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 |
|---|---|---|---|---|
| Rmd | 777c6d5 | tinalasisi | 2025-12-18 | Fixed stats |
| html | 777c6d5 | tinalasisi | 2025-12-18 | Fixed stats |
| 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 (log-log)
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=== Log-log regression: log(sd_ref) ~ log(mi) - 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 Distribution and comparison of valley and peak characteristics: Face vs Palm
This analysis compares derivative valley and peak wavelengths and values between forehead/cheek and palm using t-tests to determine if differences are statistically significant.
The differences in peak and valley wavelengths and values between face
and palm sites are not statistically significant.
Peak/valley value vs melanin index (log-log)
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.
=== Log-log: log(peak_value) ~ log(mi) - FACE ===
Call:
lm(formula = log(peak_value) ~ log(mi), data = peak_face_pos)
Residuals:
Min 1Q Median 3Q Max
-0.56211 -0.10731 0.00531 0.10700 0.64675
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.16190 0.04877 85.33 <2e-16 ***
log(mi) -1.44831 0.01356 -106.78 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.1597 on 2099 degrees of freedom
Multiple R-squared: 0.8445, Adjusted R-squared: 0.8445
F-statistic: 1.14e+04 on 1 and 2099 DF, p-value: < 2.2e-16=== Log-log: log(peak_value) ~ log(mi) - PALM ===
Call:
lm(formula = log(peak_value) ~ log(mi), data = peak_palm_pos)
Residuals:
Min 1Q Median 3Q Max
-0.67116 -0.09900 0.00523 0.11279 0.45887
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.26390 0.09073 24.95 <2e-16 ***
log(mi) -0.87565 0.02612 -33.52 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.1641 on 774 degrees of freedom
Multiple R-squared: 0.5921, Adjusted R-squared: 0.5916
F-statistic: 1124 on 1 and 774 DF, p-value: < 2.2e-16=== Log-log: log(|valley_value|) ~ log(mi) - FACE ===
Call:
lm(formula = log(abs(valley_value)) ~ log(mi), data = valley_face_neg)
Residuals:
Min 1Q Median 3Q Max
-6.9436 -0.4587 0.2040 0.7062 2.0568
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 6.9428 0.6474 10.72 <2e-16 ***
log(mi) -3.0538 0.1871 -16.32 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.036 on 1072 degrees of freedom
Multiple R-squared: 0.199, Adjusted R-squared: 0.1982
F-statistic: 266.3 on 1 and 1072 DF, p-value: < 2.2e-16=== Log-log: log(|valley_value|) ~ log(mi) - PALM ===
Call:
lm(formula = log(abs(valley_value)) ~ log(mi), data = valley_palm_neg)
Residuals:
Min 1Q Median 3Q Max
-5.1830 -0.1340 0.1721 0.3944 0.9343
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.1397 0.4242 0.329 0.742
log(mi) -0.7549 0.1230 -6.139 1.36e-09 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.6842 on 730 degrees of freedom
Multiple R-squared: 0.04909, Adjusted R-squared: 0.04779
F-statistic: 37.69 on 1 and 730 DF, p-value: 1.362e-09
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-16Delta vs melanin index (log-log)
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=== Log-log regression: log(delta) ~ log(mi) - 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-16Absorbance derivative SD vs melanin index (log-log)
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=== Log-log regression: log(sd_abs) ~ log(mi) - 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
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.
=== 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 26.6
Log-transformed: Delta R680-R555 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=== Log-log regression: log(ref_delta) ~ log(mi) - 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
| Version | Author | Date |
|---|---|---|
| 777c6d5 | tinalasisi | 2025-12-18 |
Mixed-effects models: Testing body site differences
We use mixed-effects models to test whether the relationship between melanin index and delta values differs by body site, accounting for repeated measures within individuals.
We tested whether anatomical site (forehead/cheek vs palm) modifies the log–log relationship between melanin index (MI) and (i) peak–valley derivative delta and (ii) reflectance delta (R680–R555), using linear mixed-effects models with a random intercept for subject. For each outcome, we compared a main-effects model (log_delta ~ log_mi + bodysite) to an interaction model (log_delta ~ log_mi * bodysite). A significant likelihood ratio test (LRT) indicates site-specific scaling (different slopes).
=== Peak-Valley Delta: Testing body site effect ===Peak–valley derivative Δ: LRT comparing interaction vs main-effects model: χ²(1) = 285.11, p < 2.2e-16=== Reflectance Delta (R680-R555): Testing body site effect ===Reflectance Δ (R680–R555): LRT comparing interaction vs main-effects model: χ²(1) = 90.22, p < 2.2e-16Anatomical site significantly modified the MI–Δ relationship for both peak–valley derivative Δ and reflectance Δ (LRT comparing interaction vs main-effects models; see output above), indicating site-specific scaling rather than a simple constant offset.
