Exercises (regularization)

Data for exercises are on Canvas under Files -> data_exercises –> linear-models

Exercise 1 Follow and try to run the code below for fitting Lasso model to predict BMI given all the numerical variables in the diabetes data set.

Load data & reformat data

Rows: 403
Columns: 19
$ id       <dbl> 1000, 1001, 1002, 1003, 1005, 1008, 1011, 1015, 1016, 1022, 1…
$ chol     <dbl> 203, 165, 228, 78, 249, 248, 195, 227, 177, 263, 242, 215, 23…
$ stab.glu <dbl> 82, 97, 92, 93, 90, 94, 92, 75, 87, 89, 82, 128, 75, 79, 76, …
$ hdl      <dbl> 56, 24, 37, 12, 28, 69, 41, 44, 49, 40, 54, 34, 36, 46, 30, 4…
$ ratio    <dbl> 3.6, 6.9, 6.2, 6.5, 8.9, 3.6, 4.8, 5.2, 3.6, 6.6, 4.5, 6.3, 6…
$ glyhb    <dbl> 4.31, 4.44, 4.64, 4.63, 7.72, 4.81, 4.84, 3.94, 4.84, 5.78, 4…
$ location <chr> "Buckingham", "Buckingham", "Buckingham", "Buckingham", "Buck…
$ age      <dbl> 46, 29, 58, 67, 64, 34, 30, 37, 45, 55, 60, 38, 27, 40, 36, 3…
$ gender   <chr> "female", "female", "female", "male", "male", "male", "male",…
$ height   <dbl> 62, 64, 61, 67, 68, 71, 69, 59, 69, 63, 65, 58, 60, 59, 69, 6…
$ weight   <dbl> 121, 218, 256, 119, 183, 190, 191, 170, 166, 202, 156, 195, 1…
$ frame    <chr> "medium", "large", "large", "large", "medium", "large", "medi…
$ bp.1s    <dbl> 118, 112, 190, 110, 138, 132, 161, NA, 160, 108, 130, 102, 13…
$ bp.1d    <dbl> 59, 68, 92, 50, 80, 86, 112, NA, 80, 72, 90, 68, 80, NA, 66, …
$ bp.2s    <dbl> NA, NA, 185, NA, NA, NA, 161, NA, 128, NA, 130, NA, NA, NA, N…
$ bp.2d    <dbl> NA, NA, 92, NA, NA, NA, 112, NA, 86, NA, 90, NA, NA, NA, NA, …
$ waist    <dbl> 29, 46, 49, 33, 44, 36, 46, 34, 34, 45, 39, 42, 35, 37, 36, 3…
$ hip      <dbl> 38, 48, 57, 38, 41, 42, 49, 39, 40, 50, 45, 50, 41, 43, 40, 4…
$ time.ppn <dbl> 720, 360, 180, 480, 300, 195, 720, 1020, 300, 240, 300, 90, 7…

Rows: 375
Columns: 14
$ BMI      <dbl> 22.13, 37.42, 48.37, 18.64, 27.82, 26.50, 28.20, 24.51, 35.78…
$ chol     <dbl> 203, 165, 228, 78, 249, 248, 195, 177, 263, 242, 215, 238, 19…
$ stab.glu <dbl> 82, 97, 92, 93, 90, 94, 92, 87, 89, 82, 128, 75, 76, 83, 78, …
$ hdl      <dbl> 56, 24, 37, 12, 28, 69, 41, 49, 40, 54, 34, 36, 30, 47, 38, 6…
$ ratio    <dbl> 3.6, 6.9, 6.2, 6.5, 8.9, 3.6, 4.8, 3.6, 6.6, 4.5, 6.3, 6.6, 6…
$ glyhb    <dbl> 4.31, 4.44, 4.64, 4.63, 7.72, 4.81, 4.84, 4.84, 5.78, 4.77, 4…
$ age      <dbl> 46, 29, 58, 67, 64, 34, 30, 45, 55, 60, 38, 27, 36, 33, 50, 2…
$ height   <dbl> 62, 64, 61, 67, 68, 71, 69, 69, 63, 65, 58, 60, 69, 65, 65, 6…
$ weight   <dbl> 121, 218, 256, 119, 183, 190, 191, 166, 202, 156, 195, 170, 1…
$ bp.1s    <dbl> 118, 112, 190, 110, 138, 132, 161, 160, 108, 130, 102, 130, 1…
$ bp.1d    <dbl> 59, 68, 92, 50, 80, 86, 112, 80, 72, 90, 68, 80, 66, 90, 100,…
$ waist    <dbl> 29, 46, 49, 33, 44, 36, 46, 34, 45, 39, 42, 35, 36, 37, 37, 3…
$ hip      <dbl> 38, 48, 57, 38, 41, 42, 49, 40, 50, 45, 50, 41, 40, 41, 43, 3…
$ time.ppn <dbl> 720, 360, 180, 480, 300, 195, 720, 300, 240, 300, 90, 720, 22…

