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

Transkripsi

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

2 Berikut Tabel datanya: Race Gender Yes Part Time Job No White Male Female Black Male Female 22 36

3 Prediktor > 1

4 βi merupakan besarnya pengaruh Xi pada log odds ketika Y = 1 dan X lainnya tetap. exp (β1 ) adalah penggandaan pengaruh pada odds dari penambahan X1 sebesar satu unit, pada saat x lainnya tetap

5 Memasukkan data di SAS Peubah white (1 = white, 0 = black), Peubah gender (1 = male, 0 = female), and Peubah 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)

6 DATA job; INPUT white male job count; DATALINES; ; RUN; Syntax SAS

7 PROC LOGISTIC DATA = job descending; weight count; RUN; MODEL job = white male/rsquare lackfit; descending models the probability that parttime job = 1 (yes) rather than = 0 (no). rsquare requests the R 2 value from SAS; it is interpreted the same way as the R 2 from linear regression. 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.

8 Output SAS: R2

9 Interpretasi nilai R 2 Nilai R 2 sebesar Berarti 99.07% keragaman pada respon(part-time job) pada model dapat dijelaskan oleh gender dan race.

10 Perbandingan Model untuk Melihat Faktor yang Berpengaruh Hipotesis 1 H 0 : β W = β B = 0 Hipotesis ini menyatakan bahwa, pada gender yang sama, peluang seorang remaja kerja paruh waktu bebas terhadap ras (warna kulit). Hipotesis 2 H 0 : β M = β F = 0 Hipotesis ini menyatakan bahwa, pada ras (warna kulit) yang sama, peluang seorang remaja kerja paruh waktu bebas terhadap gender.

11 Output Proc Logistic Notice that the race and gender terms are both statistically significant (p < and p = , respectively). The odds of having parttime job is 73.1% ( ) lower for whites than blacks. The logistic regression model is: log(odds) = β 0 + β 1 (white) + β 2 (male) log(odds) = (white) (male) The odds of having parttime job is times greater for males versus females.

12 Misalkan kita ingin mengetahui odds dari melakukan part-time job untuk black males versus white females: Log(odds)black males = β 0 + β 1 (0) + β 2 (1) Log(odds)white females = β 0 + β 1 (1) + β 2 (0) Log(OR) = β 0 + β 2 [β 0 + β 1 ] = β 2 β 1 Log(OR) = ( ) = OR = exp(1.9613) = 7.11 Black males have a 7.11 times greater odds of having part time job than white females.

13 Uji Kebaikan Suai Hosmer and Lemeshow (Goodness of Fit Test)

14 Interpreting the Hosmer-Lemeshow Goodness Of Fit Test Hipotesis: H o : the model is a good fit, vs H a : the model is NOT a good fit With 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 = , so we do NOT reject the null hypothesis, and we conclude the model is a good fit.

15 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

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

17 Output SAS

18 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 probability exp[ (26.3)]/{1 + exp[ (26.3)]} = a medium-light crab of average width has estimated probability exp[ (26.3)]/{1 + exp[ (26.3)]} =

19 the difference in color parameter estimates between medium-light crabs and dark crabs= = 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.

20 Paralel No interaction

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

22 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

23 WARNA ORDINAL???