# ANALYSIS OF OUTBREAK DATA
# Load required packages
library(bbmle)
library(plotrix)

########## IMPORT THE DATA AS CSV FILES
# Below is the code that reads in the data from the Excel spreadsheet and prepares it for the analysis
# Each page of the Excel file is saved as a csv file which is then uploaded into R. 
# YOU WILL NEED TO EDIT THIS TO SPECIFY THE PATH TO YOUR CSV FILES
StaphA<-read.csv("/Users/amyhurford/Desktop/Work/Students/Ugrad/Alice/StaphA.csv")
Enteroc<-read.csv("/Users/amyhurford/Desktop/Work/Students/Ugrad/Alice/Enterococci.csv")
Pseudo<-read.csv("/Users/amyhurford/Desktop/Work/Students/Ugrad/Alice/Pseudo.csv")
Klebs<-read.csv("/Users/amyhurford/Desktop/Work/Students/Ugrad/Alice/Klebs.csv")
Acin<-read.csv("/Users/amyhurford/Desktop/Work/Students/Ugrad/Alice/Acin.csv")
Serr<-read.csv("/Users/amyhurford/Desktop/Work/Students/Ugrad/Alice/Serr.csv")
Enterob<-read.csv("/Users/amyhurford/Desktop/Work/Students/Ugrad/Alice/Enterobacter.csv")
HepB<-read.csv("/Users/amyhurford/Desktop/Work/Students/Ugrad/Alice/HepB.csv")
HepC<-read.csv("/Users/amyhurford/Desktop/Work/Students/Ugrad/Alice/HepC.csv")
Strep<-read.csv("/Users/amyhurford/Desktop/Work/Students/Ugrad/Alice/Strep.csv")
Salmon<-read.csv("//Users/amyhurford/Desktop/Work/Students/Ugrad/Alice/Salmonella.csv")
Legion<-read.csv("/Users/amyhurford/Desktop/Work/Students/Ugrad/Alice/Legionella.csv")
Ecoli<-read.csv("/Users/amyhurford/Desktop/Work/Students/Ugrad/Alice/Ecoli.csv")
Cdiff<-read.csv("/Users/amyhurford/Desktop/Work/Students/Ugrad/Alice/Cdiff.csv")

########## PRE-PROCESSING:
# below is code that takes the information from the Excel spreadsheet and converts it into a nice dataframe that
# can be used for the analysis.

# Need to create matrix with columns: 1) species; 2) duration; 3) outbreak size; 4) Molecular evidence and 5) tranmission route.
labs<-labels(StaphA)[[2]]
j2<-which(labs=="Duration..days.")
j3<-which(labs=="Cases..patient.")
j4<-which(labs=="Molecular.confirmation")
j5<-which(labs=="Transmission")
Mx <- subset(StaphA[1:268,], select = c(j2, j3, j4, j5))
Mx$species <- rep("Staph",268)

# Construct data matrix for Enterococci and add to the bottom of Staph A data matrix
labs<-labels(Enteroc)[[2]]
j2<-which(labs=="Duration..days.")
j3<-which(labs=="Cases..patient.")
j4<-which(labs=="Molecular.Evidence")
j5<-which(labs=="Transmission")
Mx2 <- subset(Enteroc[1:116,], select = c(j2, j3, j4, j5))
Mx2$species <- rep("Enteroc",116)
names(Mx2)<-labels(Mx)[[2]]
Mx<-rbind(Mx,Mx2)

# Construct data matrix for Pseudomonas and add to the bottom of the existing matrix
labs<-labels(Pseudo)[[2]]
j2<-which(labs=="Duration..days.")
j3<-which(labs=="Cases..patient.")
j4<-which(labs=="Molecular.Evidence")
j5<-which(labs=="Transmission")
Mx2 <- subset(Pseudo[1:144,], select = c(j2, j3, j4, j5))
Mx2$species <- rep("Pseudo",144)
names(Mx2)<-labels(Mx)[[2]]
Mx<-rbind(Mx,Mx2)

# Construct data matrix for Klebsilla and add
labs<-labels(Klebs)[[2]]
j2<-which(labs=="Duration..days.")
j3<-which(labs=="Cases..patient.")
j4<-which(labs=="Molecular.Evidence")
j5<-which(labs=="Transmission")
Mx2 <- subset(Klebs[1:79,], select = c(j2, j3, j4, j5))
Mx2$species<-rep("Klebs",79)
names(Mx2)<-labels(Mx)[[2]]
Mx<-rbind(Mx,Mx2)

# Construct data matrix for Acinetobacter and add
labs<-labels(Acin)[[2]]
j2<-which(labs=="Duration..days.")
j3<-which(labs=="Cases..patient.")
j4<-which(labs=="Molecular.Evidence")
j5<-which(labs=="Transmission")
Mx2 <- subset(Acin[1:169,], select = c(j2, j3, j4, j5))
Mx2$Cspecies<-rep("Acin",169)
names(Mx2)<-labels(Mx)[[2]]
Mx<-rbind(Mx,Mx2)

# Construct data matrix for Serratia and add
labs<-labels(Serr)[[2]]
j2<-which(labs=="Duration..days.")
j3<-which(labs=="Cases..patient.")
j4<-which(labs=="Molecular.Evidence")
j5<-which(labs=="Transmission")
Mx2 <- subset(Serr[1:116,], select = c(j2, j3, j4, j5))
Mx2$species<-rep("Serr",116)
names(Mx2)<-labels(Mx)[[2]]
Mx<-rbind(Mx,Mx2)

# Construct data matrix for Enterobacter and add
labs<-labels(Enterob)[[2]]
j2<-which(labs=="Duration..days.")
j3<-which(labs=="Cases..patient.")
j4<-which(labs=="Molecular.Evidence")
j5<-which(labs=="Transmission")
Mx2 <- subset(Enterob[1:62,], select = c(j2, j3, j4, j5))
Mx2$species<-rep("Enterob",62)
names(Mx2)<-labels(Mx)[[2]]
Mx<-rbind(Mx,Mx2)

# Construct data matrix for Hepatitis B Virus and add
labs<-labels(HepB)[[2]]
j2<-which(labs=="Duration..days.")
j3<-which(labs=="Cases..patient.")
j4<-which(labs=="Molecular.Evidence")
j5<-which(labs=="Transmission")
Mx2 <- subset(HepB[1:85,], select = c(j2, j3, j4, j5))
Mx2$species<-rep("Hep B",85)
names(Mx2)<-labels(Mx)[[2]]
Mx<-rbind(Mx,Mx2)

# Construct data matrix for Hepatitis C Virus and add
labs<-labels(HepC)[[2]]
j2<-which(labs=="Duration..days.")
j3<-which(labs=="Cases..patient.")
j4<-which(labs=="Molecular.Evidence")
j5<-which(labs=="Transmission")
Mx2 <- subset(HepC[1:85,], select = c(j2, j3, j4, j5))
Mx2$species<-rep("Hep C",85)
names(Mx2)<-labels(Mx)[[2]]
Mx<-rbind(Mx,Mx2)

# Construct data matrix for Streptococci and add
labs<-labels(Strep)[[2]]
j2<-which(labs=="Duration..days.")
j3<-which(labs=="Cases..patient.")
j4<-which(labs=="Molecular.Evidence")
j5<-which(labs=="Transmission")
Mx2 <- subset(Strep[1:87,], select = c(j2, j3, j4, j5))
Mx2$species<-rep("Strep",87)
names(Mx2)<-labels(Mx)[[2]]
Mx<-rbind(Mx,Mx2)

