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Generalized Linear Models di Python

Ita Cirovic Donev

Data Science Consultant

Estimasi koefisien beta

Fungsi likelihood

Ringkasan keluaran model terpasang

Ringkasan keluaran model terpasang dengan statistik estimasi koefisien yang disorot.

Puncak lebih landai
$\rightarrow$ Lokasi maksimum lebih sulit ditentukan
$\rightarrow$ SE lebih besar

Visualisasi likelihood saat standard error lebih besar.

Puncak lebih tajam
$\rightarrow$ Lokasi maksimum lebih jelas
$\rightarrow$ SE lebih kecil

Visualisasi likelihood saat standard error lebih kecil.

# Extract variance-covariance matrix
print(model_GLM.cov_params())

           Intercept    weight
Intercept   0.774762 -0.325087
weight     -0.325087  0.141903

# Compute standard error for weight
std_error = np.sqrt(0.141903)

0.3767

Matriks varians-kovarians

Ilustrasi matriks varians-kovarians

Statistik z $$ \color{#2485F2}{z=\hat\beta/SE} $$
$\color{#2485F2}{z}$ besar $\Rightarrow$ koefisien $\ne0$ $\Rightarrow$ variabel signifikan
Aturan praktis: ambang 2

Contoh: model horseshoe crab
y ~ weight

$z = 1.8151/0.377 = 4.819$

$$ [\color{#5A5AF3}{bawah},\color{#D8498E}{atas}] $$

$$ [\color{#5A5AF3}{\hat\beta - 1.96 \times SE},\color{#D8498E}{\hat\beta+1.96 \times SE}] $$

Contoh: model horseshoe crab

                 coef    std err   
<hr />-------------------------------
Intercept     -3.6947      0.880  
weight         1.8151      0.377

print(model_GLM.conf_int())

                  0         1
Intercept -5.419897 -1.969555
weight     1.076826  2.553463

print(model_GLM.conf_int())

              lower         1
Intercept -5.419897 -1.969555
weight     1.076826  2.553463

print(model_GLM.conf_int())

                  0     upper
Intercept -5.419897 -1.969555
weight     1.076826  2.553463

print(np.exp(model_GLM.conf_int()))

                  0          1
Intercept  0.004428   0.139519
weight     2.935348  12.851533

Generalized Linear Models di Python