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<<data>> id y visit trt bline age x1 ltime 101 76 0 1 76 18 0 2.079441542 101 11 1 1 76 18 1 0.693147181 101 14 2 1 76 18 1 0.693147181 101 9 3 1 76 18 1 0.693147181 101 8 4 1 76 18 1 0.693147181 102 38 0 1 38 32 0 2.079441542 102 8 1 1 38 32 1 0.693147181 102 7 2 1 38 32 1 0.693147181 102 9 3 1 38 32 1 0.693147181 102 4 4 1 38 32 1 0.693147181 103 19 0 1 19 20 0 2.079441542 103 0 1 1 19 20 1 0.693147181 103 4 2 1 19 20 1 0.693147181 103 3 3 1 19 20 1 0.693147181 103 0 4 1 19 20 1 0.693147181 104 11 0 0 11 31 0 2.079441542 104 5 1 0 11 31 1 0.693147181 104 3 2 0 11 31 1 0.693147181 104 3 3 0 11 31 1 0.693147181 104 3 4 0 11 31 1 0.693147181 106 11 0 0 11 30 0 2.079441542 106 3 1 0 11 30 1 0.693147181 106 5 2 0 11 30 1 0.693147181 106 3 3 0 11 30 1 0.693147181 106 3 4 0 11 30 1 0.693147181 107 6 0 0 6 25 0 2.079441542 107 2 1 0 6 25 1 0.693147181 107 4 2 0 6 25 1 0.693147181 107 0 3 0 6 25 1 0.693147181 107 5 4 0 6 25 1 0.693147181 108 10 0 1 10 30 0 2.079441542 108 3 1 1 10 30 1 0.693147181 108 6 2 1 10 30 1 0.693147181 108 1 3 1 10 30 1 0.693147181 108 3 4 1 10 30 1 0.693147181 110 19 0 1 19 18 0 2.079441542 110 2 1 1 19 18 1 0.693147181 110 6 2 1 19 18 1 0.693147181 110 7 3 1 19 18 1 0.693147181 110 4 4 1 19 18 1 0.693147181 111 24 0 1 24 24 0 2.079441542 111 4 1 1 24 24 1 0.693147181 111 3 2 1 24 24 1 0.693147181 111 1 3 1 24 24 1 0.693147181 111 3 4 1 24 24 1 0.693147181 112 31 0 1 31 30 0 2.079441542 112 22 1 1 31 30 1 0.693147181 112 17 2 1 31 30 1 0.693147181 112 19 3 1 31 30 1 0.693147181 112 16 4 1 31 30 1 0.693147181 113 14 0 1 14 35 0 2.079441542 113 5 1 1 14 35 1 0.693147181 113 4 2 1 14 35 1 0.693147181 113 7 3 1 14 35 1 0.693147181 113 4 4 1 14 35 1 0.693147181 114 8 0 0 8 36 0 2.079441542 114 4 1 0 8 36 1 0.693147181 114 4 2 0 8 36 1 0.693147181 114 1 3 0 8 36 1 0.693147181 114 4 4 0 8 36 1 0.693147181 116 66 0 0 66 22 0 2.079441542 116 7 1 0 66 22 1 0.693147181 116 18 2 0 66 22 1 0.693147181 116 9 3 0 66 22 1 0.693147181 116 21 4 0 66 22 1 0.693147181 117 11 0 1 11 27 0 2.079441542 117 2 1 1 11 27 1 0.693147181 117 4 2 1 11 27 1 0.693147181 117 0 3 1 11 27 1 0.693147181 117 4 4 1 11 27 1 0.693147181 118 27 0 0 27 29 0 2.079441542 118 5 1 0 27 29 1 0.693147181 118 2 2 0 27 29 1 0.693147181 118 8 3 0 27 29 1 0.693147181 118 7 4 0 27 29 1 0.693147181 121 67 0 1 67 20 0 2.079441542 121 3 1 1 67 20 1 0.693147181 121 7 2 1 67 20 1 0.693147181 121 7 3 1 67 20 1 0.693147181 121 7 4 1 67 20 1 0.693147181 122 41 0 1 41 22 0 2.079441542 122 4 1 1 41 22 1 0.693147181 122 