Skin Optics Analysis based on ISSA Data
Junhui He and Tina Lasisi
2025-12-18
Last updated: 2025-12-18
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| File | Version | Author | Date | Message |
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| Rmd | 243e344 | tinalasisi | 2025-12-18 | Fixed the regressions |
| html | 243e344 | tinalasisi | 2025-12-18 | Fixed the regressions |
| Rmd | c4b2199 | tinalasisi | 2025-12-18 | Added statistical tests to log-relationships |
| html | c4b2199 | tinalasisi | 2025-12-18 | Added statistical tests to log-relationships |
| Rmd | 40b4375 | tinalasisi | 2025-12-18 | updates to tests |
| html | 40b4375 | tinalasisi | 2025-12-18 | updates to tests |
| Rmd | 90b5102 | tinalasisi | 2025-12-18 | Revise Skin Optics analysis: improved deduplication, plotting, and reproducibility |
| html | 90b5102 | tinalasisi | 2025-12-18 | Revise Skin Optics analysis: improved deduplication, plotting, and reproducibility |
| html | 9956d2d | Junhui He | 2025-12-17 | Build site. |
| Rmd | a6f7dc4 | Junhui He | 2025-12-17 | update JID_SkinOptics.Rmd |
| html | 32c3e8f | Junhui He | 2025-12-11 | Rebuild site to apply navbar layout |
| html | b2cbe44 | Junhui He | 2025-12-11 | Build site. |
| Rmd | df71367 | Junhui He | 2025-12-11 | modify face site |
| html | d98f12d | Junhui He | 2025-12-11 | Build site. |
| Rmd | 2fc3d03 | Junhui He | 2025-12-11 | add correlation analysis |
| html | 81580b5 | Junhui He | 2025-12-11 | build workflowr |
| Rmd | e11deee | Junhui He | 2025-12-11 | calculate EI |
| html | e11deee | Junhui He | 2025-12-11 | calculate EI |
| Rmd | 53d4f9c | Junhui He | 2025-12-11 | create SkinOptics |
| html | 53d4f9c | Junhui He | 2025-12-11 | create SkinOptics |
Clarifications
Melanin index (MI) is calculated from skin reflectance at 680 nm, where \(R_{680}\) is the measured reflectance percentage (0-100):
- \[MI = -100 \times \log_{10}(R_{680} / 100)\]
- This is equivalent to the standard formula \(MI = 100 \times \log_{10}(1/R)\), where \(R\) is reflectance as a decimal (0-1)
- Internally, this is computed by first calculating absorbance (\(A_{680} = -\log_{10}(R_{680} / 100)\)), then multiplying by 100
Erythema index (EI) is calculated as: \[EI = 100 \times \log_{10}\left(\frac{R_{680}}{(R_{550} + R_{560})/2}\right)\] where \(R_{550}\), \(R_{560}\), and \(R_{680}\) are the reflectance percentages at 550 nm, 560 nm, and 680 nm, respectively.
EI variability is measured by the standard deviation of EIs within a sliding window of MI values. The window size is set to 20 MI units, and the step size is 1 MI unit.
- For each center MI value in the sequence, all EI values corresponding to MI values within the window (center MI \(\pm\) 10) are collected, and their standard deviation is computed.
- The center MI values range from the 1st to the 99th percentile of observed MI values.
FACE site refers to Forehead or Cheek, while PALM site refers to the palm of the hand.
Representative FACE MI:
- For each subject, the FACE MI is given by the Forehead MI if the Forehead MI is available; otherwise, it is the Cheek MI.
- For subjects with multiple measurements at the same FACE site, we randomly select one measurement.
- Each subject has only one representative FACE reflectance spectra.
First derivatives of skin spectra are estimated using local polynomial regression with bandwidth selected by the dpill function, scaled by a factor of 0.7.
Eumelanin class are defined based on melanin index ranges as follows:
- Low: \(MI < 25\)
- Intermediate low: \(25 \leq MI < 50\)
- Intermediate: \(50 \leq MI < 75\)
- Intermediate high: \(75 \leq MI < 100\)
- High: \(MI \geq 100\)
The pdf files generated in this analysis are saved in the “output” directory.
