Regresi Logistik Multinomial

(Peubah Respon Multikategori : Nominal)

Dr. Kusman Sadik, M.Si

Program Studi Pascasarjana

Departemen Statistika IPB, 2018/2019

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We discussed logistic regression models for a binary

outcome; that is, an outcome variable that consists of

two categories.

We extend our discussion of logistic regression to

multicategory outcomes, or outcome variables with

several categories.

The multicategory logistic model can still accommodate

several predictor (or explanatory) variables, and these

can be either continuous, categorical, or both.

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Peubah Respon Y(Multikategori)

Skala Nominal(Regresi Logistik Multinomial)

Skala Ordinal(Regresi Logistik Ordinal, Regresi

Logistik Kumulatif)

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Misalkan kategori Y ada sebanyak J, yaitu j = 1,2, ..., J.

P(Y = j) = πj

π1 + π2 + ... + πJ = 1

Kategori terakhir (J ) sebagai referensi : 𝑙𝑛𝜋𝑗

𝜋𝐽

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# Model Logistik Multinomial Data GSS (Azen, sub-bab 10.1)

dataku <- read.csv(file="D:/GSS-2006-DEGREE-AGEWED.csv",

header=TRUE)

degree <- dataku$degree

agewed <- dataku$agewed

degree <- relevel(degree, ref="LT HIGH SCHOOL")

data.frame(degree,agewed)

# Perlu package : "foreign" dan "nnet"

library("foreign")

library("nnet")

table(degree)

model <- multinom(degree ~ agewed)

summary(model)

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Degree

LT HIGH SCHOOL BACHELOR GRADUATE HIGH SCHOOL

195 185 104 590

JUNIOR COLLEGE

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Call: multinom(formula = degree ~ agewed)

Coefficients:

(Intercept) agewed

BACHELOR -1.4390298 0.05931128

GRADUATE -2.2159390 0.06740282

HIGH SCHOOL 0.7576068 0.01542479

JUNIOR COLLEGE -1.7591391 0.04082775

Std. Errors:

(Intercept) agewed

BACHELOR 0.4335079 0.01817825

GRADUATE 0.4778828 0.01961857

HIGH SCHOOL 0.3821854 0.01654322

JUNIOR COLLEGE 0.5416678 0.02267685

Residual Deviance: 3098.768

AIC: 3114.768

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Output SAS : Bandingkan dengan Output R

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Output SAS : Bandingkan dengan Output R

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Interpretasi dan Pengujian Parameter

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YX

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# Model Logistik Multinomial Agresti 7.1.2

dataku <- read.csv(file="Data-Agresti-7.1.2.csv")

lake <- factor(dataku[,1])

gend <- factor(dataku[,2])

size <- factor(dataku[,3])

food <- factor(dataku[,4])

lake <- relevel(lake, ref="4Geo")

size <- relevel(size, ref="2")

food <- relevel(food, ref="1Fish")

data.frame(lake,gend,size,food)

# Perlu package : "foreign" dan "nnet"

library("foreign")

library("nnet")

model <- multinom(food ~ lake + size)

summary(model)

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lake gend size food

1 1Han M 1 1Fish

2 1Han M 1 1Fish

3 1Han M 1 1Fish

4 1Han M 1 1Fish

5 1Han M 1 1Fish

6 1Han M 1 1Fish

7 1Han M 1 1Fish

8 1Han M 2 1Fish

9 1Han M 2 1Fish

10 1Han M 2 1Fish

11 1Han M 2 1Fish

.

.

.

218 4Geo F 1 5Othe

219 4Geo F 2 5Othe

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Call:

multinom(formula = food ~ lake + size)

Coefficients:

(Intercept) lake1Han lake2Okl lake3Tra size1

2Inve -1.549021 -1.6581178 0.937237973 1.122002 1.4581457

3Rept -3.314512 1.2428408 2.458913302 2.935262 -0.3512702

4Bird -2.093358 0.6954256 -0.652622721 1.088098 -0.6306329

5Othe -1.904343 0.8263115 0.005792737 1.516461 0.3315514

Std. Errors:

(Intercept) lake1Han lake2Okl lake3Tra size1

2Inve 0.4249185 0.6128466 0.4719035 0.4905122 0.3959418

3Rept 1.0530577 1.1854031 1.1181000 1.1163844 0.5800207

4Bird 0.6622972 0.7813123 1.2020025 0.8417085 0.6424863

5Othe 0.5258313 0.5575446 0.7765655 0.6214371 0.4482504

Residual Deviance: 540.0803

AIC: 580.0803

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1. Gunakan Program R untuk data Alligator Food Choice (Agresti,

sub-bab 7.1.2 ) .

a. Lakukan pemodelan regresi logistik multinomial pada data

tersebut dengan peubah responnya adalah tipe makanan

utama alligator dan peubah bebasnya adalah Lake (L) dan

Size (S). Bandingkan hasilnya dengan buku Agresti serta

berikan interpretasi pada tiap nilai dugaan parameter model.

b. Lakukan pemodelan seperti pada poin (a) di atas, tetapi

peubah bebasnya adalah Lake (L), Size (S) dan Gender (G).

Peubah mana saja (L, S, G) yang berpengaruh nyata?

Gunakan uji Deviance untuk = 0.05.

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c. Tentukan model terbaik dengan peubah bebasnya adalah

Lake (L), Size (S) dan Gender (G) serta semua interaksinya

(L*S, L*G, S*G, dan L*S*G). Gunakan uji Deviance untuk =

0.05.

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2. Agresti (Problems 7.1, hlm. 302) .

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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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