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Body Fat Estimation

amhoesk 2023-06-12

This project uses the NAHES dataset, comprising of approximately 4000 individuals’ body measurements (such as weight, height and waist circumference) as well as body composition (gathered through DEXA scans - the gold standard). We have developed step-wise, ridge, and LASSO regression models to estimate body fat and total mass at different body segments (e.g., trunk, legs), further simplifying these regression equations for ease of interpretation and application. These predictive tools can have applications in health and fitness, as well as biomechanical studies.

Data Exploration

As missing or invalid data have been multiply imputed, the DXX_D data release file contained 5 records for each survey participant. Only 1 record was recommended to be used in calculating sample sizes while all 5 records were recommended to be used in analyses in order to obtain more accurate variance estimates. The records for some survey participants, such as pregnant females, were blank as pregnant females were not eligible for the DXA scan. DXA scans were administered to eligible survey participants aged 8-69. Only individuals were all of their data were valid and none were imputed, were selected.

List of independent and dependent variables

Dependent variables only reported for the left side of body.

description
BMXWT Weight (kg)
BMXHT Standing Height (cm)
RIAGENDR Sex (0 male, 1 female)
RIDAGEEX Exam Age (year)
BMXWAIST Waist Circumference (cm)
BMXARMC Arm Circumference (cm)
BMXTHICR Thigh Circumference (cm)
BMXCALF Maximal Calf Circumference (cm)
BMXARML Upper Arm Length (cm)
BMXLEG Upper Leg Length (cm)
BMXTRI Triceps Skinfold (mm)
BMXSUB Subscapular Skinfold (mm)

List of independent variables

description
DXXHEFAT Head Fat (kg)
DXXLAFAT Left Arm Fat (kg)
DXXLLFAT Left Leg Fat (kg)
DXXTRFAT Trunk Fat (kg)
DXDTOFAT Total Fat (kg)
DXDHETOT Head Total (kg)
DXDLATOT Left Arm Total (kg)
DXDLLTOT Left Leg Total (kg)
DXDTRTOT Trunk Total (kg)
DXDTOBMC Total Bone Mineral Content (kg)
DXDTOBMD Total Bone Mineral Density (g/cm^2)

List of dependent variables

Exploring demographics

The number of females are a little bit higher than males. Age distribution does not match the age distribution of USA population. Therefore, estimations based on this sample may predict outcome variables for young people better than old ones.

vars n mean sd median trimmed mad min max range skew kurtosis se
RIAGENDR 1 20235 0.462 0.499 0 0.452 0.000 0 1 1 0.153 -1.977 0.004
RIDAGEEX 2 20235 27.294 17.246 19 25.115 11.614 8 70 62 0.899 -0.479 0.121

Summary of demographic variables

Exploring body measurements

Some of the variables show strong linear correlations.

vars n mean sd median trimmed mad min max range skew kurtosis se
BMXWT 1 20235 64.551 19.323 63.8 64.428 19.274 20.0 131.4 111.4 0.109 -0.275 0.136
BMXHT 2 20235 163.163 13.757 164.7 164.120 13.047 112.0 192.8 80.8 -0.611 0.158 0.097
BMXARMC 3 20235 28.801 5.112 29.0 28.812 5.337 15.5 45.7 30.2 0.002 -0.429 0.036
BMXARML 4 20235 35.666 3.663 36.0 35.872 3.410 22.1 46.3 24.2 -0.492 0.199 0.026
BMXCALF 5 20235 35.759 4.533 36.0 35.864 4.448 20.2 52.8 32.6 -0.166 0.075 0.032
BMXLEG 6 20235 38.908 4.259 39.2 39.016 4.151 24.2 52.0 27.8 -0.229 -0.054 0.030
BMXSUB 7 20235 16.239 8.050 14.8 15.559 8.599 3.6 40.4 36.8 0.638 -0.399 0.057
BMXTHICR 8 20235 49.145 6.892 49.3 49.179 6.672 28.3 74.3 46.0 0.008 -0.017 0.048
BMXTRI 9 20235 15.902 7.506 14.6 15.248 8.006 3.0 42.0 39.0 0.701 -0.167 0.053
BMXWAIST 10 20235 83.046 14.844 82.0 82.655 15.716 48.0 138.7 90.7 0.273 -0.390 0.104