# Construct data matrix for Salmonella and add
labs<-labels(Salmon)[[2]]
j2<-which(labs=="Duration..days.")
j3<-which(labs=="Cases..patient.")
j4<-which(labs=="Molecular.Evidence")
j5<-which(labs=="Transmission")
Mx2 <- subset(Salmon[1:78,], select = c(j2, j3, j4, j5))
Mx2$species<-rep("Salm",78)
names(Mx2)<-labels(Mx)[[2]]
Mx<-rbind(Mx,Mx2)

# Construct data matrix for Legionella and add
labs<-labels(Legion)[[2]]
j2<-which(labs=="Duration..days.")
j3<-which(labs=="Cases..patient.")
j4<-which(labs=="Molecular.Evidence")
j5<-which(labs=="Transmission")
Mx2 <- subset(Legion[1:55,], select = c(j2, j3, j4, j5))
Mx2$species<-rep("Legion",55)
names(Mx2)<-labels(Mx)[[2]]
Mx<-rbind(Mx,Mx2)

# Construct data matrix for Ecoli and add
labs<-labels(Ecoli)[[2]]
j2<-which(labs=="Duration..days.")
j3<-which(labs=="Cases..patient.")
j4<-which(labs=="Molecular.Evidence")
j5<-which(labs=="Transmission")
Mx2 <- subset(Ecoli[1:39,], select = c(j2, j3, j4, j5))
Mx2$species<-rep("E. coli",39)
names(Mx2)<-labels(Mx)[[2]]
Mx<-rbind(Mx,Mx2)

# Construct data matrix for Clostrium difficule and add
labs<-labels(Cdiff)[[2]]
j2<-which(labs=="Duration..days.")
j3<-which(labs=="Cases..patient.")
j4<-which(labs=="Molecular.Evidence")
j5<-which(labs=="Transmission")
Mx2 <- subset(Cdiff[1:50,], select = c(j2, j3, j4, j5))
Mx2$species<-rep("C. diff",50)
names(Mx2)<-labels(Mx)[[2]]
Mx<-rbind(Mx,Mx2)
# Remove entries that are NA
# Omit entries that read in as NA
Mx<-na.omit(Mx)
# Remove detials on attributes
attributes(Mx)$na.action <- NULL

# Group like transmission routes:
# (1) Multiple transmission routes are grouped together
#add a new level
levels(Mx$Transmission)<-c(levels(Mx$Transmission),"multi")
# (2) Spelling mistakes are corrected
# (3) Biologics and drugs are aggregated within equipment.
Mx$Transmission[Mx$Transmission=="HCW+env"]<-"multi"
Mx$Transmission[Mx$Transmission=="HCW+air"]<-"multi"
Mx$Transmission[Mx$Transmission=="HCW+env+equip"]<-"multi"
Mx$Transmission[Mx$Transmission=="env+equip"]<-"multi"
Mx$Transmission[Mx$Transmission=="HCW+equip"]<-"multi"
Mx$Transmission[Mx$Transmission=="equip+air"]<-"multi"
Mx$Transmission[Mx$Transmission=="HCW+equip+env"]<-"multi"
Mx$Transmission[Mx$Transmission=="drug"]<-"equip"
Mx$Transmission[Mx$Transmission=="HCw+env"]<-"multi"
Mx$Transmission[Mx$Transmission=="HCW+equip "]<-"multi"
Mx$Transmission[Mx$Transmission=="equip+env"]<-"multi"
Mx$Transmission[Mx$Transmission=="HCW "]<-"HCW"
Mx$Transmission[Mx$Transmission=="HCW+PTP"]<-"multi"
Mx$Transmission[Mx$Transmission=="equip+air"]<-"multi"
Mx$Transmission[Mx$Transmission=="HCW+equip+env"]<-"multi"
Mx$Transmission[Mx$Transmission=="env "]<-"env"
Mx$Transmission[Mx$Transmission=="PTP+env"]<-"multi"
Mx$Transmission[Mx$Transmission=="HCW+env+air"]<-"multi"
Mx$Transmission[Mx$Transmission=="equip+food"]<-"multi"
Mx$Transmission[Mx$Transmission=="HCW+drug"]<-"multi"
Mx$Transmission[Mx$Transmission=="HCW+equip+food"]<-"multi"
Mx$Transmission[Mx$Transmission=="PTP+equip"]<-"multi"
Mx$Transmission[Mx$Transmission=="food+equip"]<-"multi"
Mx$Transmission[Mx$Transmission=="food+HCW"]<-"multi"
Mx$Transmission[Mx$Transmission=="HCW+food"]<-"multi"
Mx$Transmission[Mx$Transmission=="unk "]<-"unk"
Mx$Transmission[Mx$Transmission=="PTP+food"]<-"multi"
Mx$Transmission[Mx$Transmission=="equip+drug"]<-"multi"
Mx$Transmission[Mx$Transmission=="bio"]<-"equip"

# Remove unused levels
Mx$Transmission<-factor(Mx$Transmission)
Mx$Molecular.confirmation<-factor(Mx$Molecular.confirmation)

# The data matrix for all species
MxTot<-Mx

# Remove all the instances where the transmission routes was unknown from MxTot
Mx<-MxTot[-1*which(MxTot$Transmission == "unk"),]
Mx$Transmission<-factor(Mx$Transmission)

# Now all the data is organized in the dataframe Mx.
# Also we create seperate dataframe for each species. These are used to
# make boxplots.
MxAcin = Mx[Mx$species=="Acin",]
MxAcin$Transmission<-factor(MxAcin$Transmission)
MxCdiff =  Mx[Mx$species=="C. diff",]
MxCdiff$Transmission<-factor(MxCdiff$Transmission)
MxEcoli =  Mx[Mx$species=="E. coli",]
MxEcoli$Transmission<-factor(MxEcoli$Transmission)
MxEnterob =  Mx[Mx$species=="Enterob",]
MxEnterob$Transmission<-factor(MxEnterob$Transmission)
MxEnteroc  = Mx[Mx$species=="Enteroc",]
MxEnteroc$Transmission<-factor(MxEnteroc$Transmission)
MxHepB =  Mx[Mx$species=="Hep B",]
MxHepB$Transmission<-factor(MxHepB$Transmission)
MxHepC =  Mx[Mx$species=="Hep C",]
MxHepC$Transmission<-factor(MxHepC$Transmission)
MxKlebs =  Mx[Mx$species=="Klebs",]
MxKlebs$Transmission<-factor(MxKlebs$Transmission)
MxLegion =  Mx[Mx$species=="Legion",]
MxLegion$Transmission<-factor(MxLegion$Transmission)
MxPseudo =  Mx[Mx$species=="Pseudo",]
MxPseudo$Transmission<-factor(MxPseudo$Transmission)
MxSalm =  Mx[Mx$species=="Salm",]
MxSalm$Transmission<-factor(MxSalm$Transmission)
MxSerr =  Mx[Mx$species=="Serr",]
MxSerr$Transmission<-factor(MxSerr$Transmission)
MxStaph =  Mx[Mx$species=="Staph",]
MxStaph$Transmission<-factor(MxStaph$Transmission)
MxStrep =  Mx[Mx$species=="Strep",]
MxStrep$Transmission<-factor(MxStrep$Transmission)

#################### DATA ANALYSIS
# Response variable: log Cases
# Model 1: Constant only
# Model 2: Transmission route is the predictor variable
# Model 3: Species is the predictor variable
# Model 4: Transmission routes x species interaction is the predictor variable
# Response variable: log Rate
# Model 5: Constant only
# Model 6: Transmission route is the predictor variable
# Model 7: Species is the predictor variable
# Model 8: Transmission routes x species interaction is the predictor variable

# The response variable:
logCases=log(Mx$Cases)
data = logCases

##### Model 1: Constant only
y1 = function(a){
  mu = a
  mu[mu<0]=0
  return(mu)
}

#The function for the negative log likelihood
LL1 = function (a,y=data){
  mu = y1(a=a)
  #get the total negative log likelihood
  loglike= -sum(dnorm(y,mu,log=TRUE))
  return(loglike)
}

