Rumus model

Generalized Linear Models di Python

Ita Cirovic Donev

Data Science Consultant

Rumus dan matriks model

Awal diagram dengan sumber data X dan Y.

Rumus dan matriks model

Diagram rumus

Rumus dan matriks model

Diagram matriks model

Rumus dan matriks model

Diagram input ke kelas glm.

Matriks model

Matriks model: y ∼ X
Rumus model
```
'y ~ x1 + x2'
```

Periksa struktur matriks model

from patsy import dmatrix
dmatrix('x1 + x2')

  Intercept  x1  x2
          1   1   4
          1   2   5
          1   3   6

Transformasi variabel

import numpy as np

'y ~ x1 + np.log(x2)'

dmatrix('x1 + np.log(x2)')

DesignMatrix dengan shape (3, 3)
  Intercept  x1  np.log(x2)
          1   1     1.38629
          1   2     1.60944
          1   3     1.79176

Pemusatan dan standardisasi

Transformasi stateful

'y ~ center(x1) + standardize(x2)'

dmatrix('center(x1) + standardize(x2)')

DesignMatrix dengan shape (3, 3)
  Intercept  center(x1)  standardize(x2)
          1          -1         -1.22474
          1           0          0.00000
          1           1          1.22474

Buat transformasi sendiri

def my_transformation(x):
  return 4 * x

dmatrix('x1 + x2 + my_transformation(x2)')

DesignMatrix dengan shape (3, 4)
  Intercept  x1  x2  my_transformation(x2)
          1   1   4                     16
          1   2   5                     20
          1   3   6                     24

Operasi aritmetika

x1 = np.array([1, 2, 3])
x2 = np.array([4,5,6])

dmatrix('I(x1 + x2'))

DesignMatrix dengan shape (3, 2)
  Intercept  I(x1 + x2)
          1           5
          1           7
          1           9

x1 = [1, 2, 3]
x2 = [4,5,6]

dmatrix('I(x1 + x2)')

DesignMatrix dengan shape (6, 2)
  Intercept  I(x1 + x2)
          1           1
          1           2
          1           3
          1           4
          1           5
          1           6

Pengodean data kategorikal

Tipe warna: merah, hijau, biru

Pengodean data kategorikal

Diagram tipe warna: merah, hijau, biru dan observasi warna dalam data

Pengodean data kategorikal

Diagram one-hot encoding menggunakan warna merah, hijau, dan biru.

Pengodean Patsy

String dan boolean otomatis dikodekan
Numerik → kategorikal
- fungsi C()
Kelompok referensi
- Bawaan: kelompok pertama
- Treatment
- levels

Fungsi C()

Variabel numerik
```
dmatrix('color', data = crab)
```

DesignMatrix dengan shape (173, 2)
  Intercept  color
          1      2
          1      3
          1      1
  [... baris dihilangkan]

Ada berapa level?
```
crab['color'].value_counts()
```

Fungsi C()

Variabel kategorikal
```
dmatrix('C(color)', data = crab)
```

DesignMatrix dengan shape (173, 4)
  Intercept  C(color)[T.2]  C(color)[T.3]  C(color)[T.4]
          1              1              0              0
          1              0              1              0
          1              0              0              0
  [... baris dihilangkan]

Mengubah kelompok referensi

dmatrix('C(color, Treatment(4))', data = crab)

DesignMatrix dengan shape (173, 4)
  Intercept  C(color)[T.1]  C(color)[T.2]  C(color)[T.3]  
          1              0              1              0 
          1              0              0              1 
          1              1              0              0 
  [... baris dihilangkan]

Mengubah kelompok referensi

l = [1, 2, 3,4]
dmatrix('C(color, levels = l)', data = crab)

DesignMatrix dengan shape (173, 4)
  Intercept  C(color)[T.2]  C(color)[T.3]   C(color)[T.4] 
          1               1            0               0     
          1               0            1               0
          1               0            0               0 
  [... baris dihilangkan]

Intercept berganda

'y ~ C(color)-1'
dmatrix('C(color)-1', data = crab)

DesignMatrix dengan shape (173, 4)
  C(color)[1]  C(color)[2]  C(color)[3]  C(color)[4]
            0            1            0            0
            0            0            1            0
            1            0            0            0
  [... baris dihilangkan]

Ayo berlatih!

Generalized Linear Models di Python