Summary of body measurement variables

Exploring DXA - Body parts fat weight

Data was only ploted for the left arm and leg

vars n mean sd median trimmed mad min max range skew kurtosis se
DXXHEFAT 1 20235 1.087 0.154 1.074 1.081 0.162 0.676 1.659 0.983 0.360 -0.212 0.001
DXXLAFAT 2 20235 1.108 0.545 1.024 1.059 0.539 0.182 3.843 3.661 0.961 1.327 0.004
DXXLLFAT 3 20235 3.688 1.581 3.485 3.558 1.514 0.705 11.072 10.367 0.865 0.991 0.011
DXXTRFAT 4 20235 8.786 4.952 7.920 8.342 5.297 1.239 31.199 29.960 0.791 0.291 0.035
DXDTOFAT 5 20235 19.530 8.814 18.471 18.887 9.217 4.029 58.845 54.815 0.695 0.337 0.062

Summary of body parts fat weights

Exploring DXA - Body parts total weight

Data was only ploted for the left arm and leg

vars n mean sd median trimmed mad min max range skew kurtosis se
DXDHETOT 1 20235 4.575 0.631 4.534 4.557 0.664 2.849 6.767 3.918 0.275 -0.241 0.004
DXDLATOT 2 20235 3.689 1.289 3.583 3.645 1.350 0.968 8.288 7.320 0.328 -0.333 0.009
DXDLLTOT 3 20235 11.094 3.194 11.006 11.073 3.087 3.167 23.581 20.414 0.148 0.098 0.022
DXDTRTOT 4 20235 30.707 10.518 30.266 30.508 10.592 8.561 72.623 64.062 0.227 -0.268 0.074

Summary of body parts total weights

Building Regression Models

Using all independent variables

All independent variables were normalized (centered by subtracting the column means from their corresponding columns and divided by the centered columns by their standard deviations) except binary sex variable

Stepwise regression models

(Intercept) BMXWT BMXHT RIAGENDR RIDAGEEX BMXWAIST BMXARMC BMXTHICR BMXCALF BMXARML BMXLEG BMXTRI BMXSUB R2 RMSE
DXXHEFAT 1.121 0.114 0.007 -0.073 -0.019 -0.004 0.013 -0.006 NA -0.006 NA -0.018 0.019 0.739 0.079
DXXLAFAT 1.044 0.307 -0.128 0.139 NA 0.117 0.046 -0.065 0.008 0.025 -0.006 0.229 0.006 0.893 0.179
DXXLLFAT 3.414 0.769 -0.293 0.592 -0.028 0.173 -0.646 0.496 0.254 0.071 0.074 0.794 -0.127 0.850 0.612
DXXTRFAT 8.217 4.412 -1.157 1.234 0.202 2.283 -0.854 -0.653 -0.530 -0.158 -0.236 0.934 0.326 0.935 1.263
DXDTOFAT 18.311 6.647 -1.957 2.639 0.131 2.868 -2.025 0.229 NA NA -0.101 2.970 0.109 0.937 2.203
DXDHETOT 4.689 0.441 0.095 -0.247 -0.038 -0.107 0.078 0.017 NA -0.026 -0.014 -0.087 0.078 0.736 0.324
DXDLATOT 3.779 1.219 -0.139 -0.195 -0.026 -0.218 0.518 -0.216 -0.069 0.092 0.046 -0.102 0.026 0.970 0.225
DXDLLTOT 11.094 2.911 -0.038 NA -0.156 -0.628 -0.613 0.736 0.499 0.116 0.211 0.320 -0.102 0.966 0.586
DXDTRTOT 30.407 10.649 0.303 0.650 0.416 1.772 0.174 -1.085 -0.877 -0.458 -0.441 -0.379 0.123 0.987 1.217
DXDTOBMC 2.109 0.416 0.253 0.076 0.051 -0.263 0.122 0.076 -0.040 NA NA -0.129 0.021 0.856 0.235
DXDTOBMD 1.073 0.030 0.069 0.047 0.022 -0.066 0.055 0.046 -0.010 NA -0.002 -0.044 0.018 0.667 0.090

