Regresi Logistik II

(Peubah Bebas : Kategorik)

Dr. Kusman Sadik, M.Si

Program Studi Pascasarjana

Departemen Statistika IPB, 2018/2019

2

In the case of logistic regression, the response variable

is a binary or dichotomous variable, which means it

can only take on one of two possible values.

Case: logistic regression models in which the

predictors are categorical or qualitative variables (such

as gender, location, and socioeconomic status).

All of the material on logistic regression modeling remains

the same, but the coding of the predictors (dummy

coding) and interpretation of the regression coefficients

changes due to the categorical nature of the predictors.

3

The interpretation of the model parameters

(intercept, slope) discussed for continuous predictor

variables does not change fundamentally for

categorical predictor variables.

The main difference between quantitative or

continuous predictors and qualitative or

categorical predictors is that the latter need to be

coded such that (C – 1) indicator variables are

required to represent a total of C categories.

4

When dummy coding is used, the last category of the

variable is used as a reference category.

Therefore, the parameter associated with the last

category is set to zero, and each of the remaining

parameters of the model is interpreted relative to the

last category.

5

6

7

8

9

10

11

12

13

Inferensia

14

Catatan : Uji G2 sama dengan Uji Deviance

15

16

Pengaruh Interaksi

17

18

Gender SES Interaksi

19

20

21

22

* Model Logistik untuk Data Horseshoe Crab (Agresti, 5.4.4) *

dataku <- read.csv(file="Data-Horseshoe.Crab-Agresti.csv")

c <- factor(dataku[,1])

s <- factor(dataku[,2])

w <- dataku[,3]

wt <- dataku[,4]

sa <- dataku[,5]

y <- c(1:173)

for (i in 1:length(sa)) {

if (sa[i] > 0) (y[i] = 1) else (y[i] = 0)

}

color <- relevel(c, ref="4")

width <- w

data.frame(color,s,width,wt,sa,y)

model <- glm(y ~ color+width, family=binomial("link"=logit))

summary(model)

dugaan <- round(fitted(model),2)

data.frame(color,width,y,dugaan)

23

Call:

glm(formula = y ~ color+width, family = binomial(link =

logit))

Coefficients:

Estimate Std. Error z value Pr(>|z|)

Intercept -12.7151 2.7617 -4.604 4.14e-06 ***

color1 1.3299 0.8525 1.560 0.1188

color2 1.4023 0.5484 2.557 0.0106 *

color3 1.1061 0.5921 1.868 0.0617 .

width 0.4680 0.1055 4.434 9.26e-06 ***

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’

Null deviance: 225.76 on 172 degrees of freedom

Residual deviance: 187.46 on 168 degrees of freedom

AIC: 197.46

24

color width y dugaan

1 2 28.3 1 0.87

2 3 26.0 1 0.64

3 3 25.6 0 0.59

4 4 21.0 0 0.05

5 2 29.0 1 0.91

6 1 25.0 1 0.58

7 4 26.2 0 0.39

8 2 24.9 0 0.58

.

.

.

171 2 26.5 1 0.75

172 3 26.1 1 0.65

173 2 24.5 0 0.54

25

26

27

H0 : β1 = β2 = β3 = 0

Call: H0glm(formula = y ~ width, family = binomial(link = logit))

Null deviance : 225.76 on 172 degrees of freedom

Residual deviance: 194.45 on 171 degrees of freedom

AIC: 198.45

Call: H1glm(formula = y ~ color + width, family = binomial(link =

logit))

Null deviance : 225.76 on 172 degrees of freedom

Residual deviance: 187.46 on 168 degrees of freedom

AIC: 197.46

Apa kesimpulan dari uji deviance tersebut?

28

29

1. Gunakan Program R untuk data Horseshoe Crabs Revisited

(Agresti, sub-bab 5.4.4 ) .

a. Lakukan pemodelan regresi logistik dengan peubah bebasnya

adalah Width (x) dan Color (c). Bandingkan hasil output R

dengan output SAS di dalam buku Agresti. Jelaskan

interpretasinya.

b. Lakukan pemodelan regresi logistik dengan peubah bebasnya

adalah Width (x), Color (c), dan Spine (s), tanpa interaksi.

Apakah Spine berpengaruh nyata? Gunakan uji Deviance

untuk = 0.05.

c. Pada model bagian (b) di atas, lalukan uji Deviance pada

= 0.05 untuk mengetahui apakah ada interaksi antara Color

dan Spine. Jelaskan interpretasinya.

30

2. Gunakan Program R untuk menyelesaikan Problems 9.5 (Azen,

hlm. 241 ) .

31

32

Pustaka

1. Azen, R. dan Walker, C.R. (2011). Categorical Data

Analysis for the Behavioral and Social Sciences.

Routledge, Taylor and Francis Group, New York.

2. Agresti, A. (2002). Categorical Data Analysis 2nd. New

York: Wiley.

3. Pustaka lain yang relevan.

33

Bisa di-download di

kusmansadik.wordpress.com

34

Terima Kasih