18 2 1 41 22 1 0.693147181 122 2 3 1 41 22 1 0.693147181 122 5 4 1 41 22 1 0.693147181 123 12 0 0 12 31 0 2.079441542 123 6 1 0 12 31 1 0.693147181 123 4 2 0 12 31 1 0.693147181 123 0 3 0 12 31 1 0.693147181 123 2 4 0 12 31 1 0.693147181 124 7 0 1 7 28 0 2.079441542 124 2 1 1 7 28 1 0.693147181 124 1 2 1 7 28 1 0.693147181 124 1 3 1 7 28 1 0.693147181 124 0 4 1 7 28 1 0.693147181 126 52 0 0 52 42 0 2.079441542 126 40 1 0 52 42 1 0.693147181 126 20 2 0 52 42 1 0.693147181 126 23 3 0 52 42 1 0.693147181 126 12 4 0 52 42 1 0.693147181 128 22 0 1 22 23 0 2.079441542 128 0 1 1 22 23 1 0.693147181 128 2 2 1 22 23 1 0.693147181 128 4 3 1 22 23 1 0.693147181 128 0 4 1 22 23 1 0.693147181 129 13 0 1 13 40 0 2.079441542 129 5 1 1 13 40 1 0.693147181 129 4 2 1 13 40 1 0.693147181 129 0 3 1 13 40 1 0.693147181 129 3 4 1 13 40 1 0.693147181 130 23 0 0 23 37 0 2.079441542 130 5 1 0 23 37 1 0.693147181 130 6 2 0 23 37 1 0.693147181 130 6 3 0 23 37 1 0.693147181 130 5 4 0 23 37 1 0.693147181 135 10 0 0 10 28 0 2.079441542 135 14 1 0 10 28 1 0.693147181 135 13 2 0 10 28 1 0.693147181 135 6 3 0 10 28 1 0.693147181 135 0 4 0 10 28 1 0.693147181 137 46 0 1 46 33 0 2.079441542 137 11 1 1 46 33 1 0.693147181 137 14 2 1 46 33 1 0.693147181 137 25 3 1 46 33 1 0.693147181 137 15 4 1 46 33 1 0.693147181 139 36 0 1 36 21 0 2.079441542 139 10 1 1 36 21 1 0.693147181 139 5 2 1 36 21 1 0.693147181 139 3 3 1 36 21 1 0.693147181 139 8 4 1 36 21 1 0.693147181 141 52 0 0 52 36 0 2.079441542 141 26 1 0 52 36 1 0.693147181 141 12 2 0 52 36 1 0.693147181 141 6 3 0 52 36 1 0.693147181 141 22 4 0 52 36 1 0.693147181 143 38 0 1 38 35 0 2.079441542 143 19 1 1 38 35 1 0.693147181 143 7 2 1 38 35 1 0.693147181 143 6 3 1 38 35 1 0.693147181 143 7 4 1 38 35 1 0.693147181 145 33 0 0 33 24 0 2.079441542 145 12 1 0 33 24 1 0.693147181 145 6 2 0 33 24 1 0.693147181 145 8 3 0 33 24 1 0.693147181 145 4 4 0 33 24 1 0.693147181 147 7 0 1 7 25 0 2.079441542 147 1 1 1 7 25 1 0.693147181 147 1 2 1 7 25 1 0.693147181 147 2 3 1 7 25 1 0.693147181 147 3 4 1 7 25 1 0.693147181 201 18 0 0 18 23 0 2.079441542 201 4 1 0 18 23 1 0.693147181 201 4 2 0 18 23 1 0.693147181 201 6 3 0 18 23 1 0.693147181 201 2 4 0 18 23 1 0.693147181 202 42 0 0 42 36 0 2.079441542 202 7 1 0 42 36 1 0.693147181 202 9 2 0 42 36 1 0.693147181 202 12 3 0 42 36 1 0.693147181 202 14 4 0 42 36 1 0.693147181 203 36 0 1 36 26 0 2.079441542 203 6 1 1 36 26 1 0.693147181 203 10 2 1 36 26 1 0.693147181 203 8 3 1 36 26 1 0.693147181 203 8 4 1 36 26 1 0.693147181 204 11 0 1 11 25 0 2.079441542 204 2 1 1 11 25 1 0.693147181 