split data and scale

Rows: 258
Columns: 14
$ BMI      <dbl> 48.37, 27.82, 26.50, 28.20, 40.75, 33.20, 27.02, 26.12, 24.90…
$ chol     <dbl> 0.4524462, 0.9164540, 0.8943584, -0.2767090, 0.1652032, 0.673…
$ stab.glu <dbl> -0.28652567, -0.32418417, -0.24886718, -0.28652567, 0.3913272…
$ hdl      <dbl> -0.749786859, -1.261997828, 1.071407700, -0.522137539, -0.920…
$ ratio    <dbl> 0.89155394, 2.35907876, -0.52161816, 0.13061530, 0.94590692, …
$ glyhb    <dbl> -0.42464460, 0.91116765, -0.35091467, -0.33790342, -0.2815218…
$ age      <dbl> 0.70202683, 1.05915385, -0.72648126, -0.96456594, -0.48839658…
$ height   <dbl> -1.2668725014, 0.5081249676, 1.2688381686, 0.7616960346, -2.0…
$ weight   <dbl> 1.8615300087, 0.1191556829, 0.2862326730, 0.3101008145, 0.405…
$ bp.1s    <dbl> 2.23602108, 0.03429933, -0.21974548, 1.00813780, -1.48996957,…
$ bp.1d    <dbl> 0.62214432, -0.24471383, 0.18871524, 2.06690792, -1.11157199,…
$ waist    <dbl> 1.8500049, 1.0090936, -0.3363645, 1.3454581, 0.6727291, -0.50…
$ hip      <dbl> 2.42867737, -0.36396335, -0.18942330, 1.03235701, 1.20689706,…
$ time.ppn <dbl> -0.5033145, -0.1207312, -0.4554916, 1.2183102, -0.7902519, 1.…

Rows: 117
Columns: 14
$ BMI      <dbl> 22.13, 37.42, 18.64, 24.51, 35.78, 25.96, 30.45, 21.63, 32.61…
$ chol     <dbl> -0.09994410, -0.93957728, -2.86189536, -0.67442996, 1.2257925…
$ stab.glu <dbl> -0.47481814, -0.19237944, -0.26769642, -0.38067191, -0.343013…
$ hdl      <dbl> 0.331547411, -1.489647148, -2.172595108, -0.066838899, -0.579…
$ ratio    <dbl> -0.52161816, 1.27202352, 1.05461237, -0.52161816, 1.10896509,…
$ glyhb    <dbl> -0.56776732, -0.51138558, -0.42898155, -0.33790342, 0.0697795…
$ age      <dbl> -0.01222722, -1.02408711, 1.23771736, -0.07174839, 0.52346332…
$ height   <dbl> -1.0133014344, -0.5061593004, 0.2545539006, 0.7616960346, -0.…
$ weight   <dbl> -1.3606691, 0.9545406, -1.4084054, -0.2866027, 0.5726504, -0.…
$ bp.1s    <dbl> -0.81251672, -1.06656154, -1.15124315, 0.96579699, -1.2359247…
$ bp.1d    <dbl> -1.7617156, -1.1115720, -2.4118592, -0.2447138, -0.8226193, 0…
$ waist    <dbl> -1.5136404, 1.3454581, -0.8409113, -0.6727291, 1.1772759, 0.1…
$ hip      <dbl> -0.88758348, 0.85781697, -0.88758348, -0.53850339, 1.20689706…
$ time.ppn <dbl> 1.21831021, 0.07056041, 0.45314368, -0.12073122, -0.31202285,…

fit Lasso

train Lasso model

create final model

[1] 0.03005165

14 x 1 sparse Matrix of class "dgCMatrix"
                     s0
(Intercept) 28.82120155
chol        -0.01914479
stab.glu    -0.03099725
hdl          .         
ratio        .         
glyhb        .         
age          .         
height      -3.18952689
weight       6.27956187
bp.1s        0.02225091
bp.1d        .         
waist        .         
hip          0.47057628
time.ppn    -0.00453767

We can see that the largest coefficients (in terms of absolute values) are for weight and height, which of course it makes sense as we are predicting BMI that was defined based on weight and height in the first place. This is naturally for demonstration purposes only.

predict BMI

[1] 0.9945698