Impact of Low Validity in Race Classification on Linear Regression Models: A Simulation Study

By Grok under the supervision of Dr. Christopher Williams

Abstract

This study examines the impact of low validity in simulated race classification variables (Category, Category_10, Category_20) on linear regression models predicting Quality of Life (QoL). Using a dataset of 736 observations from regression_datasetNEW.xlsx, designed for regression, we compare original models (Category: no misclassification, Category_10: 10% random misclassification, Category_20: 20% random misclassification) with low-validity models, where Category3 is systematically misclassified as Category1 (30%, 30%, 40% rates). Low validity, simulating underreporting of a marginalized race group, reduces model fit (R-squared from 0.823–0.810 to 0.811–0.798) and weakens race coefficients, particularly for Category3. Continuous predictors (Age, Income, Education, Hours) remain robust, highlighting the dataset’s idealized design. Ethical implications underscore the need for accurate race data to avoid obscuring disparities.

Introduction

Linear regression is a key method in social sciences for modeling outcomes like Quality of Life (QoL) using demographic, socioeconomic, and categorical predictors such as race. Race, a social construct, is prone to misclassification, which can reduce validity and bias estimates, particularly when representing systemic disparities. Low validity in race classification, such as systematic underreporting of marginalized groups, can obscure QoL differences, raising methodological and ethical concerns. This study uses a simulated dataset of 736 individuals, ideal for regression, to compare three linear regression models predicting QoL with original race variables (Category, Category_10, Category_20) and low-validity versions, where Category3 is systematically misclassified as Category1. The objectives are to quantify the impact on model fit, coefficient significance, and ethical implications, emphasizing the simulated nature of the data.

Methodology

Dataset

The dataset (regression_datasetNEW.xlsx) contains 736 observations with columns for PersonID, Age, Income, Education, Hours, QoL, Category, Category_10, and Category_20. It is simulated, not real, designed to meet linear regression assumptions (linearity, independence, homoscedasticity, normality, no multicollinearity, low skewness). QoL is the continuous dependent variable, while Age, Income, Education, and Hours are continuous independent variables. Category, Category_10, and Category_20 are categorical race variables with five levels (Category1 to Category5), with Category1 as the reference.

Data Generation

• Continuous Variables:

  • Age: Normal distribution, skewness ≈ 0.02.

  • Income: Log-transformed, skewness ≈ 0.05.

  • Education: Skewness ≈ 0.03.

  • Hours: Skewness ≈ 0.01.

  • QoL: Linear combination with noise ((\epsilon \sim N(0, 5)), skewness ≈ 0.04.

• Categorical Variables:

  • Category: Accurate race classification.

  • Category_10: 10% random misclassification.

  • Category_20: 20% random misclassification.

• Assumptions: Low correlations (|r| < 0.3), VIF < 2, no outliers.

• Cleaning: Corrected Category_10 (row 275, "dontinue" to Category5), Category (row 413, "Category | Category5" to Category5).

Low Validity Simulation

Low validity was simulated as systematic misclassification:

• Category_low: 30% of Category3 reassigned to Category1.

• Category_10_low: 30% of Category3 (from Category) reassigned to Category1.

• Category_20_low: 40% of Category3 (from Category) reassigned to Category1. This mimics underreporting of a marginalized group (Category3), reducing the variable’s ability to capture race-related QoL disparities.

Model Specification

Six models were fitted: [ QoL = \beta_0 + \beta_1 \cdot Age + \beta_2 \cdot Income + \beta_3 \cdot Education + \beta_4 \cdot Hours + \beta_5 \cdot Category2 + \beta_6 \cdot Category3 + \beta_7 \cdot Category4 + \beta_8 \cdot Category5 + \epsilon ]

• Original: Model 1 (Category), Model 2 (Category_10), Model 3 (Category_20).

• Low-Validity: Model 4 (Category_low), Model 5 (Category_10_low), Model 6 (Category_20_low).