204 1 2 1 11 25 1 0.693147181 204 0 3 1 11 25 1 0.693147181 204 0 4 1 11 25 1 0.693147181 205 87 0 0 87 26 0 2.079441542 205 16 1 0 87 26 1 0.693147181 205 24 2 0 87 26 1 0.693147181 205 10 3 0 87 26 1 0.693147181 205 9 4 0 87 26 1 0.693147181 206 50 0 0 50 26 0 2.079441542 206 11 1 0 50 26 1 0.693147181 206 0 2 0 50 26 1 0.693147181 206 0 3 0 50 26 1 0.693147181 206 5 4 0 50 26 1 0.693147181 208 22 0 1 22 32 0 2.079441542 208 4 1 1 22 32 1 0.693147181 208 3 2 1 22 32 1 0.693147181 208 2 3 1 22 32 1 0.693147181 208 4 4 1 22 32 1 0.693147181 209 41 0 1 41 25 0 2.079441542 209 8 1 1 41 25 1 0.693147181 209 6 2 1 41 25 1 0.693147181 209 5 3 1 41 25 1 0.693147181 209 7 4 1 41 25 1 0.693147181 210 18 0 0 18 28 0 2.079441542 210 0 1 0 18 28 1 0.693147181 210 0 2 0 18 28 1 0.693147181 210 3 3 0 18 28 1 0.693147181 210 3 4 0 18 28 1 0.693147181 211 32 0 1 32 35 0 2.079441542 211 1 1 1 32 35 1 0.693147181 211 3 2 1 32 35 1 0.693147181 211 1 3 1 32 35 1 0.693147181 211 5 4 1 32 35 1 0.693147181 213 111 0 0 111 31 0 2.079441542 213 37 1 0 111 31 1 0.693147181 213 29 2 0 111 31 1 0.693147181 213 28 3 0 111 31 1 0.693147181 213 29 4 0 111 31 1 0.693147181 214 56 0 1 56 21 0 2.079441542 214 18 1 1 56 21 1 0.693147181 214 11 2 1 56 21 1 0.693147181 214 28 3 1 56 21 1 0.693147181 214 13 4 1 56 21 1 0.693147181 215 18 0 0 18 32 0 2.079441542 215 3 1 0 18 32 1 0.693147181 215 5 2 0 18 32 1 0.693147181 215 2 3 0 18 32 1 0.693147181 215 5 4 0 18 32 1 0.693147181 217 20 0 0 20 21 0 2.079441542 217 3 1 0 20 21 1 0.693147181 217 0 2 0 20 21 1 0.693147181 217 6 3 0 20 21 1 0.693147181 217 7 4 0 20 21 1 0.693147181 218 24 0 1 24 41 0 2.079441542 218 6 1 1 24 41 1 0.693147181 218 3 2 1 24 41 1 0.693147181 218 4 3 1 24 41 1 0.693147181 218 0 4 1 24 41 1 0.693147181 219 12 0 0 12 29 0 2.079441542 219 3 1 0 12 29 1 0.693147181 219 4 2 0 12 29 1 0.693147181 219 3 3 0 12 29 1 0.693147181 219 4 4 0 12 29 1 0.693147181 220 9 0 0 9 21 0 2.079441542 220 3 1 0 9 21 1 0.693147181 220 4 2 0 9 21 1 0.693147181 220 3 3 0 9 21 1 0.693147181 220 4 4 0 9 21 1 0.693147181 221 16 0 1 16 32 0 2.079441542 221 3 1 1 16 32 1 0.693147181 221 5 2 1 16 32 1 0.693147181 221 4 3 1 16 32 1 0.693147181 221 3 4 1 16 32 1 0.693147181 222 17 0 0 17 32 0 2.079441542 222 2 1 0 17 32 1 0.693147181 222 3 2 0 17 32 1 0.693147181 222 3 3 0 17 32 1 0.693147181 222 5 4 0 17 32 1 0.693147181 225 22 0 1 22 26 0 2.079441542 225 1 1 1 22 26 1 0.693147181 225 23 2 1 22 26 1 0.693147181 225 19 3 1 22 26 1 0.693147181 225 8 4 1 22 26 1 0.693147181 226 28 0 0 28 25 0 2.079441542 226 8 1 0 28 25 1 