Menafsirkan kecocokan model

Generalized Linear Models di Python

Ita Cirovic Donev

Data Science Consultant

Estimasi parameter

Estimasi kemungkinan maksimum (MLE)
Iteratively reweighted least squares (IRLS)

Fungsi respons

Model regresi Poisson $$ log(\lambda)=\beta_0+\beta_1x_1 $$
Fungsi respons: $$ \lambda=exp(\beta_0 + \beta_1x_1) $$ atau $$ \lambda=exp(\beta_0) \times exp(\beta_1x_1) $$

Fungsi respons

Model regresi Poisson $$ log(\lambda)=\beta_0+\beta_1x_1 $$
Fungsi respons: $$ \lambda=exp(\beta_0 + \beta_1x_1) $$ atau $$ \lambda=exp(\beta_0) \color{red}{\times} exp(\beta_1x_1) $$

Interpretasi parameter

$exp(\beta_0)$
- Efek pada mean $\lambda$ saat $x=0$
$exp(\beta_1)$
- Efek multiplikatif pada mean $\lambda$ untuk kenaikan 1 unit pada $x$

Menafsirkan efek koefisien

Jika $\color{#FF550D}{\beta_1 > 0}$
- $exp(\beta_1)>1$
- $\lambda$ $\color{#FF550D}{exp(\beta_1)\text{ kali lebih besar}}$ dibanding saat $x=0$

Jika $\color{#D04A73}{\beta<0}$
- $exp(\beta_1)<1$
- $\lambda$ $\color{#D04A73}{exp(\beta_1) \text{ kali lebih kecil}}$ dibanding saat $x=0$

Jika $\color{#0099FF}{\beta_1 = 0}$
- $exp(\beta_1)=1$
- $\lambda=exp(\beta_0)$
- Faktor multiplikatif = 1
- $y$ dan $x$ $\text{\color{#0099FF}{tidak berhubungan}}$

Contoh

model = glm('sat ~ weight', data = crab, 
            family = sm.families.Poisson()).fit()

                 Generalized Linear Model Regression Results (print cut)                 
=============================================================================
                 coef    std err          z      P>|z|      [0.025     0.975]
-----------------------------------------------------------------------------
Intercept     -0.4284      0.179     -2.394      0.017      -0.779     -0.078
weight         0.5893      0.065      9.064      0.000       0.462      0.717
=============================================================================

Contoh - interpretasi beta

Ekstrak koefisien model
```
model.params
```

Intercept   -0.428405
weight       0.589304

Hitung efeknya
```
np.exp(0.589304)
```

1.803

Interval kepercayaan untuk ...

$\beta_1$

print(model.conf_int())

                  0         1
Intercept -0.779112 -0.077699
weight     0.461873  0.716735

Efek multiplikatif pada mean

print(np.exp(crab_fit.conf_int()))

                  0         1
Intercept  0.458813  0.925243
weight     1.587044  2.047737

Ayo berlatih!

Generalized Linear Models di Python