Visualizations
Face readings before deduplication: 4603 Unique individuals with face readings: 2102 Face readings after deduplication: 2102 Palm readings before deduplication: 776 Unique individuals with palm readings: 776 Palm readings after deduplication: 776 Distribution of melanin index by site
Final data summary:Face: n = 2101 | Unique individuals: 2101 Palm: n = 776 | Unique individuals: 776 Combined: n = 2877 
Unique subjects per site across representative face melanin index bins (Heatmap)
| Eumelanin class | Number of subjects |
|---|---|
| Low | 77 |
| Intermediate low | 1800 |
| Intermediate | 191 |
| Intermediate high | 30 |
| High | 3 |
| Eumelanin class | Number of subjects |
|---|---|
| Low | 127 |
| Intermediate low | 621 |
| Intermediate | 27 |
| Intermediate high | 1 |
Reflectance by eumelanin class
face reflectance by face eumelanin class
palm reflectance by palm eumelanin class
First derivatives of reflectance by eumelanin class
face reflectance derivatives by face eumelanin class
palm reflectance derivatives by palm eumelanin class
Composite figure: face reflectance and derivatives by eumelanin class
First derivatives of absorbance by eumelanin class
face absorbance derivatives by face eumelanin class
palm absorbance derivatives by palm eumelanin class
Correlation between reflectance derivative sd and melanin index
- Regression analysis
Call:
lm(formula = sd_ref ~ log_mi + I(log_mi^2), data = sd_face)
Residuals:
Min 1Q Median 3Q Max
-0.069033 -0.014140 -0.001695 0.011080 0.100513
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.558619 0.066400 23.47 <2e-16 ***
log_mi -0.681307 0.035862 -19.00 <2e-16 ***
I(log_mi^2) 0.076171 0.004826 15.78 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.02264 on 2098 degrees of freedom
Multiple R-squared: 0.6497, Adjusted R-squared: 0.6494
F-statistic: 1946 on 2 and 2098 DF, p-value: < 2.2e-16
Call:
lm(formula = sd_ref ~ log_mi, data = sd_palm)
Residuals:
Min 1Q Median 3Q Max
-0.066053 -0.016370 0.000337 0.015371 0.071971
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.560165 0.013160 42.56 <2e-16 ***
log_mi -0.120567 0.003789 -31.82 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.0238 on 774 degrees of freedom
Multiple R-squared: 0.5668, Adjusted R-squared: 0.5662
F-statistic: 1013 on 1 and 774 DF, p-value: < 2.2e-16
Log-transformed: Derivative SD vs melanin index (reflectance)
A log-log regression tests for a power-law relationship between derivative variability and melanin content. The slope in log-log space represents the exponent of this power-law relationship.
=== Log-log regression: log(sd_ref) ~ log(mi) ===FACE:
Call:
lm(formula = log(sd_ref) ~ log(mi), data = sd_face)
Residuals:
Min 1Q Median 3Q Max
-0.80045 -0.14091 0.00135 0.13879 0.78775
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.35968 0.06520 36.19 <2e-16 ***
log(mi) -1.32148 0.01813 -72.89 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.2134 on 2099 degrees of freedom
Multiple R-squared: 0.7168, Adjusted R-squared: 0.7166
F-statistic: 5312 on 1 and 2099 DF, p-value: < 2.2e-16
PALM:
Call:
lm(formula = log(sd_ref) ~ log(mi), data = sd_palm)
Residuals:
Min 1Q Median 3Q Max
-0.81944 -0.10556 0.01225 0.13604 0.49637
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.46811 0.10826 13.56 <2e-16 ***
log(mi) -0.99743 0.03117 -32.00 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.1958 on 774 degrees of freedom
Multiple R-squared: 0.5695, Adjusted R-squared: 0.569
F-statistic: 1024 on 1 and 774 DF, p-value: < 2.2e-16
Derivative peak and valley analysis (500-650 nm)
For each individual spectrum, we identify the peak (maximum) and valley (minimum) of the first derivative within the 500-650 nm wavelength range. This range captures the hemoglobin absorption features.
