Dr. Kusman Sadik, M.Si

Program Studi Magister (S2)

Departemen Statistika IPB, 2017/2018

Regresi Logistik Ordinal

(Peubah Respon Multikategori : Ordinal)

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The main feature of the ordinal logistic models is that

they predict the log odds, odds, or probability of a

response occurring at or below any given outcome

category.

For example, ordering the educational attainment

categories from lowest to highest (less than high

school, high school, junior college, bachelor’s degree,

graduate degree) we can use this model to predict the

probability of being (for example) at the bachelor’s

level or below from age at first marriage.

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.... (a)

a

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a

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The slopes are assumed to be the same for all logits

and, under this assumption, the model is known as the

proportional odds model.

The underlying assumption of equivalent slopes across

all logits can, and should, be tested to verify that this

model is appropriate.

If this assumption appears to be violated, then one

could fit the nominal, or more complicated alternative

models.

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We use data from the 2006 GSS to predict a

respondent’s educational attainment level (degree),

measured as either less than high school, high school,

junior college, bachelor’s degree, or graduate degree,

from the respondent’s age when first married

(agewed).

The outcome variable (educational attainment level) is

treated as ordinal, so the proportional odds model is

used.

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# Model Logistik Ordinal untuk Data GSS (Azen, sub-bab 10.5)

# Data Respon : Harus Data Terurut

dataku <- read.csv(file=“Data-GSS-2006.csv", header=TRUE)

degree <- factor(dataku$degree)

degree.order <- factor(dataku$degree.order)

agewed <- dataku$agewed

data.frame(degree,degree.order,agewed)

# Package yang diperlukan #

library("foreign")

library("MASS")

library("nnet")

table(degree,degree.order)

model <- polr(degree.order ~ agewed, method="logistic")

summary(model)

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degree degree.order agewed

1 HIGH SCHOOL 2 22

2 HIGH SCHOOL 2 23

3 HIGH SCHOOL 2 24

4 HIGH SCHOOL 2 22

5 LT HIGH SCHOOL 1 28

6 LT HIGH SCHOOL 1 21

7 HIGH SCHOOL 2 29

8 LT HIGH SCHOOL 1 19

9 LT HIGH SCHOOL 1 28

10 LT HIGH SCHOOL 1 29

.

.

.

1158 HIGH SCHOOL 2 21

1159 HIGH SCHOOL 2 22

1160 BACHELOR 4 28

Catatan : yang dipakai “degree.order” bukan

“degree”, karena “degree” belum terurut.

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degree.order

degree 1 2 3 4 5

LT HIGH SCHOOL 195 0 0 0 0

BACHELOR 0 0 0 185 0

GRADUATE 0 0 0 0 104

HIGH SCHOOL 0 590 0 0 0

JUNIOR COLLEGE 0 0 86 0 0

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Coefficients:

Value Std. Error t value

agewed 0.05059 0.01031 4.908

Intercepts:

Value Std. Error t value

1|2 -0.4549 0.2431 -1.8711

2|3 1.9226 0.2501 7.6886

3|4 2.2940 0.2530 9.0670

4|5 3.5242 0.2682 13.1389

Residual Deviance: 3096.156

AIC: 3106.156

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Output SAS : Bandingkan dengan Output R

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Output SAS : Bandingkan dengan Output R

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Perbedaan Model antara R, SPSS, dan SAS

R dan SPSS

SAS

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Perbedaan Model antara R, SPSS, dan SAS

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Interpretasi dan Pengujin Parameter

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Ilustrasi Interpretasi Parameter (Output R)

Coefficients:

Value Std. Error t value

agewed 0.05059 0.01031 4.908

Intercepts:

Value Std. Error t value

1|2 -0.4549 0.2431 -1.8711

2|3 1.9226 0.2501 7.6886

3|4 2.2940 0.2530 9.0670

4|5 3.5242 0.2682 13.1389

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Ilustrasi Interpretasi Parameter (Output R)

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Ilustrasi Interpretasi Parameter (Output R)

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1. Gunakan Program R untuk data Mental Impairment (Agresti, sub-

bab 7.2.4, hlm. 279 ) .

a. Bandingkan hasilnya dengan output SAS pada buku Agresti

tersebut serta berikan interpretasi pada tiap nilai dugaan

parameter model.

b. Berdasarkan hasil pada poin (a) di atas, tentukan nilai dugaan

P(Y = 1), P(Y = 3), dan P(Y > 2).

c. Tentukan model terbaik.

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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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Bisa di-download di

kusmansadik.wordpress.com

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