Step-wise regression model based on all independent variables

Ridge regression

(Intercept) BMXWT BMXHT RIAGENDR RIDAGEEX BMXWAIST BMXARMC BMXTHICR BMXCALF BMXARML BMXLEG BMXTRI BMXSUB R2 RMSE
DXXHEFAT 1.122 0.107 0.003 -0.076 -0.015 0.000 0.008 0.000 0.000 0.000 0.000 -0.015 0.015 0.738 0.079
DXXLAFAT 1.046 0.270 -0.104 0.134 0.002 0.131 0.045 -0.039 0.000 0.014 -0.010 0.227 0.008 0.892 0.179
DXXLLFAT 3.415 0.726 -0.270 0.590 -0.028 0.176 -0.621 0.499 0.255 0.062 0.070 0.790 -0.119 0.850 0.612
DXXTRFAT 8.217 4.371 -1.138 1.232 0.202 2.291 -0.837 -0.642 -0.528 -0.162 -0.242 0.932 0.325 0.935 1.263
DXDTOFAT 18.312 6.588 -1.979 2.637 0.126 2.875 -2.004 0.222 0.015 0.048 -0.100 2.967 0.116 0.938 2.203
DXDHETOT 4.689 0.423 0.085 -0.247 -0.037 -0.089 0.075 0.017 0.000 -0.016 -0.006 -0.085 0.072 0.736 0.324
DXDLATOT 3.782 1.144 -0.106 -0.201 -0.023 -0.184 0.514 -0.189 -0.061 0.085 0.038 -0.102 0.024 0.969 0.225
DXDLLTOT 11.093 2.839 -0.011 0.002 -0.159 -0.602 -0.587 0.742 0.503 0.107 0.210 0.313 -0.096 0.966 0.586
DXDTRTOT 30.412 10.658 0.305 0.641 0.420 1.769 0.161 -1.072 -0.880 -0.457 -0.447 -0.373 0.116 0.987 1.217
DXDTOBMC 2.113 0.386 0.257 0.067 0.049 -0.242 0.119 0.069 -0.022 0.001 0.000 -0.125 0.016 0.856 0.236
DXDTOBMD 1.077 0.004 0.072 0.039 0.020 -0.045 0.053 0.043 0.000 0.000 0.000 -0.040 0.013 0.665 0.090