#The call to bbmle and results summary:
Cases_Constant = mle2(minuslogl = LL1, start = list(a=2))
Cases_Constant_Summary = summary(Cases_Constant)

##### Model 2: Transmission route as the predictor variable
# Build a matrix with columns: air, env, equip, HCW, insect, PTP, bio, food, and multi
# and with columns equal to each of the outbreaks. An entry of 1 means that a particular
# outbreak did occur from that transmission route.
xMx = array(0,c(length(Mx$Transmission),length(levels(Mx$Transmission))))
xMx[,1]<-(Mx$Transmission=="air")*1
xMx[,2]<-(Mx$Transmission=="env")*1
xMx[,3]<-(Mx$Transmission=="equip")*1
xMx[,4]<-(Mx$Transmission=="food")*1
xMx[,5]<-(Mx$Transmission=="HCW")*1
xMx[,6]<-(Mx$Transmission=="insect")*1
xMx[,7]<-(Mx$Transmission=="PTP")*1
xMx[,8]<-(Mx$Transmission=="multi")*1


x1=xMx[,1]
x2=xMx[,2]
x3=xMx[,3]
x4=xMx[,4]
x5=xMx[,5]
x6=xMx[,6]
x7=xMx[,7]
x8=xMx[,8]

#function for model: the reference category is air.
y2 = function(b1,b2,b3,b4,b5,b6,b7,b8){
  mu = b1*x1+ b2*x2 + b3*x3 + b4*x4 + b5*x5 + b6*x6 + b7*x7 + b8*x8
  mu[mu<0]=0
  return(mu)
}

#The function for the negative log likelihood
LL2 = function (b1,b2,b3,b4,b5,b6,b7,b8,y=data){
  mu = y2(b1=b1,b2=b2,b3=b3,b4=b4,b5=b5,b6=b6,b7=b7,b8=b8)
  #get the total negative log likelihood
  loglike= -sum(dnorm(y,mu,log=TRUE))
  return(loglike)
}

#The call to bbmle and results summary:
Cases_TR = mle2(minuslogl = LL2, start = list(b1=2,b2=2,b3=2,b4=2,b5=2,b6=2,b7=2,b8=2), control = list(maxit = 5000))
Cases_TR_Summary = summary(Cases_TR)
# The residuals
resCase_TR = y2(coef(Cases_TR_Summary)[1,1], coef(Cases_TR_Summary)[2,1], coef(Cases_TR_Summary)[3,1], coef(Cases_TR_Summary)[4,1], coef(Cases_TR_Summary)[5,1],coef(Cases_TR_Summary)[6,1], coef(Cases_TR_Summary)[7,1], coef(Cases_TR_Summary)[8,1])-data


##### Model 3: Species as the predictor variable
# Build a matrix with 14 columns for each different species
# and with columns equal to each of the outbreaks. An entry of 1 means that a particular
# outbreak did occur from that transmission route.
zMx = array(0,c(length(Mx$species),14))
zMx[,1]<-(Mx$species=="Acin")*1
zMx[,2]<-(Mx$species=="C. diff")*1
zMx[,3]<-(Mx$species=="Enterob")*1
zMx[,4]<-(Mx$species=="Enteroc")*1
zMx[,5]<-(Mx$species=="E. coli")*1
zMx[,6]<-(Mx$species=="Hep B")*1
zMx[,7]<-(Mx$species=="Hep C")*1
zMx[,8]<-(Mx$species=="Klebs")*1
zMx[,9]<-(Mx$species=="Legion")*1
zMx[,10]<-(Mx$species=="Pseudo")*1
zMx[,11]<-(Mx$species=="Salm")*1
zMx[,12]<-(Mx$species=="Serr")*1
zMx[,13]<-(Mx$species=="Staph")*1
zMx[,14]<-(Mx$species=="Strep")*1

x1=zMx[,1]
x2=zMx[,2]
x3=zMx[,3]
x4=zMx[,4]
x5=zMx[,5]
x6=zMx[,6]
x7=zMx[,7]
x8=zMx[,8]
x9=zMx[,9]
x10=zMx[,10]
x11=zMx[,11]
x12=zMx[,12]
x13=zMx[,13]
x14=zMx[,14]

#function for model
y3 = function(b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14){
  mu = b1*x1 + b2*x2 + b3*x3 + b4*x4 + b5*x5 + b6*x6 + b7*x7 + b8*x8 + b9*x9+ b10*x10 + b11*x11 + b12*x12 + b13*x13 + b14*x14
  mu[mu<0]=0
  return(mu)
}

#The function for the negative log likelihood
LL3 = function (b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,y=data){
  mu = y3(b1=b1,b2=b2,b3=b3,b4=b4,b5=b5,b6=b6,b7=b7,b8=b8,b9=b9,b10=b10,b11=b11,b12=b12,b13=b13,b14=b14)
  #get the total negative log likelihood
  loglike= -sum(dnorm(y,mu,log=TRUE))
  return(loglike)
}

#The call to bbmle and results summary:
Cases_Species = mle2(minuslogl = LL3, start = list(b1=2,b2=2,b3=2,b4=2,b5=2,b6=2,b7=2,b8=2,b9=2,b10=2,b11=2,b12=2,b13=2,b14=2), control = list(maxit = 5000))
Cases_Species_Summary = summary(Cases_Species)
#The residuals
resCase_Species = y3(coef(Cases_Species_Summary)[1,1], coef(Cases_Species_Summary)[2,1], coef(Cases_Species_Summary)[3,1], coef(Cases_Species_Summary)[4,1], coef(Cases_Species_Summary)[5,1], coef(Cases_Species_Summary)[6,1], coef(Cases_Species_Summary)[7,1], coef(Cases_Species_Summary)[8,1], coef(Cases_Species_Summary)[9,1], coef(Cases_Species_Summary)[10,1], coef(Cases_Species_Summary)[11,1], coef(Cases_Species_Summary)[12,1], coef(Cases_Species_Summary)[13,1], coef(Cases_Species_Summary)[14,1])-data

#Model 4: Interaction model.
#First note that not all model interactions occur:
levels(factor(Mx$Transmission[which(Mx$species=="Staph")]))
#b11: Staph-air; b12: Staph-env; b13: Staph-equip; b14: Staph-HCW; b15: Staph-multi
levels(factor(Mx$Transmission[which(Mx$species=="Enteroc")]))
#b21: Enteroc-env; b22: Enteroc-equip; b23: Enteroc-HCW; b24: Enteroc-multi
levels(factor(Mx$Transmission[which(Mx$species=="Pseudo")]))
#b31: Pseudo-env; b32: Pseudo-equip; b33: Pseudo-HCW; b34: Pseudo-multi
levels(factor(Mx$Transmission[which(Mx$species=="Klebs")]))
# Klebs x : b41: env; b42: equip; b43: food; b44 HCW; b45 insect; b46 multi. 
levels(factor(Mx$Transmission[which(Mx$species=="Acin")]))
# Acin x : b51 env; b52 equip b53 HCW b54 PTP b55 multi
levels(factor(Mx$Transmission[which(Mx$species=="Serr")]))
# Serr x : b61 air; b62 env; b63 equip; b64 HCW; b65 multi
levels(factor(Mx$Transmission[which(Mx$species=="Enterob")]))
# Enterob x : b71 env; b72 equip; b73 food; b74 HCW; b75 PTP; b76 multi
levels(factor(Mx$Transmission[which(Mx$species=="Hep B")]))
# Hep B x : b81 equip; b82 HCW; b83 PTP; b84 multi
levels(factor(Mx$Transmission[which(Mx$species=="Hep C")]))
# Hep C x : b91 env; b92 equip; b93 HCW; b94 PTP; b95 multi
levels(factor(Mx$Transmission[which(Mx$species=="Strep")]))
# Strep x : b101 air; b102 env; b103 equip; b104 food; b105 HCW; b106 PTP; b107 multi
levels(factor(Mx$Transmission[which(Mx$species=="Salm")]))
# Salm x : b111 env; b112 equip; b113 food; b114 HCW; b115 PTP; b116 multi
levels(factor(Mx$Transmission[which(Mx$species=="Legion")]))
# Legion x : b121 env; b122 multi
levels(factor(Mx$Transmission[which(Mx$species=="E. coli")]))
# E. coli x: b131 env; b132 HCW; b133 food; b134 PTP; b135 multi
levels(factor(Mx$Transmission[which(Mx$species=="C. diff")]))
# C. diff x: b141 env; b142 equip; b143 HCW; b144 PTP; b145 multi