Face derivative peak/valley summary (500-650 nm):Peak wavelength - Mean: 593.4 SD: 8.8 Valley wavelength - Mean: 530.1 SD: 11.2
Palm derivative peak/valley summary (500-650 nm):Peak wavelength - Mean: 591.2 SD: 3.2 Valley wavelength - Mean: 529.8 SD: 1.6 
Regression: Peak/valley location and value vs melanin index
=== FACE: Peak and Valley vs Melanin Index ===Peak wavelength ~ MI:
Call:
lm(formula = peak_wavelength ~ mi, data = face_peak_valley)
Residuals:
Min 1Q Median 3Q Max
-34.898 -3.530 -1.138 1.738 42.895
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 576.68823 0.55179 1045.1 <2e-16 ***
mi 0.44617 0.01412 31.6 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 7.239 on 2099 degrees of freedom
Multiple R-squared: 0.3223, Adjusted R-squared: 0.322
F-statistic: 998.3 on 1 and 2099 DF, p-value: < 2.2e-16
Valley wavelength ~ MI:
Call:
lm(formula = valley_wavelength ~ mi, data = face_peak_valley)
Residuals:
Min 1Q Median 3Q Max
-31.727 -1.898 -0.790 0.548 120.351
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 538.70815 0.82978 649.22 <2e-16 ***
mi -0.22953 0.02123 -10.81 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 10.89 on 2099 degrees of freedom
Multiple R-squared: 0.05273, Adjusted R-squared: 0.05228
F-statistic: 116.8 on 1 and 2099 DF, p-value: < 2.2e-16
Peak value ~ MI:
Call:
lm(formula = peak_value ~ mi, data = face_peak_valley)
Residuals:
Min 1Q Median 3Q Max
-0.18771 -0.04834 -0.01068 0.03352 0.35911
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.7393814 0.0054962 134.53 <2e-16 ***
mi -0.0095523 0.0001407 -67.92 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.0721 on 2099 degrees of freedom
Multiple R-squared: 0.6872, Adjusted R-squared: 0.6871
F-statistic: 4612 on 1 and 2099 DF, p-value: < 2.2e-16
Valley value ~ MI:
Call:
lm(formula = valley_value ~ mi, data = face_peak_valley)
Residuals:
Min 1Q Median 3Q Max
-0.149037 -0.021909 0.004065 0.025444 0.101464
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -7.788e-02 2.892e-03 -26.93 <2e-16 ***
mi 1.810e-03 7.401e-05 24.46 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.03794 on 2099 degrees of freedom
Multiple R-squared: 0.2218, Adjusted R-squared: 0.2214
F-statistic: 598.3 on 1 and 2099 DF, p-value: < 2.2e-16
=== PALM: Peak and Valley vs Melanin Index ===Peak wavelength ~ MI:
Call:
lm(formula = peak_wavelength ~ mi, data = palm_peak_valley)
Residuals:
Min 1Q Median 3Q Max
-5.1837 -1.4310 -0.9626 -0.0740 10.3396
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 586.86185 0.47421 1237.565 <2e-16 ***
mi 0.13084 0.01405 9.313 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 3.04 on 774 degrees of freedom
Multiple R-squared: 0.1008, Adjusted R-squared: 0.09961
F-statistic: 86.74 on 1 and 774 DF, p-value: < 2.2e-16
Valley wavelength ~ MI:
Call:
lm(formula = valley_wavelength ~ mi, data = palm_peak_valley)
Residuals:
Min 1Q Median 3Q Max
-9.9124 0.1110 0.1858 0.2405 10.1440
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 530.260853 0.254584 2082.852 <2e-16 ***
mi -0.013826 0.007542 -1.833 0.0672 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.632 on 774 degrees of freedom
Multiple R-squared: 0.004323, Adjusted R-squared: 0.003036
F-statistic: 3.36 on 1 and 774 DF, p-value: 0.06717
Peak value ~ MI:
Call:
lm(formula = peak_value ~ mi, data = palm_peak_valley)
Residuals:
Min 1Q Median 3Q Max
-0.187325 -0.048439 -0.007921 0.049163 0.249649
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.8273744 0.0109182 75.78 <2e-16 ***
mi -0.0106817 0.0003235 -33.02 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.07 on 774 degrees of freedom
Multiple R-squared: 0.5849, Adjusted R-squared: 0.5843
F-statistic: 1091 on 1 and 774 DF, p-value: < 2.2e-16
Valley value ~ MI:
Call:
lm(formula = valley_value ~ mi, data = palm_peak_valley)
Residuals:
Min 1Q Median 3Q Max
-0.114064 -0.031746 -0.004144 0.027809 0.161850
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.1913198 0.0068269 -28.02 <2e-16 ***
mi 0.0030023 0.0002023 14.84 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.04377 on 774 degrees of freedom
Multiple R-squared: 0.2216, Adjusted R-squared: 0.2206
F-statistic: 220.3 on 1 and 774 DF, p-value: < 2.2e-16Visualization: Peak/valley wavelength vs melanin index
| Version | Author | Date |
|---|---|---|
| 40b4375 | tinalasisi | 2025-12-18 |
Log-transformed: Peak/valley wavelength vs melanin index
Log-transforming both axes tests whether peak and valley wavelength positions follow a power-law relationship with melanin content. Since wavelengths vary little, we expect minimal relationships.
