Dr. Kusman Sadik, M.Si

Program Studi Magister (S2)

Departemen Statistika IPB, 2017/2018

Regresi Logistik II

(Peubah Bebas : Kategorik)

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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.

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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.

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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.

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Inferensia

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Catatan : Uji G2 sama dengan Uji Deviance

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Pengaruh Interaksi

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Gender SES Interaksi

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* 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)

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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

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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

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171 2 26.5 1 0.75

172 3 26.1 1 0.65

173 2 24.5 0 0.54

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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.

b. Lakukan pemodelan regresi logistik dengan peubah bebasnya

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

berpengaruh nyata? Gunakan uji Deviance untuk = 0.05.

c. Bandingkan model bagian (a) dan (b) di atas melalui uji

Deviance pada = 0.05. Model mana yang lebih baik?

Jelaskan.

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

241 ) .

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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.

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kusmansadik.wordpress.com

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