x11=(Mx$species=="Staph" & Mx$Transmission == "air")*1
x12=(Mx$species=="Staph" & Mx$Transmission == "env")*1
x13=(Mx$species=="Staph" & Mx$Transmission == "equip")*1
x14=(Mx$species=="Staph" & Mx$Transmission == "HCW")*1;
x15=(Mx$species=="Staph" & Mx$Transmission == "multi")*1;
x21=(Mx$species=="Enteroc" & Mx$Transmission == "env")*1;
x22=(Mx$species=="Enteroc" & Mx$Transmission == "equip")*1;
x23=(Mx$species=="Enteroc" & Mx$Transmission == "HCW")*1;
x24=(Mx$species=="Enteroc" & Mx$Transmission == "multi")*1;
x31=(Mx$species=="Pseudo" & Mx$Transmission == "env")*1;
x32=(Mx$species=="Pseudo" & Mx$Transmission == "equip")*1;
x33=(Mx$species=="Pseudo" & Mx$Transmission == "HCW")*1;
x34=(Mx$species=="Pseudo" & Mx$Transmission == "multi")*1;
x41=(Mx$species=="Klebs" & Mx$Transmission == "env")*1;
x42=(Mx$species=="Klebs" & Mx$Transmission == "equip")*1;
x43=(Mx$species=="Klebs" & Mx$Transmission == "food")*1;
x44=(Mx$species=="Klebs" & Mx$Transmission == "HCW")*1;
x45=(Mx$species=="Klebs" & Mx$Transmission == "insect")*1;
x46=(Mx$species=="Klebs" & Mx$Transmission == "multi")*1;
x51=(Mx$species=="Acin" & Mx$Transmission == "env")*1;
x52=(Mx$species=="Acin" & Mx$Transmission == "equip")*1;
x53=(Mx$species=="Acin" & Mx$Transmission == "HCW")*1;
x54=(Mx$species=="Acin" & Mx$Transmission == "PTP")*1;
x55=(Mx$species=="Acin" & Mx$Transmission == "multi")*1;
x61=(Mx$species=="Serr" & Mx$Transmission == "air")*1;
x62=(Mx$species=="Serr" & Mx$Transmission == "env")*1;
x63=(Mx$species=="Serr" & Mx$Transmission == "equip")*1;
x64=(Mx$species=="Serr" & Mx$Transmission == "HCW")*1;
x65=(Mx$species=="Serr" & Mx$Transmission == "multi")*1;
x71=(Mx$species=="Enterob" & Mx$Transmission == "env")*1;
x72=(Mx$species=="Enterob" & Mx$Transmission == "equip")*1;
x73=(Mx$species=="Enterob" & Mx$Transmission == "food")*1;
x74=(Mx$species=="Enterob" & Mx$Transmission == "HCW")*1;
x75=(Mx$species=="Enterob" & Mx$Transmission == "PTP")*1;
x76=(Mx$species=="Enterob" & Mx$Transmission == "multi")*1;
x81=(Mx$species=="Hep B" & Mx$Transmission == "equip")*1;
x82=(Mx$species=="Hep B" & Mx$Transmission == "HCW")*1;
x83=(Mx$species=="Hep B" & Mx$Transmission == "PTP")*1;
x84=(Mx$species=="Hep B" & Mx$Transmission == "multi")*1;
x91=(Mx$species=="Hep C" & Mx$Transmission == "env")*1;
x92=(Mx$species=="Hep C" & Mx$Transmission == "equip")*1;
x93=(Mx$species=="Hep C" & Mx$Transmission == "HCW")*1;
x94=(Mx$species=="Hep C" & Mx$Transmission == "PTP")*1;
x95=(Mx$species=="Hep C" & Mx$Transmission == "multi")*1;
x101=(Mx$species=="Strep" & Mx$Transmission == "air")*1;
x102=(Mx$species=="Strep" & Mx$Transmission == "env")*1;
x103=(Mx$species=="Strep" & Mx$Transmission == "equip")*1;
x104=(Mx$species=="Strep" & Mx$Transmission == "food")*1;
x105=(Mx$species=="Strep" & Mx$Transmission == "HCW")*1;
x106=(Mx$species=="Strep" & Mx$Transmission == "PTP")*1;
x107=(Mx$species=="Strep" & Mx$Transmission == "multi")*1;
x111=(Mx$species=="Salm" & Mx$Transmission == "env")*1;
x112=(Mx$species=="Salm" & Mx$Transmission == "equip")*1;
x113=(Mx$species=="Salm" & Mx$Transmission == "food")*1;
x114=(Mx$species=="Salm" & Mx$Transmission == "HCW")*1;
x115=(Mx$species=="Salm" & Mx$Transmission == "PTP")*1;
x116=(Mx$species=="Salm" & Mx$Transmission == "multi")*1;
x121=(Mx$species=="Legion" & Mx$Transmission == "env")*1;
x122=(Mx$species=="Legion" & Mx$Transmission == "multi")*1;
x131=(Mx$species=="E. coli" & Mx$Transmission == "env")*1;
x132=(Mx$species=="E. coli" & Mx$Transmission == "food")*1;
x133=(Mx$species=="E. coli" & Mx$Transmission == "HCW")*1;
x134=(Mx$species=="E. coli" & Mx$Transmission == "PTP")*1;
x135=(Mx$species=="E. coli" & Mx$Transmission == "multi")*1;
x141=(Mx$species=="C. diff" & Mx$Transmission == "env")*1;
x142=(Mx$species=="C. diff" & Mx$Transmission == "equip")*1;
x143=(Mx$species=="C. diff" & Mx$Transmission == "HCW")*1;
x144=(Mx$species=="C. diff" & Mx$Transmission == "PTP")*1;
x145=(Mx$species=="C. diff" & Mx$Transmission == "multi")*1;

y4 = function(b11, b12, b13, b14, b15, b21, b22, b23, b24, b31,b32,b33,b34,b41,b42,b43,b44,b45,b46,b51,b52,b53, b54, b55, b61, b62, b63, b64, b65, b71, b72, b73, b74, b75, b76, b81, b82, b83, b84, b91, b92, b93, b94, b95, b101, b102, b103, b104,
              b105, b106, b107, b111, b112, b113, b114, b115, b116, b121, b122, b131, b132, b133,
              b134, b135, b141, b142, b143, b144, b145){
  
  mu = b11*x11+ b12*x12 + b13*x13 + b14*x14 + b15*x15+b21*x21 + b22*x22 + b23*x23 + b24*x24 + b31*x31 + b32*x32 + b33*x33 + b34*x34+ b41*x41 + b42*x42 + b43*x43 + b44*x44 + b45*x45 + b46*x46 + b51*x51 + b52*x52 + b53*x53 + b54*x54 + b55*x55+ b61*x61 + b62*x62 + b63*x63 + b64*x64 + b65*x65+ b71*x71 + b72*x72 + b73*x73 + b74*x74 + b75*x75 + b76*x76+ b81*x81 + b82*x82 + b83*x83 + b84*x84+ b91*x91 + b92*x92 + b93*x93 + b94*x94 + b95*x95+ b101*x101 + b102*x102 + b103*x103 + b104*x104 + b105*x105 + b106*x106 + b107*x107+ b111*x111 + b112*x112+ b113*x113 + b114*x114 + b115*x115 + b116*x116+ b121*x121 + b112*x122+ b131*x131 + b132*x132 + b133*x133 + b134*x134 + b135*x135+ b141*x141 + b142*x142 + b143*x143 + b144*x144+b145*x145
  mu[mu<0]=0
  return(mu)
}