Log-transformed: Peak/valley value vs melanin index
Log-log regression tests whether the amplitude of derivative peak and valley values follow a power-law relationship with melanin content. Note that valley values are negative, so we use absolute values for the log transformation.
Delta (peak - valley) vs melanin index
The delta represents the amplitude of the hemoglobin absorption feature in the derivative spectrum - the difference between the peak and valley values.
Delta (peak - valley) summary:Face: Min. 1st Qu. Median Mean 3rd Qu. Max.
0.04004 0.27772 0.37771 0.39182 0.49500 0.93954
Palm: Min. 1st Qu. Median Mean 3rd Qu. Max.
0.1015 0.4844 0.5746 0.5692 0.6605 0.9887 === FACE: Delta (peak - valley) vs Melanin Index ===
Call:
lm(formula = delta ~ mi, data = face_peak_valley)
Residuals:
Min 1Q Median 3Q Max
-0.27745 -0.07247 -0.01447 0.05338 0.47412
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.8172622 0.0081496 100.28 <2e-16 ***
mi -0.0113627 0.0002086 -54.48 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.1069 on 2099 degrees of freedom
Multiple R-squared: 0.5858, Adjusted R-squared: 0.5856
F-statistic: 2968 on 1 and 2099 DF, p-value: < 2.2e-16
=== PALM: Delta (peak - valley) vs Melanin Index ===
Call:
lm(formula = delta ~ mi, data = palm_peak_valley)
Residuals:
Min 1Q Median 3Q Max
-0.282128 -0.069668 -0.003611 0.075198 0.314928
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.0186942 0.0161829 62.95 <2e-16 ***
mi -0.0136839 0.0004794 -28.54 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.1038 on 774 degrees of freedom
Multiple R-squared: 0.5128, Adjusted R-squared: 0.5122
F-statistic: 814.6 on 1 and 774 DF, p-value: < 2.2e-16
Log-transformed: Delta vs melanin index
The delta (peak minus valley) represents the amplitude of the hemoglobin absorption feature in the first derivative. Log-log regression tests whether this amplitude follows a power-law relationship with melanin content.
=== Log-log regression: log(delta) ~ log(mi) ===FACE:
Call:
lm(formula = log(delta) ~ log(mi), data = delta_face)
Residuals:
Min 1Q Median 3Q Max
-0.89324 -0.15612 0.00565 0.15903 0.79202
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.20782 0.07044 73.93 <2e-16 ***
log(mi) -1.74330 0.01959 -89.00 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.2306 on 2099 degrees of freedom
Multiple R-squared: 0.7905, Adjusted R-squared: 0.7904
F-statistic: 7921 on 1 and 2099 DF, p-value: < 2.2e-16
PALM:
Call:
lm(formula = log(delta) ~ log(mi), data = delta_palm)
Residuals:
Min 1Q Median 3Q Max
-0.94014 -0.11438 0.02426 0.15211 0.53171
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.8407 0.1233 23.04 <2e-16 ***
log(mi) -0.9945 0.0355 -28.02 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.223 on 774 degrees of freedom
Multiple R-squared: 0.5035, Adjusted R-squared: 0.5029
F-statistic: 784.9 on 1 and 774 DF, p-value: < 2.2e-16
Correlation between absorbance derivative sd and melanin index
Log-transformed: Derivative SD vs melanin index (absorbance)
This log-log regression tests for a power-law relationship between absorbance derivative variability and melanin content.