0.693147181 226 12 2 0 28 25 1 0.693147181 226 2 3 0 28 25 1 0.693147181 226 8 4 0 28 25 1 0.693147181 227 55 0 0 55 30 0 2.079441542 227 18 1 0 55 30 1 0.693147181 227 24 2 0 55 30 1 0.693147181 227 76 3 0 55 30 1 0.693147181 227 25 4 0 55 30 1 0.693147181 228 25 0 1 25 21 0 2.079441542 228 2 1 1 25 21 1 0.693147181 228 3 2 1 25 21 1 0.693147181 228 0 3 1 25 21 1 0.693147181 228 1 4 1 25 21 1 0.693147181 230 9 0 0 9 40 0 2.079441542 230 2 1 0 9 40 1 0.693147181 230 1 2 0 9 40 1 0.693147181 230 2 3 0 9 40 1 0.693147181 230 1 4 0 9 40 1 0.693147181 232 13 0 1 13 36 0 2.079441542 232 0 1 1 13 36 1 0.693147181 232 0 2 1 13 36 1 0.693147181 232 0 3 1 13 36 1 0.693147181 232 0 4 1 13 36 1 0.693147181 234 10 0 0 10 19 0 2.079441542 234 3 1 0 10 19 1 0.693147181 234 1 2 0 10 19 1 0.693147181 234 4 3 0 10 19 1 0.693147181 234 2 4 0 10 19 1 0.693147181 236 12 0 1 12 37 0 2.079441542 236 1 1 1 12 37 1 0.693147181 236 4 2 1 12 37 1 0.693147181 236 3 3 1 12 37 1 0.693147181 236 2 4 1 12 37 1 0.693147181 238 47 0 0 47 22 0 2.079441542 238 13 1 0 47 22 1 0.693147181 238 15 2 0 47 22 1 0.693147181 238 13 3 0 47 22 1 0.693147181 238 12 4 0 47 22 1 0.693147181 <<code>> seizure<- read.csv('C:/Users/UX303LB/Desktop/class/R/seizure.csv') head(seizure) glm(seizure$y~seizure$trt+seizure$age,offset=seizure$ltime,family=poisson) #第一題 y<-(seizure$y) X<-cbind(1,seizure$trt,seizure$age) head(X) time<-exp(seizure$ltime) f3<-function(beta){ mu<-exp(X%*%beta)*time ymu<-y-mu gradient<-t(X)%*%ymu hessian<--t(X)%*%diag(as.vector(mu))%*%X return(list(gradient, hessian)) } newton <- function(f3, x0, tol = 1e-9, n.max = 100) { x <- x0 f3.x <- f3(x) n <- 0 while ((max(abs(f3.x[[1]])) > tol) & (n < n.max)) { x <- x - solve.default(f3.x[[2]], tol= 1e-19)%*% f3.x[[1]] f3.x <- f3(x) n <- n + 1 } if (n == n.max) { cat('newton failed to converge\n') } else { return(x) } } newton(f3,c(0, 0, 0),1e-9) #第二題 result<-glm(seizure$y~seizure$trt+seizure$age,offset=seizure$ltime,family=poisson) b<-newton(f3,c(0, 0, 0),1e-9) vcov(result) solve(-hessian) solve(-f3(b)[[2]], tol= 1e-19) #第三題 beta<-newton(f3,c(0, 0, 0),1e-9) result<-glm(seizure$y~seizure$trt+seizure$age,offset=seizure$ltime,family=poisson) logLik(result) loglike<-sum((-exp(X%*%beta)%*%time)+(y%*%X%*%beta)+(y%*%(seizure$ltime))-(log(factorial(y)))) a<--exp(X%*%beta)%*%time b<-y%*%X%*%beta c<-y%*%(seizure$ltime) d<--log(factorial(y)) loglike<-sum(a+diag(b)+diag(c)+d) loglike<-sum(-mu+diag(y%*%log(mu))-log(factorial(y))) loglike<-sum(-mu+diag(y%*%log(mu))-log(factorial(y)))
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