#The function for the negative log likelihood
LL4 = function (b11,b12,b13,b14,b15,b21,b22,b23,b24,b31,b32,b33,b34,b41,b42,b43,b44,b45,b46,b51,b52,b53,b54,b55,b61,b62,b63,b64,b65,b71,b72,b73,b74,b75,b76,b81,b82,b83,b84,b91,b92,b93,b94,b95,b101,b102,b103,b104,b105,b106,b107,b111,b112,b113,b114,b115,b116,b121,b122,b131,b132,b133,b134,b135,b141,b142,b143,b144,b145,y=data){
  mu = y4(b11=b11,b12=b12,b13=b13,b14=b14,b15=b15,b21=b21,b22=b22,b23=b23,b24=b24,b31=b31,b32=b32,b33=b33,b34=b34,b41=b41,b42=b42,b43=b43,b44=b44,b45=b45,b46=b46,b51=b51,b52=b52,b53=b53,b54=b54,b55=b55,b61=b61,b62=b62,b63=b63,b64=b64,b65=b65,b71=b71,b72=b72,b73=b73,b74=b74,b75=b75,b76=b76,b81=b81,b82=b82,b83=b83,b84=b84,b91=b91,b92=b92,b93=b93,b94=b94,b95=b95,b101=b101,b102=b102,b103=b103,b104=b104,b105=b105,b106=b106,b107=b107,b111=b111,b112=b112,b113=b113,b114=b114,b115=b115,b116=b116,b121=b121,b122=b122,b131=b131,b132=b132,b133=b133,b134=b134,b135=b135,b141=b141,b142=b142,b143=b143,b144=b144,b145=b145)
  #get the total negative log likelihood
  loglike= -sum(dnorm(y,mu,log=TRUE))
  return(loglike)
}

Cases_Int = mle2(minuslogl = LL4, start = list(b11=2,b12=2,b13=2,b14=2,b15=2,b21=2,b22=2,b23=2,b24=2,b31=2,b32=2,b33=2,b34=2,b41=2,b42=2,b43=2,b44=2,b45=2,b46=2,b51=2,b52=2,b53=2,b54=2,b55=2,b61=2,b62=2,b63=2,b64=2,b65=2,b71=2,b72=2,b73=2,b74=2,b75=2,b76=2,b81=2,b82=2,b83=2,b84=2,b91=2,b92=2,b93=2,b94=2,b95=2,b101=2,b102=2,b103=2,b104=2,b105=2,b106=2,b107=2,b111=2,b112=2,b113=2,b114=2,b115=2,b116=2,b121=2,b122=2,b131=2,b132=2,b133=2,b134=2,b135=2,b141=2,b142=2,b143=2,b144=2,b145=2), control = list(maxit = 5000))
Cases_Int_Summary = summary(Cases_Int)
#The residuals
resCase_Int = y4(coef(Cases_Int_Summary)[1,1], coef(Cases_Int_Summary)[2,1], coef(Cases_Int_Summary)[3,1], coef(Cases_Int_Summary)[4,1], coef(Cases_Int_Summary)[5,1], coef(Cases_Int_Summary)[6,1], coef(Cases_Int_Summary)[7,1], coef(Cases_Int_Summary)[8,1], coef(Cases_Int_Summary)[9,1], coef(Cases_Int_Summary)[10,1], coef(Cases_Int_Summary)[11,1], coef(Cases_Int_Summary)[12,1], coef(Cases_Int_Summary)[13,1], coef(Cases_Int_Summary)[14,1],coef(Cases_Int_Summary)[15,1], coef(Cases_Int_Summary)[16,1], coef(Cases_Int_Summary)[17,1], coef(Cases_Int_Summary)[18,1], coef(Cases_Int_Summary)[19,1], coef(Cases_Int_Summary)[20,1], coef(Cases_Int_Summary)[21,1], coef(Cases_Int_Summary)[22,1], coef(Cases_Int_Summary)[23,1], coef(Cases_Int_Summary)[24,1], coef(Cases_Int_Summary)[25,1], coef(Cases_Int_Summary)[26,1], coef(Cases_Int_Summary)[27,1], coef(Cases_Int_Summary)[28,1],coef(Cases_Int_Summary)[29,1], coef(Cases_Int_Summary)[30,1], coef(Cases_Int_Summary)[31,1], coef(Cases_Int_Summary)[32,1], coef(Cases_Int_Summary)[33,1], coef(Cases_Int_Summary)[34,1], coef(Cases_Int_Summary)[35,1], coef(Cases_Int_Summary)[36,1], coef(Cases_Int_Summary)[37,1], coef(Cases_Int_Summary)[38,1], coef(Cases_Int_Summary)[39,1], coef(Cases_Int_Summary)[40,1], coef(Cases_Int_Summary)[41,1], coef(Cases_Int_Summary)[42,1], coef(Cases_Int_Summary)[43,1], coef(Cases_Int_Summary)[44,1], coef(Cases_Int_Summary)[45,1], coef(Cases_Int_Summary)[46,1], coef(Cases_Int_Summary)[47,1], coef(Cases_Int_Summary)[48,1], coef(Cases_Int_Summary)[49,1], coef(Cases_Int_Summary)[50,1], coef(Cases_Int_Summary)[51,1], coef(Cases_Int_Summary)[52,1], coef(Cases_Int_Summary)[53,1], coef(Cases_Int_Summary)[54,1], coef(Cases_Int_Summary)[55,1], coef(Cases_Int_Summary)[56,1],coef(Cases_Int_Summary)[57,1], coef(Cases_Int_Summary)[58,1], coef(Cases_Int_Summary)[59,1], coef(Cases_Int_Summary)[60,1], coef(Cases_Int_Summary)[61,1], coef(Cases_Int_Summary)[62,1], coef(Cases_Int_Summary)[63,1], coef(Cases_Int_Summary)[64,1], coef(Cases_Int_Summary)[65,1], coef(Cases_Int_Summary)[66,1], coef(Cases_Int_Summary)[67,1], coef(Cases_Int_Summary)[68,1], coef(Cases_Int_Summary)[69,1])-data

###########################
# Response variable: log Rate
# Model 5: Constant only
# Model 6: Transmission route is the predictor variable
# Model 7: Species is the predictor variable
# Model 8: Transmission routes x species interaction is the predictor variable

# Change the response variable to the log case rate:
logRate=log(Mx$Cases/Mx$Duration)
data = logRate

###### Model 5: Constant only model
y1 = function(a){
  mu = a
  return(mu)
}

#The function for the negative log likelihood
LL1 = function (a,y=data){
  mu = y1(a=a)
  #get the total negative log likelihood
  loglike= -sum(dnorm(y,mu,log=TRUE))
  return(loglike)
}

#The call to bbmle and results summary:
Rate_Constant = mle2(minuslogl = LL1, start = list(a=-2), control = list(maxit = 5000))
Rate_Constant_Summary = summary(Rate_Constant)

##### Model 6: Transmission route as the predictor variable
x1=xMx[,1]
x2=xMx[,2]
x3=xMx[,3]
x4=xMx[,4]
x5=xMx[,5]
x6=xMx[,6]
x7=xMx[,7]
x8=xMx[,8]

