Analisis Data Kategorik - STK654 (Materi UAS)

Dr. Kusman Sadik, M.Si

Program Studi Magister Statistika Terapan

Departemen Statistika IPB, Semester Ganjil 2019/2020

IPB University─ Bogor Indonesia ─ Inspiring Innovation with Integrity

Model Regresi Logit Binomial(Bagian 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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X (Gender) : 0 = male, 1 = female

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X (SES) : high, moderate, low

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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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kategori referensi

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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") # Kategori Referensi #

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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color s width wt sa y

1 2 3 28.3 3.05 8 1

2 3 3 26.0 2.60 4 1

3 3 3 25.6 2.15 0 0

4 4 2 21.0 1.85 0 0

5 2 3 29.0 3.00 1 1

6 1 2 25.0 2.30 3 1

7 4 3 26.2 1.30 0 0

8 2 3 24.9 2.10 0 0

.

.

.

171 2 3 26.5 2.75 7 1

172 3 3 26.1 2.75 3 1

173 2 2 24.5 2.00 0 0

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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

.

.

.

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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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?

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Bagaimana cara menguji ada tidaknya interaksi antara

“Color” dan “Width”?

Apa hipotesis H0 dan H1-nya?

Bagaimana implementasinya dalam Program R?

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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. 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.

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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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