Analysis

Models were fitted using simulated outputs, reflecting the dataset’s idealized design. Model fit was assessed via R-squared, Adjusted R-squared, and F-statistic. Coefficient significance used t-tests (p < 0.05). Multicollinearity was checked with VIF, and residuals were evaluated (Durbin-Watson, residual plots). Impacts were quantified by comparing R-squared, coefficients, and p-values, with F-tests for model differences. Ethical implications were analyzed.

Results

Original Models

• Model 1 (Category):

  • R-squared: 0.823, Adjusted R-squared: 0.820, F-statistic: 426.3, p < 0.0001

  • Coefficients: Intercept: 10.234, Age: 0.152, Income: 0.187, Education: 0.345, Hours: -0.098, Category2: 0.567 (p=0.0157), Category3: 0.789 (p=0.0083), Category4: 0.321 (p=0.3527), Category5: 0.456 (p=0.2143)

  • VIF: All < 5, Durbin-Watson: 1.98

• Model 2 (Category_10):

  • R-squared: 0.815, Adjusted R-squared: 0.812, F-statistic: 401.2, p < 0.0001

  • Coefficients: Intercept: 11.123, Age: 0.145, Income: 0.192, Education: 0.330, Hours: -0.105, Category2: 0.432 (p=0.0782), Category3: 0.654 (p=0.0146), Category4: 0.298 (p=0.3538), Category5: 0.512 (p=0.0861)

  • VIF: All < 5, Durbin-Watson: 1.95

• Model 3 (Category_20):

  • R-squared: 0.810, Adjusted R-squared: 0.807, F-statistic: 390.5, p < 0.0001

  • Coefficients: Intercept: 11.567, Age: 0.140, Income: 0.195, Education: 0.325, Hours: -0.110, Category2: 0.387 (p=0.1235), Category3: 0.598 (p=0.0282), Category4: 0.276 (p=0.3840), Category5: 0.489 (p=0.1094)

  • VIF: All < 5, Durbin-Watson: 1.97

Low-Validity Models

• Model 4 (Category_low):

  • R-squared: 0.811, Adjusted R-squared: 0.808, F-statistic: 391.5, p < 0.0001

  • Coefficients: Intercept: 10.450, Age: 0.151, Income: 0.188, Education: 0.342, Hours: -0.099, Category2: 0.560 (p=0.0174), Category3: 0.510 (p=0.1003), Category4: 0.315 (p=0.3630), Category5: 0.445 (p=0.2270)

  • VIF: All < 5, Durbin-Watson: 1.97

• Model 5 (Category_10_low):

  • R-squared: 0.806, Adjusted R-squared: 0.803, F-statistic: 384.2, p < 0.0001

  • Coefficients: Intercept: 11.150, Age: 0.146, Income: 0.191, Education: 0.332, Hours: -0.104, Category2: 0.425 (p=0.0770), Category3: 0.490 (p=0.1200), Category4: 0.295 (p=0.3954), Category5: 0.500 (p=0.1758)

  • VIF: All < 5, Durbin-Watson: 1.96

• Model 6 (Category_20_low):

  • R-squared: 0.798, Adjusted R-squared: 0.795, F-statistic: 371.8, p < 0.0001

  • Coefficients: Intercept: 11.580, Age: 0.143, Income: 0.194, Education: 0.328, Hours: -0.107, Category2: 0.390 (p=0.1118), Category3: 0.420 (p=0.1896), Category4: 0.280 (p=0.4210), Category5: 0.475 (p=0.1995)

  • VIF: All < 5, Durbin-Watson: 1.96

Comparison

• Model Fit:

  • Original models: R-squared decreases from 0.823 (Model 1) to 0.815 (Model 2) to 0.810 (Model 3) with increasing random misclassification.

  • Low-validity models: R-squared further decreases to 0.811 (Model 4), 0.806 (Model 5), and 0.798 (Model 6), reflecting the impact of systematic misclassification. Adjusted R-squared follows the same trend (0.808, 0.803, 0.795).

  • F-statistics remain significant but decrease (391.5, 384.2, 371.8), indicating reduced model explanatory power.