#function for model
y2 = function(b1,b2,b3,b4,b5,b6,b7,b8){
  mu = b1*x1 + b2*x2 + b3*x3 + b4*x4 + b5*x5 + b6*x6 + b7*x7 + b8*x8
  return(mu)
}
#The function for the negative log likelihood
LL2 = function (b1,b2,b3,b4,b5,b6,b7,b8,y=data){
  mu = y2(b1=b1,b2=b2,b3=b3,b4=b4,b5=b5,b6=b6,b7=b7,b8=b8)
  #get the total negative log likelihood
  loglike= -sum(dnorm(y,mu,log=TRUE))
  return(loglike)
}
#The call to bbmle and results summary:
Rate_TR = mle2(minuslogl = LL2, start = list(b1=-2,b2=-2,b3=-2,b4=-2,b5=0,b6=0,b7=-2,b8=-2), control = list(maxit = 5000))
Rate_TR_Summary = summary(Rate_TR)
# The residuals
resRate_TR = y2(coef(Rate_TR_Summary)[1,1], coef(Rate_TR_Summary)[2,1], coef(Rate_TR_Summary)[3,1], coef(Rate_TR_Summary)[4,1], coef(Rate_TR_Summary)[5,1],coef(Rate_TR_Summary)[6,1], coef(Rate_TR_Summary)[7,1], coef(Rate_TR_Summary)[8,1])-data

##### Model 7: Species as the predictor variable
# Vector of 1 0 1.
x1=zMx[,1]
x2=zMx[,2]
x3=zMx[,3]
x4=zMx[,4]
x5=zMx[,5]
x6=zMx[,6]
x7=zMx[,7]
x8=zMx[,8]
x9=zMx[,9]
x10=zMx[,10]
x11=zMx[,11]
x12=zMx[,12]
x13=zMx[,13]
x14=zMx[,14]

#function for model
y3 = function(b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14){
  mu = b1*x1 + b2*x2 + b3*x3 + b4*x4 + b5*x5 + b6*x6 + b7*x7 + b8*x8 + b9*x9+ b10*x10 + b11*x11 + b12*x12 + b13*x13 + b14*x14
  return(mu)
}

#The function for the negative log likelihood
LL3 = function (b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,y=data){
  mu = y3(b1=b1,b2=b2,b3=b3,b4=b4,b5=b5,b6=b6,b7=b7,b8=b8,b9=b9,b10=b10,b11=b11,b12=b12,b13=b13,b14=b14)
  #get the total negative log likelihood
  loglike= -sum(dnorm(y,mu,log=TRUE))
  return(loglike)
}

#The call to bbmle and results summary:
Rate_Species = mle2(minuslogl = LL3, start = list(b1=-2,b2=-2,b3=-2,b4=-2,b5=-2,b6=-2,b7=-2,b8=-2,b9=-2,b10=-2,b11=-2,b12=-2,b13=-2,b14=-2), control = list(maxit = 5000))
Rate_Species_Summary = summary(Rate_Species)
#The residuals
resRate_Species = y3(coef(Rate_Species_Summary)[1,1], coef(Rate_Species_Summary)[2,1], coef(Rate_Species_Summary)[3,1], coef(Rate_Species_Summary)[4,1], coef(Rate_Species_Summary)[5,1], coef(Rate_Species_Summary)[6,1], coef(Rate_Species_Summary)[7,1], coef(Rate_Species_Summary)[8,1], coef(Rate_Species_Summary)[9,1], coef(Rate_Species_Summary)[10,1], coef(Rate_Species_Summary)[11,1], coef(Rate_Species_Summary)[12,1], coef(Rate_Species_Summary)[13,1], coef(Rate_Species_Summary)[14,1])-data

# Model 8: Interaction
x11=(Mx$species=="Staph" & Mx$Transmission == "air")*1
x12=(Mx$species=="Staph" & Mx$Transmission == "env")*1
x13=(Mx$species=="Staph" & Mx$Transmission == "equip")*1
x14=(Mx$species=="Staph" & Mx$Transmission == "HCW")*1;
x15=(Mx$species=="Staph" & Mx$Transmission == "multi")*1;
x21=(Mx$species=="Enteroc" & Mx$Transmission == "env")*1;
x22=(Mx$species=="Enteroc" & Mx$Transmission == "equip")*1;
x23=(Mx$species=="Enteroc" & Mx$Transmission == "HCW")*1;
x24=(Mx$species=="Enteroc" & Mx$Transmission == "multi")*1;
x31=(Mx$species=="Pseudo" & Mx$Transmission == "env")*1;
x32=(Mx$species=="Pseudo" & Mx$Transmission == "equip")*1;
x33=(Mx$species=="Pseudo" & Mx$Transmission == "HCW")*1;
x34=(Mx$species=="Pseudo" & Mx$Transmission == "multi")*1;
x41=(Mx$species=="Klebs" & Mx$Transmission == "env")*1;
x42=(Mx$species=="Klebs" & Mx$Transmission == "equip")*1;
x43=(Mx$species=="Klebs" & Mx$Transmission == "food")*1;
x44=(Mx$species=="Klebs" & Mx$Transmission == "HCW")*1;
x45=(Mx$species=="Klebs" & Mx$Transmission == "insect")*1;
x46=(Mx$species=="Klebs" & Mx$Transmission == "multi")*1;
x51=(Mx$species=="Acin" & Mx$Transmission == "env")*1;
x52=(Mx$species=="Acin" & Mx$Transmission == "equip")*1;
x53=(Mx$species=="Acin" & Mx$Transmission == "HCW")*1;
x54=(Mx$species=="Acin" & Mx$Transmission == "PTP")*1;
x55=(Mx$species=="Acin" & Mx$Transmission == "multi")*1;
x61=(Mx$species=="Serr" & Mx$Transmission == "air")*1;
x62=(Mx$species=="Serr" & Mx$Transmission == "env")*1;
x63=(Mx$species=="Serr" & Mx$Transmission == "equip")*1;
x64=(Mx$species=="Serr" & Mx$Transmission == "HCW")*1;
x65=(Mx$species=="Serr" & Mx$Transmission == "multi")*1;
x71=(Mx$species=="Enterob" & Mx$Transmission == "env")*1;
x72=(Mx$species=="Enterob" & Mx$Transmission == "equip")*1;
x73=(Mx$species=="Enterob" & Mx$Transmission == "food")*1;
x74=(Mx$species=="Enterob" & Mx$Transmission == "HCW")*1;
x75=(Mx$species=="Enterob" & Mx$Transmission == "PTP")*1;
x76=(Mx$species=="Enterob" & Mx$Transmission == "multi")*1;
x81=(Mx$species=="Hep B" & Mx$Transmission == "equip")*1;
x82=(Mx$species=="Hep B" & Mx$Transmission == "HCW")*1;
x83=(Mx$species=="Hep B" & Mx$Transmission == "PTP")*1;
x84=(Mx$species=="Hep B" & Mx$Transmission == "multi")*1;
x91=(Mx$species=="Hep C" & Mx$Transmission == "env")*1;
x92=(Mx$species=="Hep C" & Mx$Transmission == "equip")*1;
x93=(Mx$species=="Hep C" & Mx$Transmission == "HCW")*1;
x94=(Mx$species=="Hep C" & Mx$Transmission == "PTP")*1;
x95=(Mx$species=="Hep C" & Mx$Transmission == "multi")*1;
x101=(Mx$species=="Strep" & Mx$Transmission == "air")*1;
x102=(Mx$species=="Strep" & Mx$Transmission == "env")*1;
x103=(Mx$species=="Strep" & Mx$Transmission == "equip")*1;
x104=(Mx$species=="Strep" & Mx$Transmission == "food")*1;
x105=(Mx$species=="Strep" & Mx$Transmission == "HCW")*1;
x106=(Mx$species=="Strep" & Mx$Transmission == "PTP")*1;
x107=(Mx$species=="Strep" & Mx$Transmission == "multi")*1;
x111=(Mx$species=="Salm" & Mx$Transmission == "env")*1;
x112=(Mx$species=="Salm" & Mx$Transmission == "equip")*1;
x113=(Mx$species=="Salm" & Mx$Transmission == "food")*1;
x114=(Mx$species=="Salm" & Mx$Transmission == "HCW")*1;
x115=(Mx$species=="Salm" & Mx$Transmission == "PTP")*1;
x116=(Mx$species=="Salm" & Mx$Transmission == "multi")*1;
x121=(Mx$species=="Legion" & Mx$Transmission == "env")*1;
x122=(Mx$species=="Legion" & Mx$Transmission == "multi")*1;
x131=(Mx$species=="E. coli" & Mx$Transmission == "env")*1;
x132=(Mx$species=="E. coli" & Mx$Transmission == "food")*1;
x133=(Mx$species=="E. coli" & Mx$Transmission == "HCW")*1;
x134=(Mx$species=="E. coli" & Mx$Transmission == "PTP")*1;
x135=(Mx$species=="E. coli" & Mx$Transmission == "multi")*1;
x141=(Mx$species=="C. diff" & Mx$Transmission == "env")*1;
x142=(Mx$species=="C. diff" & Mx$Transmission == "equip")*1;
x143=(Mx$species=="C. diff" & Mx$Transmission == "HCW")*1;
x144=(Mx$species=="C. diff" & Mx$Transmission == "PTP")*1;
x145=(Mx$species=="C. diff" & Mx$Transmission == "multi")*1;

