VII. The following data was collected on a patient that was admitted to the Emergency Department.(ED). The data collected sequentially in time was 1) Body temperature (temp) 2) Heart rate (hrtrate) 3) respiratory rate (resprate), 4)oxygen saturation (02sat), 5) systolic blood pressure (sbp) 6) diastolic blood pressure (dbp) the data appears in the text file patientED.tex Fit a Hidden Markov |Model (HMM) to this data assuming that the 6 variables being measured follow a Multivariate Normal distribution when the patient is in a given state. a. Fit the HMM model with two states, three states and four states. b. In each case determine the Viterbi sequence of states c. Carry out the likelihood ratio test to see if three states are required over two states, if four states are required over three states Here is the data screenshot. Here is the data code provided as an example. ourData2states.R P1data<-read.table("C:/Users/wilhl/OneDrive/Desktop/patientHMM.txt", header=FALSE) y<-data.matrix(P1data) # now use makeDepmix to create a depmix model for this 3-dim normal timeseries # response is a 2-dim list of response models. Models <- list() rModels[[1]] <- list(MVNresponse(y~1)) Models[[2]] <- list(MVNresponse(y~1)) trstart=c(0.9,0.1,0.2,0.8) 97.3 80 18 99 138 78 98.5 82 18 100 142 78 98.2 73 20 99 122 60 97.6 70 18 98 153 66 97.8 70 18 98 123 60 98 70 18 95 122 61 98.3 71 16 100 134 57 98.8 78 19 100 151 75 transition <-list() 99.5 75 18 98 180 74 97.4 71 16 96 119 59 97.9 62 16 95 145 63 98.7 65 19 99 116 76 98.7 50 12 98 50 12 98.6 72 18 97.8 70 18 97.9 72 20 98 105 42 100 119 56 100 125 62 100 118 59 100 135 64 100.2 73 15 98 149 53 98.4 72 16 96 134 53 97.9 70 17 97 131 58 98.2 72 17 96 126 70 98.1 69 18 98.5 95 16 98.5 76 16 97.9 73 16 97 118 64 100 158 71 100 149 60 100 144 59 98.5 81 18 98 157 80 98.9 120 16 96 120 71 102.4 123 20 99 107 69 transition[[1]] <- transInit(~1,nstates=2,data=data.frame(1),pstart=c(trstart[1:2])) transition[[2]] <- transInit(~1,nstates=2,data=data.frame(1),pstart=c(trstart[3:4])) instart=runif(2) inMod <- transInit(~1,ns-2,ps-instart.data-data.frame(1)) mod <- makeDepmix(response-rModels.transition-transition prior-inMod) fm2 <- fit(mod.emc-em.control(random=TRUE)) summary(fm2) postvit2<-posterior(fm2,type="global") plot(postvit2,type="[") ourData3states.R Models <- list() Models [[1]] <- list(MVNresponse(y-1)) Models [[2]] <- list(MVNresponse(y-1)) Models [[3]] <- list(MVNresponse(y-1)) trstart=c(0.8,0.1,0.1,0.1,0.8,0.1,0.1,0.1,0.8) transition<-list() transition[[1]] <- transInit(~1,nstates=3,data=data.frame(1),pstart=c(trstart[1:3])) transition[[2]] <- translnit(~1,nstates=3,data=data.frame(1),pstart=c(trstart[4:6])) transition[[3]] <- transInit(~1,nstates=3,data=data.frame(1),pstart=c(trstart[7:9])) instart-runif(3) inMod <- transInit(~1,ns=3,ps=instart.data=data.frame(1)) mod <- makeDepmix(response-rModels.transition-transition prior-inMod) fm3<- fit(mod.emc-em.control(random=TRUE)) summary(fm3) postvit3<-posterior(fm3,type="global") plot(postvit3,type="l") Uratio(fm3.fm2)