=== Log-log regression: log(sd_abs) ~ log(mi) ===FACE:
Call:
lm(formula = log(sd_abs) ~ log(mi), data = sd_face)
Residuals:
Min 1Q Median 3Q Max
-0.85684 -0.18033 -0.01627 0.13516 1.14607
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -4.23656 0.08862 -47.81 <2e-16 ***
log(mi) -0.61138 0.02464 -24.81 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.2901 on 2099 degrees of freedom
Multiple R-squared: 0.2267, Adjusted R-squared: 0.2264
F-statistic: 615.5 on 1 and 2099 DF, p-value: < 2.2e-16
PALM:
Call:
lm(formula = log(sd_abs) ~ log(mi), data = sd_palm)
Residuals:
Min 1Q Median 3Q Max
-1.13969 -0.11919 0.00882 0.14246 0.72193
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -5.12360 0.11652 -43.974 <2e-16 ***
log(mi) -0.28220 0.03355 -8.412 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.2107 on 774 degrees of freedom
Multiple R-squared: 0.08377, Adjusted R-squared: 0.08259
F-statistic: 70.77 on 1 and 774 DF, p-value: < 2.2e-16
Reflectance delta (680 nm - 555 nm) vs melanin index
The erythema index is based on the ratio of reflectance at 680 nm to the average reflectance at 550-560 nm (approximating 555 nm). Here we examine the raw reflectance difference (delta) between these wavelengths as a function of melanin index.
=== Reflectance delta (R680 - R555_approx) summary ===# A tibble: 2 × 7
site mean_delta sd_delta min_delta max_delta mean_R680 mean_R555
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 Forehead/Cheek 21.9 4.72 4.42 37.2 43.4 21.5
2 Palm 21.1 4.04 8.42 33.9 47.6 26.6Visualization: Reflectance delta vs melanin index
Log-transformed: Reflectance delta vs melanin index
Log-log regression tests whether the reflectance difference between 680 nm and ~555 nm follows a power-law relationship with melanin content. Note: only positive delta values can be log-transformed.
Face: 2101 of 2101 have positive deltaPalm: 776 of 776 have positive delta
=== Log-log regression: log(ref_delta) ~ log(mi) ===FACE:
Call:
lm(formula = log(ref_delta) ~ log(mi), data = delta_face_pos)
Residuals:
Min 1Q Median 3Q Max
-0.72504 -0.07492 0.01592 0.09346 0.36331
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.97324 0.04102 145.62 <2e-16 ***
log(mi) -0.81198 0.01141 -71.18 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.1343 on 2099 degrees of freedom
Multiple R-squared: 0.7071, Adjusted R-squared: 0.7069
F-statistic: 5067 on 1 and 2099 DF, p-value: < 2.2e-16
PALM:
Call:
lm(formula = log(ref_delta) ~ log(mi), data = delta_palm_pos)
Residuals:
Min 1Q Median 3Q Max
-0.40429 -0.09321 0.00782 0.09911 0.40584
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.11102 0.07690 66.46 <2e-16 ***
log(mi) -0.60078 0.02214 -27.13 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.1391 on 774 degrees of freedom
Multiple R-squared: 0.4875, Adjusted R-squared: 0.4868
F-statistic: 736.2 on 1 and 774 DF, p-value: < 2.2e-16
Correlation between erythema index and melanin index by site
Face erythema index vs face melanin index
=== Linear regression: face_ei ~ face_mi ===
Call:
lm(formula = ei ~ mi, data = face_spectrum)
Residuals:
Min 1Q Median 3Q Max
-15.5732 -3.6643 -0.1162 3.5673 22.7126
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 25.08333 0.40679 61.66 <2e-16 ***
mi 0.16625 0.01041 15.97 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 5.337 on 2099 degrees of freedom
Multiple R-squared: 0.1083, Adjusted R-squared: 0.1079
F-statistic: 255 on 1 and 2099 DF, p-value: < 2.2e-16
Log-transformed: Face erythema index vs face melanin index
Log-log regression tests whether face erythema index follows a power-law relationship with face melanin content.
=== Log-log regression: log(face_ei) ~ log(face_mi) ===
Call:
lm(formula = log(ei) ~ log(mi), data = face_spectrum %>% filter(ei >
0, mi > 0))
Residuals:
Min 1Q Median 3Q Max
-0.68767 -0.10831 0.01047 0.12229 0.58094
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.54659 0.05325 47.82 <2e-16 ***
log(mi) 0.24548 0.01481 16.58 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.1743 on 2099 degrees of freedom
Multiple R-squared: 0.1158, Adjusted R-squared: 0.1153
F-statistic: 274.8 on 1 and 2099 DF, p-value: < 2.2e-16
Palm erythema index vs face melanin index
=== Linear regression: palm_ei ~ face_mi ===
Call:
lm(formula = ei ~ face_mi, data = palm_spectrum)
Residuals:
Min 1Q Median 3Q Max
-11.1036 -3.3381 -0.0785 2.9910 16.9668
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 18.59875 0.51007 36.46 <2e-16 ***
face_mi 0.19474 0.01283 15.18 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 4.689 on 774 degrees of freedom
Multiple R-squared: 0.2294, Adjusted R-squared: 0.2284
F-statistic: 230.5 on 1 and 774 DF, p-value: < 2.2e-16
Log-transformed: Palm erythema index vs face melanin index
Log-log regression tests whether palm erythema index follows a power-law relationship with face melanin content. This cross-site comparison may reveal systemic hemoglobin patterns independent of local melanin.