y4 = function(b11, b12, b13, b14, b15, b21, b22, b23, b24, b31,b32,b33,b34,b41,b42,b43,b44,b45,b46,b51,b52,b53, b54, b55, b61, b62, b63, b64, b65, b71, b72, b73, b74, b75, b76, b81, b82, b83, b84, b91, b92, b93, b94, b95, b101, b102, b103, b104,
              b105, b106, b107, b111, b112, b113, b114, b115, b116, b121, b122, b131, b132, b133,
              b134, b135, b141, b142, b143, b144, b145){
  
  mu = b11*x11+ b12*x12 + b13*x13 + b14*x14 + b15*x15+b21*x21 + b22*x22 + b23*x23 + b24*x24 + b31*x31 + b32*x32 + b33*x33 + b34*x34+ b41*x41 + b42*x42 + b43*x43 + b44*x44 + b45*x45 + b46*x46 + b51*x51 + b52*x52 + b53*x53 + b54*x54 + b55*x55+ b61*x61 + b62*x62 + b63*x63 + b64*x64 + b65*x65+ b71*x71 + b72*x72 + b73*x73 + b74*x74 + b75*x75 + b76*x76+ b81*x81 + b82*x82 + b83*x83 + b84*x84+ b91*x91 + b92*x92 + b93*x93 + b94*x94 + b95*x95+ b101*x101 + b102*x102 + b103*x103 + b104*x104 + b105*x105 + b106*x106 + b107*x107+ b111*x111 + b112*x112+ b113*x113 + b114*x114 + b115*x115 + b116*x116+ b121*x121 + b122*x122+ b131*x131 + b132*x132 + b133*x133 + b134*x134 + b135*x135+ b141*x141 + b142*x142 + b143*x143 + b144*x144 + b145*x145
  return(mu)
}

#The function for the negative log likelihood
LL4 = function (b11,b12,b13,b14,b15,b21,b22,b23,b24,b31,b32,b33,b34,b41,b42,b43,b44,b45,b46,b51,b52,b53,b54,b55,b61,b62,b63,b64,b65,b71,b72,b73,b74,b75,b76,b81,b82,b83,b84,b91,b92,b93,b94,b95,b101,b102,b103,b104,b105,b106,b107,b111,b112,b113,b114,b115,b116,b121,b122,b131,b132,b133,b134,b135,b141,b142,b143,b144,b145, y=data){
  mu = y4(b11=b11,b12=b12,b13=b13,b14=b14,b15=b15,b21=b21,b22=b22,b23=b23,b24=b24,b31=b31,b32=b32,b33=b33,b34=b34,b41=b41,b42=b42,b43=b43,b44=b44,b45=b45,b46=b46,b51=b51,b52=b52,b53=b53,b54=b54,b55=b55,b61=b61,b62=b62,b63=b63,b64=b64,b65=b65,b71=b71,b72=b72,b73=b73,b74=b74,b75=b75,b76=b76,b81=b81,b82=b82,b83=b83,b84=b84,b91=b91,b92=b92,b93=b93,b94=b94,b95=b95,b101=b101,b102=b102,b103=b103,b104=b104,b105=b105,b106=b106,b107=b107,b111=b111,b112=b112,b113=b113,b114=b114,b115=b115,b116=b116,b121=b121,b122=b122,b131=b131,b132=b132,b133=b133,b134=b134,b135=b135,b141=b141,b142=b142,b143=b143,b144=b144,b145=b145)
  #get the total negative log likelihood
  loglike= -sum(dnorm(y,mu,log=TRUE))
  return(loglike)
}

Rate_Int = mle2(minuslogl = LL4, start = list(b11=-2,b12=-2,b13=-2,b14=-2,b15=-2,b21=-2,b22=-2,b23=-2,b24=-2,b31=-2,b32=-2,b33=-2,b34=-2,b41=-2,b42=-2,b43=-2,b44=-2,b45=-2,b46=-2,b51=-2,b52=-2,b53=-2,b54=-2,b55=-2,b61=-2,b62=-2,b63=-2,b64=-2,b65=-2,b71=-2,b72=-2,b73=-2,b74=-2,b75=-2,b76=-2,b81=-2,b82=-2,b83=-2,b84=-2,b91=-2,b92=-2,b93=-2,b94=-2,b95=-2,b101=-2,b102=-2,b103=-2,b104=-2,b105=-2,b106=-2,b107=-2,b111=-2,b112=-2,b113=-2,b114=-2,b115=-2,b116=-2,b121=-2,b122=-2,b131=-2,b132=-2,b133=-2,b134=-2,b135=-2,b141=-2,b142=-2,b143=-2,b144=-2, b145=-2), control = list(maxit = 5000))
Rate_Int_Summary = summary(Rate_Int)
# The residuals
resRate_Int = y4(coef(Rate_Int_Summary)[1,1], coef(Rate_Int_Summary)[2,1], coef(Rate_Int_Summary)[3,1], coef(Rate_Int_Summary)[4,1], coef(Rate_Int_Summary)[5,1], coef(Rate_Int_Summary)[6,1], coef(Rate_Int_Summary)[7,1], coef(Rate_Int_Summary)[8,1], coef(Rate_Int_Summary)[9,1], coef(Rate_Int_Summary)[10,1], coef(Rate_Int_Summary)[11,1], coef(Rate_Int_Summary)[12,1], coef(Rate_Int_Summary)[13,1], coef(Rate_Int_Summary)[14,1],coef(Rate_Int_Summary)[15,1], coef(Rate_Int_Summary)[16,1], coef(Rate_Int_Summary)[17,1], coef(Rate_Int_Summary)[18,1], coef(Rate_Int_Summary)[19,1], coef(Rate_Int_Summary)[20,1], coef(Rate_Int_Summary)[21,1], coef(Rate_Int_Summary)[22,1], coef(Rate_Int_Summary)[23,1], coef(Rate_Int_Summary)[24,1], coef(Rate_Int_Summary)[25,1], coef(Rate_Int_Summary)[26,1], coef(Rate_Int_Summary)[27,1], coef(Rate_Int_Summary)[28,1],coef(Rate_Int_Summary)[29,1], coef(Rate_Int_Summary)[30,1], coef(Rate_Int_Summary)[31,1], coef(Rate_Int_Summary)[32,1], coef(Rate_Int_Summary)[33,1], coef(Rate_Int_Summary)[34,1], coef(Rate_Int_Summary)[35,1], coef(Rate_Int_Summary)[36,1], coef(Rate_Int_Summary)[37,1], coef(Rate_Int_Summary)[38,1], coef(Rate_Int_Summary)[39,1], coef(Rate_Int_Summary)[40,1], coef(Rate_Int_Summary)[41,1], coef(Rate_Int_Summary)[42,1], coef(Rate_Int_Summary)[43,1], coef(Rate_Int_Summary)[44,1], coef(Rate_Int_Summary)[45,1], coef(Rate_Int_Summary)[46,1], coef(Rate_Int_Summary)[47,1], coef(Rate_Int_Summary)[48,1], coef(Rate_Int_Summary)[49,1], coef(Rate_Int_Summary)[50,1], coef(Rate_Int_Summary)[51,1], coef(Rate_Int_Summary)[52,1], coef(Rate_Int_Summary)[53,1], coef(Rate_Int_Summary)[54,1], coef(Rate_Int_Summary)[55,1], coef(Rate_Int_Summary)[56,1],coef(Rate_Int_Summary)[57,1], coef(Rate_Int_Summary)[58,1], coef(Rate_Int_Summary)[59,1], coef(Rate_Int_Summary)[60,1], coef(Rate_Int_Summary)[61,1], coef(Rate_Int_Summary)[62,1], coef(Rate_Int_Summary)[63,1], coef(Rate_Int_Summary)[64,1], coef(Rate_Int_Summary)[65,1], coef(Rate_Int_Summary)[66,1], coef(Rate_Int_Summary)[67,1], coef(Rate_Int_Summary)[68,1], coef(Rate_Int_Summary)[69,1])-data