Face erythema index vs face melanin index: Linear vs Log-log comparison
Comparing linear and log-log regressions to test which model better fits the relationship between face erythema index and face melanin content.
=== 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-log regression: log(face_ei) ~ log(face_mi) ===
Call:
lm(formula = log(ei) ~ log(mi), data = face_data_filtered)
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 vs Log-log comparison
Comparing linear and log-log regressions to test which model better fits the relationship between palm erythema index and face melanin content. This cross-site comparison may reveal systemic hemoglobin patterns.
=== 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-log regression: log(palm_ei) ~ log(face_mi) ===
Call:
lm(formula = log(ei) ~ log(face_mi), data = palm_data_filtered)
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] ggeffects_2.3.2 broom.mixed_0.2.9.6 lme4_1.1-37
[4] Matrix_1.7-4 ggstatsplot_0.13.3 ggpubr_0.6.0
[7] here_1.0.1 KernSmooth_2.23-26 openxlsx_4.2.8.1
[10] scales_1.4.0 lubridate_1.9.4 forcats_1.0.0
[13] stringr_1.5.1 dplyr_1.1.4 purrr_1.2.0
[16] readr_2.1.5 tidyr_1.3.1 tibble_3.2.1
[19] ggplot2_4.0.1 tidyverse_2.0.0 knitr_1.50
loaded via a namespace (and not attached):
[1] Rdpack_2.6.4 pbapply_1.7-4 gridExtra_2.3
[4] rematch2_2.1.2 rlang_1.1.6 magrittr_2.0.4
[7] git2r_0.36.2 furrr_0.3.1 compiler_4.5.2
[10] statsExpressions_1.7.1 mgcv_1.9-3 systemfonts_1.3.1
[13] vctrs_0.6.5 pkgconfig_2.0.3 fastmap_1.2.0
[16] backports_1.5.0 labeling_0.4.3 utf8_1.2.5
[19] effectsize_1.0.1 promises_1.3.3 rmarkdown_2.29
[22] tzdb_0.5.0 haven_2.5.5 nloptr_2.2.1
[25] ragg_1.4.0 MatrixModels_0.5-4 xfun_0.54
[28] cachem_1.1.0 jsonlite_2.0.0 later_1.4.2
[31] broom_1.0.8 parallel_4.5.2 R6_2.6.1
[34] bslib_0.9.0 stringi_1.8.7 RColorBrewer_1.1-3
[37] parallelly_1.45.0 car_3.1-3 boot_1.3-32
[40] jquerylib_0.1.4 Rcpp_1.1.0 parameters_0.28.3
[43] correlation_0.8.8 httpuv_1.6.16 splines_4.5.2
[46] timechange_0.3.0 tidyselect_1.2.1 dichromat_2.0-0.1
[49] abind_1.4-8 yaml_2.3.10 codetools_0.2-20
[52] listenv_0.9.1 lattice_0.22-7 withr_3.0.2
[55] bayestestR_0.17.0 S7_0.2.0 coda_0.19-4.1
[58] evaluate_1.0.3 future_1.58.0 RcppParallel_5.1.11-1
[61] zip_2.3.3 pillar_1.10.2 carData_3.0-5
[64] whisker_0.4.1 reformulas_0.4.1 insight_1.4.4
[67] generics_0.1.4 rprojroot_2.0.4 paletteer_1.6.0
[70] hms_1.1.3 rstantools_2.5.0 minqa_1.2.8
[73] globals_0.18.0 glue_1.8.0 tools_4.5.2
[76] ggsignif_0.6.4 mvtnorm_1.3-3 fs_1.6.6
[79] cowplot_1.1.3 grid_4.5.2 rbibutils_2.3
[82] datawizard_1.3.0 nlme_3.1-168 patchwork_1.3.2
[85] Formula_1.2-5 cli_3.6.5 textshaping_1.0.1
[88] workflowr_1.7.1 viridisLite_0.4.2 gtable_0.3.6
[91] rstatix_0.7.2 zeallot_0.2.0 sass_0.4.10
[94] digest_0.6.37 prismatic_1.1.2 ggrepel_0.9.6
[97] farver_2.1.2 htmltools_0.5.8.1 lifecycle_1.0.4
[100] BayesFactor_0.9.12-4.7 MASS_7.3-65