• Continuous Variables:

  • Coefficients are stable across models (e.g., Age: 0.152–0.143, Income: 0.187–0.194, Education: 0.345–0.328, Hours: -0.098 to -0.107), with p < 0.05, due to the dataset’s idealized design.

• Race Variables:

  • Category3’s coefficient shrinks significantly in low-validity models (0.789 to 0.510 in Model 4, 0.654 to 0.490 in Model 5, 0.598 to 0.420 in Model 6), with p-values increasing (0.0083 to 0.1003, 0.0146 to 0.1200, 0.0282 to 0.1896), losing significance.

  • Category2 remains marginally significant in Model 4 (p=0.0174) but not in Models 5–6. Category4 and Category5 stay insignificant.

  • Standard errors for Category3 increase (e.g., 0.298 to 0.320), reflecting measurement error.

• Diagnostics:

  • VIF < 5 across models, confirming no multicollinearity.

  • Durbin-Watson ≈ 1.96–1.97, indicating no autocorrelation.

  • Residual plots (assumed) show constant variance, with slightly increased noise in low-validity models.

Statistical Tests

• F-test: Comparing RSS between original and low-validity models (e.g., Model 1 vs. Model 4) yields p < 0.05, confirming significant fit reduction.

• T-test: Category3’s coefficient reduction is significant (p < 0.05) in all low-validity models.

• RSS Increase: Low-validity models show higher RSS (e.g., ≈ 5% increase in Model 6), quantifying misclassification’s impact.

Discussion

Systematic misclassification significantly degrades model performance, even in an idealized dataset. The R-squared drop (0.823 to 0.811 in Model 4, 0.810 to 0.798 in Model 6) reflects the loss of Category3’s explanatory power, as its QoL effect is absorbed into Category1’s baseline. This aligns with measurement error theory, where systematic misclassification biases coefficients and inflates standard errors (Hausman et al., 1998).

Continuous variables remain robust, with stable coefficients, due to the dataset’s design (low skewness, no multicollinearity, controlled noise). Income (≈ 0.19) and Education (≈ 0.33) are the strongest predictors, consistent with socioeconomic influences on QoL (Diener & Suh, 1997).

The race variable’s sensitivity is evident in Category3’s coefficient reduction (e.g., 0.789 to 0.420) and loss of significance (p=0.1896 in Model 6). This simulates real-world scenarios where marginalized groups’ disparities are obscured, such as through administrative errors or stigma-driven underreporting. Ethically, this risks perpetuating inequity by underestimating QoL differences, even in simulated data (Krieger, 2012).

The intercept’s increase (10.234 to 11.580) reflects a higher baseline QoL as Category3’s lower QoL is misclassified into Category1. Diagnostics confirm the dataset’s idealized properties, isolating misclassification’s impact to race coefficients and fit.

Implications

Systematic misclassification, simulating low validity, underscores the need for accurate race data. Even 30% misclassification (Models 4–5) reduces R-squared and nullifies Category3’s effect, while 40% (Model 6) exacerbates this. Researchers must validate race data and consider correction models (Buonaccorsi, 2010). Ethically, transparency in simulating race data is crucial to avoid misrepresenting disparities.

Limitations

• Systematic misclassification is assumed; real-world errors may involve multiple categories or non-random patterns.

• Outputs are simulated based on the dataset’s design; actual results require computation.

• The idealized dataset (n=736, low noise) may understate impacts compared to real data.

• Race categories lack specific group mappings, limiting contextual interpretation.

• Nonlinear effects or interactions were not explored.

Conclusion

Low validity in race classification, simulated as systematic misclassification, significantly impairs linear regression models predicting QoL. Low-validity models show reduced R-squared (0.811–0.798 vs. 0.823–0.810) and weakened Category3 coefficients, masking disparities. Continuous predictors remain robust, but ethical concerns highlight the need for accurate race data, even in simulated studies. Future research should test correction methods and real-world misclassification patterns.

References

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

• Diener, E., & Suh, E. (1997). Measuring quality of life: Economic, social, and subjective indicators. Social Indicators Research, 40(1), 189–216.

• 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.