=== Log-log regression: log(palm_ei) ~ log(face_mi) ===
Call:
lm(formula = log(ei) ~ log(face_mi), data = palm_spectrum %>%
filter(ei > 0, face_mi > 0))
Residuals:
Min 1Q Median 3Q Max
-0.55226 -0.12605 0.01504 0.12895 0.50267
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.17983 0.08561 25.46 <2e-16 ***
log(face_mi) 0.29439 0.02384 12.35 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.1854 on 774 degrees of freedom
Multiple R-squared: 0.1646, Adjusted R-squared: 0.1635
F-statistic: 152.5 on 1 and 774 DF, p-value: < 2.2e-16
Correlation between erythema index variability and melanin index by site
- EI variability is measured by the standard deviation of EIs within a
sliding window of MI values. The window size is set to 20 MI units, and
the step size is 1 MI unit.
- For each center MI value in the sequence, all EI values corresponding to MI values within the window (center MI ± 10) are collected, and their standard deviation is computed.
- The center MI values range from the 1st to the 99th percentile of observed MI values.
R version 4.5.2 (2025-10-31)
Platform: aarch64-apple-darwin20
Running under: macOS Tahoe 26.1
Matrix products: default
BLAS: /System/Library/Frameworks/Accelerate.framework/Versions/A/Frameworks/vecLib.framework/Versions/A/libBLAS.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/lib/libRlapack.dylib; LAPACK version 3.12.1
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
time zone: America/Detroit
tzcode source: internal
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] ggpubr_0.6.0 here_1.0.1 KernSmooth_2.23-26 openxlsx_4.2.8.1
[5] scales_1.4.0 lubridate_1.9.4 forcats_1.0.0 stringr_1.5.1
[9] dplyr_1.1.4 purrr_1.0.4 readr_2.1.5 tidyr_1.3.1
[13] tibble_3.2.1 ggplot2_4.0.1 tidyverse_2.0.0 knitr_1.50
loaded via a namespace (and not attached):
[1] gtable_0.3.6 xfun_0.54 bslib_0.9.0 rstatix_0.7.2
[5] lattice_0.22-7 tzdb_0.5.0 vctrs_0.6.5 tools_4.5.2
[9] generics_0.1.4 pkgconfig_2.0.3 Matrix_1.7-4 RColorBrewer_1.1-3
[13] S7_0.2.0 lifecycle_1.0.4 compiler_4.5.2 farver_2.1.2
[17] git2r_0.36.2 textshaping_1.0.1 codetools_0.2-20 carData_3.0-5
[21] httpuv_1.6.16 htmltools_0.5.8.1 sass_0.4.10 yaml_2.3.10
[25] Formula_1.2-5 later_1.4.2 pillar_1.10.2 car_3.1-3
[29] jquerylib_0.1.4 whisker_0.4.1 cachem_1.1.0 abind_1.4-8
[33] nlme_3.1-168 tidyselect_1.2.1 zip_2.3.3 digest_0.6.37
[37] stringi_1.8.7 splines_4.5.2 labeling_0.4.3 cowplot_1.1.3
[41] rprojroot_2.0.4 fastmap_1.2.0 grid_4.5.2 cli_3.6.5
[45] magrittr_2.0.3 utf8_1.2.5 dichromat_2.0-0.1 broom_1.0.8
[49] withr_3.0.2 promises_1.3.3 backports_1.5.0 timechange_0.3.0
[53] rmarkdown_2.29 gridExtra_2.3 ggsignif_0.6.4 workflowr_1.7.1
[57] ragg_1.4.0 hms_1.1.3 evaluate_1.0.3 viridisLite_0.4.2
[61] mgcv_1.9-3 rlang_1.1.6 Rcpp_1.1.0 glue_1.8.0
[65] jsonlite_2.0.0 R6_2.6.1 systemfonts_1.3.1 fs_1.6.6