Kasus

Survey terhadap remaja usia 15-16 tahun apakah pernah melakukan kerja paruh waktu (part-time)??

Berikut Tabel datanya:Race

GenderPart Time Job

Yes NoWhite Male 43 134

Female 26 149Black Male 29 23

Female 22 36

Prediktor > 1

exp (β1 ) adalah penggandaan pengaruh pada odds dari penambahan X1 sebesar satu unit, pada saat x lainnya tetap

βi merupakan besarnya pengaruh Xi pada log odds ketika Y = 1 dan X lainnya tetap.

Memasukkan data di SASPeubah “white” (1 = white, 0 = black), Peubah “gender” (1 = male, 0 = female), andPeubah “part-time job” (1 = yes, 0 =no).

Ingin diketahui odds melakukan part-time job dengan ras dan gender sebagai prediktor.

(Enter the code on the next slide into SAS)

Syntax SASDATA job;INPUT white male job count;DATALINES;1 1 1 431 1 0 1341 0 1 261 0 0 1490 1 1 290 1 0 230 0 1 220 0 0 36;RUN;

PROC LOGISTIC DATA = job descending; weight count;MODEL job = white male/rsquare lackfit;

RUN;

“lackfit” requests the Hosmer and Lemeshow Goodness-of-Fit Test. This tells you if the model you have created is a good fit for the data.

“descending” models the probability that part-time job = 1 (yes) rather than = 0 (no).

“rsquare” requests the R2 value from SAS; it is interpreted the same way as the R2 from linear regression.

Output SAS: R2

Interpretasi nilai R2Nilai R2 sebesar 0.9907. Berarti 99.07% keragaman pada respon(part-time job) pada model dapat dijelaskan oleh gender dan race.

Perbandingan Model untuk Melihat Faktor yang BerpengaruhHipotesis 1H0: βW = βB = 0Hipotesis ini menyatakan bahwa, pada gender yang sama, peluang seorang remaja kerja paruh waktu bebas terhadap ras (warna kulit).Hipotesis 2H0: βM = βF = 0Hipotesis ini menyatakan bahwa, pada ras (warna kulit) yang sama, peluang seorang remaja kerja paruh waktu bebas terhadap gender .

Output Proc Logistic

Notice that the race and gender terms are both statistically significant (p < 0.0001 and p = 0.0040, respectively).The logistic regression model is:log(odds) = β0 + β1(white) + β2(male)log(odds) = -0.4555 – 1.3135(white) + 0.6478(male)The odds of having part-

blacks.

The odds of having part-time job is 73.1% (1-0.269) lower for whites than blacks. The odds of having part-

females.

The odds of having part-time job is 1.911 times greater for males versus females.

Misalkan kita ingin mengetahui odds dari melakukan part-time job untuk black males versus white females:Log(odds)black males = β0 + β1(0) + β2(1)Log(odds)white females = β0 + β1(1) + β2(0)Log(OR) = β0 + β2 – [β0 + β1] = β2 – β1Log(OR) = 0.6478 – (-1.3135) = 1.9613OR = exp(1.9613) = 7.11Black males have a 7.11 times greater odds of having part time job than white females.

Uji Kebaikan SuaiHosmer and Lemeshow (Goodness of Fit Test)

Interpreting the Hosmer-LemeshowGoodness Of Fit TestHipotesis:Ho: the model is a good fit, vsHa: the model is NOT a good fitWith this test, we want to FAIL to reject the null hypothesis, because that means our model is a good fit (this is different from most of the hypothesis testing you have seen).Look for a p_value > 0.10 in the H-L GOF test. This indicates the model is a good fit.In this case, the p_value = 0.2419, so we do NOT reject the null hypothesis, and we conclude the model is a good fit.

Ilustrasi : Data Crab• Respon Jumlah satelit• Prediktor lebar cangkang dan warna cangkang• Warna terdiri dari lima kategori:

light, medium light, medium, medium dark, dark. (semakin tua kepiting, semakin gelap warnanya)Note: data tidak ada kepiting dengan warna “light”

Model regresi

The crab color is dark (category 4) when c1 = c2 = c3 = 0.

Output SAS

• For each color, a 1 cm increase in width has a multiplicative effect of exp(0.468) = 1.60 on the odds that Y = 1.• a dark crab of average width (26.3 cm) has estimated probabilityexp[−12.715 + 0.468(26.3)]/{1 + exp[−12.715 + 0.468(26.3)]} = 0.399.• a medium-light crab of average width has estimated probabilityexp[−11.385 + 0.468(26.3)]/{1 + exp[−11.385 + 0.468(26.3)]} = 0.715.

• the difference in color parameter estimatesbetween medium-light crabs and dark crabs= 12.715-11.385=1.330.• at any given width, the estimated odds that a medium-light crab has a satellite are exp(1.330) = 3.8 times the estimated odds for a dark crab• Using the probabilities at width 26.3, the odds equal 0.399/0.601 = 0.66 for a dark crab and 0.715/0.285 = 2.51 for a medium-light crab, for which 2.51/0.66 = 3.8.

Paralel No interaction

Are certain terms needed in a model?• To test this, we can compare the maximizedlog-likelihood values for that model and the simpler model without those terms.

To test whether color contributes to model(4.11)• H0: β1 = β2 = β3 = 0 (controlling for width, the probability of a

satellite is independent of color)• Statistik Uji

−2(L0 − L1) = 7.0 ~ Chi-square(db=3)• P-value = 0.07• Warna berpengaruh terhadap peluang memiliki satelit

WARNA ORDINAL???