OPTIMIZATION OF BINARY LOGISTIC REGRESSION PARAMETERS USING THE BROYDEN-FLETCHER-GOLDFARB-SHANNO ALGORITHM IN THE QUASI-NEWTON METHOD
The following is the syntax of the BFGS algorithm in Binary Logistic Regression Case Study: Study Period Status of FMIPA Undergraduate Program Graduates Mulawarman University in 2021
The research variables consist of a dependent variable (Y) and an independent variable (X). The dependent variable is the study period statistics of graduates of the FMIPA Mulawarman University Undergraduate Program in 2021 (Y). Independent variables include Grade Point Average (GPA) (X1), gender (X2), TOEFL score (X3), study program (X4), high school origin status (X5), region of origin (X6), and age (X7) . Variable notation, data types, operational definitions of variables.
The binary logistic regression parameter estimates were calculated with the help of R software using the "maxLik" package.
Syntax:
##Statistic Deskription
library("pastecs") library("dplyr") data=read.csv(file.choose(), header=TRUE, sep= ";") View(data) names(data) data$X2<-as.factor(data$X2) data$X4<-as.factor(data$X4) data$X41<-ifelse(data$X4==1,1,0) data$X41<-as.factor(data$X41) data$X42<-ifelse(data$X4==2,1,0) data$X42<-as.factor(data$X42) data$X43<-ifelse(data$X4==3,1,0) data$X43<-as.factor(data$X43) data$X5<-as.factor(data$X5) data$X6<-as.factor(data$X6) str(data) attach(data) summary(data$X1) summary(data$X3) summary(data$X7)
##Multikolinieritas Detection
library("car") reg=lm(V~X1+X3+X7,data=data) vif(reg) #Tabulasi X2 dengan X41 tab.x2.x4=table(data$X2,data$X4) tab.x2.x4 ind.test.x2.x4=chisq.test(tab.x2.x4) ind.test.x2.x4 #Tabulasi X2 dengan X5 tab.x2.x5=table(data$X2,data$X5) tab.x2.x5 ind.test.x2.x5=chisq.test(tab.x2.x5) ind.test.x2.x5 #Tabulasi X2 dengan X6 tab.x2.x6=table(data$X2,data$X6) tab.x2.x6 ind.test.x2.x6=chisq.test(tab.x2.x6) ind.test.x2.x6 #Tabulasi X4 dengan X5 tab.x4.x5=table(data$X4,data$X5) tab.x4.x5 ind.test.x4.x5=chisq.test(tab.x4.x5) ind.test.x4.x5 #Tabulasi X4 dengan X6 tab.x4.x6=table(data$X6,data$X4) tab.x4.x6 ind.test.x4.x6=chisq.test(tab.x4.x6) ind.test.x4.x6 #Tabulasi X5 dengan X6 tab.x5.x6=table(data$X5,data$X6) tab.x5.x6 ind.test.x5.x6=chisq.test(tab.x5.x6) ind.test.x5.x6
##Parameter Estimation
library("maxLik") library("optimx") library("pscl")
#Likelihood Function
ll<- function(par){ y<- as.vector(data$Y) x<- as.matrix(cbind(1, data$X1, data$X2, data$X3, data$X5, data$X6, data$X7)) beta <- par[1:7] m = length(par) n = length(y) loglik = rep(0,n) for(i in 1:n){ xbeta= as.numeric(x[i,]%*%beta) yd = y[i]*xbeta loglik[i]=yd-log(1+exp(xbeta)) } return(loglik) }
#Gradien
gl<- function(par){ y<- as.matrix(data$Y) x <- as.matrix(cbind(1, data$X1, data$X2, data$X3, data$X5, data$X6, data$X7)) beta <- par[1:7] n = length(y) m = length(par) gg <- matrix(0,n,m) p<- matrix(n,1) xbeta<- matrix(n,1) for(i in 1:n){ for(j in 1:m){ xbeta[i] <- as.numeric(x[i,]%%beta) p[i]<- exp(xbeta[i])/(1+exp(xbeta[i])) gg[i,j] <- x[i,j]%%(y[i]-p[i]) } } return(gg) }
#MaxLikBFGS
sv<- c(Intercept=0, B1=0, B2=0, B3=0, B5=0, B6=0, B7=0) max <- maxControl(tol=1e-3,print.level=3,iterlim=200) mle<-maxLik(logLik=ll, grad = gl, start= sv, method="BFGS", control=max) mle gradient(mle) hessian(mle)
##Simultan Test
library("MASS") llfull<-as.matrix(ll(c(coef(mle)))) llreduced<-as.matrix(ll(c(0,0,0,0,0,0,0,0,0,0))) model_full <- as.numeric(colSums(llfull)) model_full model_reduced <-as.numeric(colSums(llreduced)) model_reduced LRT <- -2*(model_reduced-model_full) LRT p.val <-pchisq(LRT, df = 9, lower.tail=FALSE) p.val
##Parsial Test
BFGS=coef(mle) BFGS se=stdEr(mle) W<-BFGS/se W
##Odd Ratio
Ob1<-4.4899213 Ob7<--1.9893193 #Odd Ratio B1 OR1<-exp(Ob1)*0.01 OR1 #Odd Ratio B7 OR7<-exp(Ob7)*1 OR7