Ridge regression model based on all independent variables

Lasso regression

(Intercept) BMXWT BMXHT RIAGENDR RIDAGEEX BMXWAIST BMXARMC BMXTHICR BMXCALF BMXARML BMXLEG BMXTRI BMXSUB R2 RMSE
DXXHEFAT 1.122 0.107 0.003 -0.076 -0.015 0.000 0.008 0.000 0.000 0.000 0.000 -0.015 0.015 0.738 0.079
DXXLAFAT 1.046 0.270 -0.104 0.134 0.002 0.131 0.045 -0.039 0.000 0.014 -0.010 0.227 0.008 0.892 0.179
DXXLLFAT 3.415 0.726 -0.270 0.590 -0.028 0.176 -0.621 0.499 0.255 0.062 0.070 0.790 -0.119 0.850 0.612
DXXTRFAT 8.217 4.371 -1.138 1.232 0.202 2.291 -0.837 -0.642 -0.528 -0.162 -0.242 0.932 0.325 0.935 1.263
DXDTOFAT 18.312 6.588 -1.979 2.637 0.126 2.875 -2.004 0.222 0.015 0.048 -0.100 2.967 0.116 0.938 2.203
DXDHETOT 4.689 0.423 0.085 -0.247 -0.037 -0.089 0.075 0.017 0.000 -0.016 -0.006 -0.085 0.072 0.736 0.324
DXDLATOT 3.782 1.144 -0.106 -0.201 -0.023 -0.184 0.514 -0.189 -0.061 0.085 0.038 -0.102 0.024 0.969 0.225
DXDLLTOT 11.093 2.839 -0.011 0.002 -0.159 -0.602 -0.587 0.742 0.503 0.107 0.210 0.313 -0.096 0.966 0.586
DXDTRTOT 30.412 10.658 0.305 0.641 0.420 1.769 0.161 -1.072 -0.880 -0.457 -0.447 -0.373 0.116 0.987 1.217
DXDTOBMC 2.113 0.386 0.257 0.067 0.049 -0.242 0.119 0.069 -0.022 0.001 0.000 -0.125 0.016 0.856 0.236
DXDTOBMD 1.077 0.004 0.072 0.039 0.020 -0.045 0.053 0.043 0.000 0.000 0.000 -0.040 0.013 0.665 0.090

Lasso regression model based on all independent variables

Using only five independent variables

Stepwise regression models

(Intercept) BMXWT BMXHT RIAGENDR RIDAGEEX BMXWAIST R2 RMSE
DXXHEFAT 1.126 0.118 0.002 -0.085 -0.014 NA 0.732 0.080
DXXLAFAT 0.948 0.406 -0.216 0.346 -0.013 0.227 0.823 0.230
DXXLLFAT 2.985 1.534 -0.505 1.523 -0.285 0.189 0.717 0.841
DXXTRFAT 7.855 2.366 -1.568 2.017 0.272 3.214 0.912 1.470
DXDTOFAT 16.895 6.400 -3.011 5.704 -0.342 4.047 0.892 2.893
DXDHETOT 4.712 0.544 0.049 -0.297 -0.022 -0.112 0.727 0.329
DXDLATOT 3.865 1.376 -0.057 -0.382 0.048 -0.179 0.951 0.284
DXDLLTOT 10.815 4.193 NA 0.604 -0.439 -0.951 0.942 0.769
DXDTRTOT 30.777 7.681 0.105 -0.151 0.820 2.354 0.981 1.467
DXDTOBMC 2.161 0.560 0.257 -0.037 0.061 -0.323 0.839 0.249
DXDTOBMD 1.086 0.137 0.054 0.019 0.023 -0.090 0.629 0.095

Step-wise regression model based on only five easily-measurable independent variables

Ridge regression

(Intercept) BMXWT BMXHT RIAGENDR RIDAGEEX BMXWAIST R2 RMSE
DXXHEFAT 1.126 0.117 0.002 -0.084 -0.012 0.000 0.732 0.080
DXXLAFAT 0.949 0.395 -0.211 0.344 -0.012 0.231 0.823 0.230
DXXLLFAT 2.986 1.520 -0.498 1.521 -0.284 0.196 0.717 0.841
DXXTRFAT 7.855 2.372 -1.568 2.016 0.272 3.207 0.912 1.470
DXDTOFAT 16.896 6.420 -3.017 5.703 -0.337 4.028 0.892 2.893
DXDHETOT 4.712 0.523 0.055 -0.297 -0.023 -0.096 0.727 0.329
DXDLATOT 3.864 1.339 -0.041 -0.380 0.043 -0.151 0.951 0.285
DXDLLTOT 10.817 4.168 0.005 0.599 -0.440 -0.931 0.942 0.769
DXDTRTOT 30.776 7.718 0.092 -0.148 0.823 2.325 0.981 1.467
DXDTOBMC 2.161 0.542 0.263 -0.036 0.058 -0.306 0.839 0.249
DXDTOBMD 1.088 0.117 0.060 0.015 0.019 -0.072 0.627 0.095

Ridge regression model based on only five easily-measurable independent variables

