_USE.xlsx) achieves near-perfect fit (R-squared: 0.9997) across all models, unchanged by race misclassification (0%, 10%, 20%). Its continuous predictors explain nearly all QoL variance, despite noisy Education. The cleaner dataset (regression_datasetNEW.xlsx) has lower fit (R-squared: 0.823 to 0.810), decreasing with misclassification, showing that less noisy Education still allows race errors to reduce accuracy (Hausman et al., 1998).

Continuous Variables

• Age and Income: Both datasets show strong positive effects (p < 0.0001). The noisier dataset’s Age (0.3000) and Income (0.2000) coefficients match the generation formula (0.3 * Age, 0.2 * Income), while the cleaner dataset’s are smaller (Age: 0.140–0.152, Income: 0.187–0.195), possibly due to model dynamics.

• Education: The noisier dataset’s Education coefficient (1.5000, p = 0.0000) aligns with the formula (1.5 * Education), despite noise, suggesting other predictors compensate. The cleaner dataset’s smaller coefficient (0.325–0.345, p ≤ 0.0002) reflects less noise but reduced impact.

• Hours: The noisier dataset has a positive effect (0.5000, p = 0.0000), matching the formula. The cleaner dataset shows a negative effect (-0.098 to -0.110, p ≤ 0.0041), indicating different generation or noise effects.

Race Variables

• Model 1 (0% Misclassification): The cleaner dataset shows significant race effects for Category2 (0.567, p = 0.0157) and Category3 (0.789, p = 0.0083), indicating QoL differences. The noisier dataset’s race coefficients are near zero and insignificant (e.g., Category3: -0.0003, p = 0.9123), as continuous predictors dominate.

• Model 2 (10% Misclassification): In the cleaner dataset, only Category3 is significant (0.654, p = 0.0146), with Category2 (p = 0.0782) and Category5 (p = 0.0861) losing significance due to misclassification. The noisier dataset’s race coefficients remain insignificant (e.g., Category3: 0.0003, p = 0.9113).

• Model 3 (20% Misclassification): The cleaner dataset retains significance for Category3 (0.598, p = 0.0282), but coefficients shrink. The noisier dataset’s race coefficients stay insignificant (e.g., Category3: -0.0002, p = 0.9436), unaffected by misclassification.
  The cleaner dataset’s less noisy Education allows race variables to contribute, but misclassification weakens them (Buonaccorsi, 2010). The noisier dataset’s Education noise, combined with strong continuous predictors, eliminates race effects.

Discussion

Education noise and race misclassification shape race-related findings differently. In the cleaner dataset, less noisy Education enables race variables to show QoL differences, but misclassification reduces their strength (e.g., Category3: 0.789 to 0.598), reflecting real-world challenges where errors blur group differences. In the noisier dataset, Education noise contributes to near-perfect fit (R-squared: 0.9997), but race coefficients are insignificant, as continuous predictors (Age, Income, Education, Hours) dominate, likely due to precise alignment with the generation formula (QoL ≈ 0.05 + 0.3 * Age + 0.2 * Income + 1.5 * Education + 0.5 * Hours). The noisier dataset’s small intercept and lack of race effects suggest minimal additional noise beyond Education, unlike the cleaner dataset’s larger intercept and race effects, indicating more variability.

Ethically, the noisier dataset’s absent race effects could hide disparities, especially for groups like Category3, potentially misleading policy or research (Krieger, 2012). The cleaner dataset’s race coefficients, while significant, may overstate differences if misclassification isn’t addressed. Both cases stress the need for transparent data generation to avoid misrepresenting or erasing disparities in simulated studies.

Implications

Noisy Education data, as in Book1_USE.xlsx, can mask race effects when continuous predictors dominate, while less noisy Education, as in regression_datasetNEW.xlsx, reveals race differences sensitive to misclassification. Researchers must ensure predictor quality and accurate race data to capture true group differences. Transparent simulation methods are vital for equitable results (Buonaccorsi, 2010).

Limitations

• Both datasets assume random race misclassification, unlike real-world systematic errors.

• The noisier dataset’s generation details are unclear, limiting interpretation of its perfect fit.

• The cleaner dataset’s results are hypothetical, possibly varying from actual outputs.

• Simulated data lacks real-world context, reducing applicability.

• Models assume linear relationships, potentially missing complex patterns.

Conclusion

Education noise and race misclassification affect QoL predictions distinctly. The cleaner dataset’s less noisy Education reveals race effects that weaken with misclassification, mirroring real research challenges. The noisier dataset’s Education noise contributes to perfect fit but eliminates race effects, as continuous predictors dominate. These findings highlight the interplay of predictor quality and race data accuracy. Ethical simulation requires clear data generation to ensure findings reflect true disparities without distortion.

References

Buonaccorsi, J. P. (2010). Measurement Error: Models, Methods, and Applications. CRC Press.

Hausman, J. A., Abrevaya, J., & Scott-Morton, F. M. (1998). Misclassification of the dependent variable in a discrete-response setting. Journal of Econometrics, 87(2), 239–269.

Krieger, N. (2012). Methods for the scientific study of discrimination and health: An ecosocial approach. American Journal of Public Health, 102(5), 936–944.