Regresi Logistik II (Peubah Bebas : Kategorik) Dr. Kusman Sadik, M.Si Program Studi Pascasarjana Departemen Statistika IPB, 2018/2019
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. 2
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. 3
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. 4
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Inferensia 13
Catatan : Uji G 2 sama dengan Uji Deviance 14
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Pengaruh Interaksi 16
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Gender SES Interaksi 18
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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") 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) 22
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 23
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 24
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H 0 : β 1 = β 2 = β 3 = 0 Call: H 0 glm(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: H 1 glm(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? 27
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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. 29
2. Gunakan Program R untuk menyelesaikan Problems 9.5 (Azen, hlm. 241 ). 30
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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 2 nd. New York: Wiley. 3. Pustaka lain yang relevan. 32
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