Lasso regression

(Intercept) BMXWT BMXHT RIAGENDR RIDAGEEX BMXWAIST R2 RMSE
DXXHEFAT 1.126 0.117 0.002 -0.084 -0.012 0.000 0.732 0.080
DXXLAFAT 0.949 0.395 -0.211 0.344 -0.012 0.231 0.823 0.230
DXXLLFAT 2.986 1.520 -0.498 1.521 -0.284 0.196 0.717 0.841
DXXTRFAT 7.855 2.372 -1.568 2.016 0.272 3.207 0.912 1.470
DXDTOFAT 16.896 6.420 -3.017 5.703 -0.337 4.028 0.892 2.893
DXDHETOT 4.712 0.523 0.055 -0.297 -0.023 -0.096 0.727 0.329
DXDLATOT 3.864 1.339 -0.041 -0.380 0.043 -0.151 0.951 0.285
DXDLLTOT 10.817 4.168 0.005 0.599 -0.440 -0.931 0.942 0.769
DXDTRTOT 30.776 7.718 0.092 -0.148 0.823 2.325 0.981 1.467
DXDTOBMC 2.161 0.542 0.263 -0.036 0.058 -0.306 0.839 0.249
DXDTOBMD 1.088 0.117 0.060 0.015 0.019 -0.072 0.627 0.095

Lasso regression model based on only five easily-measurable independent variables

Simple formulas

The following formulas were generated based on lasso regression analysis and can be used to provide rougher estimation of body parts fat and total mass. Independent variables should be used in original, non-normalized, form.

DXXHEFAT = (0.006) × BMXWT + (0.000) × BMXHT + (-0.084) × RIAGENDR + (-0.001) × RIDAGEEX + (0.732)

DXXLAFAT = (0.020) × BMXWT + (-0.015) × BMXHT + (0.344) × RIAGENDR + (-0.001) × RIDAGEEX + (0.016) × BMXWAIST + (0.852)

DXXLLFAT = (0.079) × BMXWT + (-0.036) × BMXHT + (1.521) × RIAGENDR + (-0.016) × RIDAGEEX + (0.013) × BMXWAIST + (3.164)

DXXTRFAT = (0.123) × BMXWT + (-0.114) × BMXHT + (2.016) × RIAGENDR + (0.016) × RIDAGEEX + (0.216) × BMXWAIST + (0.150)

DXDTOFAT = (0.332) × BMXWT + (-0.219) × BMXHT + (5.703) × RIAGENDR + (-0.020) × RIDAGEEX + (0.271) × BMXWAIST + (9.227)

DXDHETOT = (0.027) × BMXWT + (0.004) × BMXHT + (-0.297) × RIAGENDR + (-0.001) × RIDAGEEX + (-0.006) × BMXWAIST + (2.879)

DXDLATOT = (0.069) × BMXWT + (-0.003) × BMXHT + (-0.380) × RIAGENDR + (0.002) × RIDAGEEX + (-0.010) × BMXWAIST + (0.657)

DXDLLTOT = (0.216) × BMXWT + (0.000) × BMXHT + (0.599) × RIAGENDR + (-0.025) × RIDAGEEX + (-0.063) × BMXWAIST + (2.737)

DXDTRTOT = (0.399) × BMXWT + (0.007) × BMXHT + (-0.148) × RIAGENDR + (0.048) × RIDAGEEX + (0.157) × BMXWAIST + (-10.401)

DXDTOBMC = (0.028) × BMXWT + (0.019) × BMXHT + (-0.036) × RIAGENDR + (0.003) × RIDAGEEX + (-0.021) × BMXWAIST + (-1.147)

DXDTOBMD = (0.006) × BMXWT + (0.004) × BMXHT + (0.015) × RIAGENDR + (0.001) × RIDAGEEX + (-0.005) × BMXWAIST + (0.359)

References

https://www.datacamp.com/tutorial/tutorial-ridge-lasso-elastic-net

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Estimating body segments fat mass using anthropometric measurements

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