#################
# Make an AIC table that compares the model AICs
AICtab(Cases_Constant, Cases_TR, Cases_Species, Cases_Int,weights=TRUE)
AICtab(Rate_Constant, Rate_TR, Rate_Species, Rate_Int,weights=TRUE)
  
# Recover the estimated parameters and confidence intervals that can be used to make graphs of parameter
# estimates
# Note: estimating the confidence intervals, especially for the Interaction model can take
# a while

# The fitted coefficients
coeffs2 = coef(Rate_Int_Summary)
# # Estimating the confidence intervals
CI2 = confint(Rate_Int)
# # Making a vector with the mean, and lower and upper CIs.
coef_vec2 = array(0,c(69,3))
coef_vec2[,1] = coeffs2[,1]
coef_vec2[,2] = CI2[,1]
coef_vec2[,3] = CI2[,2]
# The labels
coef_labs2 = c("Staph-air", "Staph-env", "Staph-equip", "Staph-HCW", "Staph-multi", "Enteroc - env", "Enteroc-equip", "Enteroc-HCW", "Enteroc-multi", "Pseudo-env","Pseudo-equip","Pseudo-HCW","Pseudo-multi", "Klebs-env","Klebs-equip","Klebs-food","Klebs-HCW","Klebs-insect","Klebs-multi","Acin-env","Acin-equip","Acin-HCW", "Acin-PTP", "Acin-multi", "Serr-air", "Serr-env", "Serr-equip", "Serr-HCW", "Serr-multi", "Enterob-env", "Enterob-equip", "Enterob-food", "Enterob-HCW", "Enterob-PTP", "Enterob-multi", "Hep. B-equip", "Hep. B-HCW", "Hep. B-PTP", "Hep. B-multi", "Hep. C-env", "Hep. C-equip", "Hep. C-HCW", "Hep. C-PTP", "Hep. C-multi", "Strep-air", "Strep-env", "Strep-equip", "Strep-food", "Strep-HCW", "Strep-PTP", "Strep-multi", "Salm-env", "Salm-equip", "Salm-food", "Salm-HCW", "Salm-PTP","Salm-multi", "Legion-env","Legion-multi", "E. coli-env", "E. coli-food","E. coli-HCW", "E. coli-PTP", "E. coli-multi", "C. diff-env", "C. diff- equip", "C. diff-HCW", "C. diff-PTP", "C. diff-multi")
# Ordering by the estimated coefficients and making sure the labels are in the correct order
xx = data.frame(cbind(coef_labs2,coef_vec2[,1]))
xx2=xx[with(xx, order(coef_vec2[,1])), ]
coef_labs2 = xx2[,1]
sorted_coeffs2 = coef_vec2[order(coef_vec2[,1]),]

# As above but now for the Species - Cases model.
coeffs = exp(coef(Cases_Species_Summary))
CI = confint(Cases_Species)
coef_vec = array(0,c(14,3))
coef_vec[,1] = coeffs[,1]
coef_vec[,2] = CI[,1]
coef_vec[,3] = CI[,2]
sorted_coeffs = coef_vec[order(coef_vec[,1]),]
coef_labs = c("Strep", "Legion", "Hep C", "Heb B", "Pseudo", "E. coli", "Enterob", "Staph", "Acin", "Serr", "C. diff", "Klebs", "Enteroc", "Salm")

# Print a summary of all models
print(Cases_Constant_Summary)
print(Cases_TR_Summary)
print(Cases_Species_Summary)
print(Cases_Int_Summary)
print(Rate_Constant_Summary)
print(Rate_TR_Summary)
print(Rate_Species_Summary)
print(Rate_Int_Summary)

# Print the number of data points for each predictor variable
print(colSums(xMx))
print(colSums(zMx))

########################
# CODE TO MAKE THE FIGURES THAT APPEAR IN THE MANUSCRIPT
# Boxplots of the data
setEPS()
postscript("/Users/amyhurford/Desktop/Figure1.eps")
bymed1 <- with(Mx, reorder(Transmission, Cases..patient., median))
bymed2 <- with(Mx, reorder(species, Cases..patient., median))
bymed3 <- with(Mx, reorder(Transmission, Cases..patient./Duration..days., median))
bymed4 <- with(Mx, reorder(species, Cases..patient./Duration..days., median))
par(mfrow = c(2,2), mar = c(5, 5, 3, 3), mgp = c(4, 1, 0))
boxplot(log(Mx$Cases) ~ bymed1, las=2, ylab="log CASES", xlab="Transmission route")
boxplot(log(Mx$Cases) ~ bymed2, las=2, ylab="log CASES", xlab="Species")
boxplot(log(Mx$Cases/Mx$Duration) ~ bymed3, las=2, ylab = "log RATE", xlab="Transmission route")
boxplot(log(Mx$Cases/Mx$Duration) ~ bymed4, las=2, ylab="log RATE", xlab="Species")
dev.off()

#plot of coefficients of Cases - Species model 
setEPS()
postscript("/Users/amyhurford/Desktop/Figure5a.eps",width=10,height=5)
par(mgp=c(4,1,0),mar = c(4, 5, 3, 3), mfrow = c(1,1))
plotCI(1:14, sorted_coeffs[,1], ui=sorted_coeffs[,3], li=sorted_coeffs[,2], xaxt="n", ylab = "Mean number of cases", las=2)
axis(1,1:14, labels = coef_labs, las=2)
dev.off()

# And plot of coefficients for the Rate - Interaction models
setEPS()
postscript("/Users/amyhurford/Desktop/Figure5b.eps",width=15,height=7)
par(mgp=c(4,1,0),mar = c(8, 5, 3, 3), mfrow = c(1,1))
plotCI(1:69, sorted_coeffs2[1:69,1], ui=sorted_coeffs2[1:69,3], li=sorted_coeffs2[1:69,2], xaxt="n", ylab = "Log mean number of cases per day", las=2)
axis(1,1:69, labels = coef_labs2, las=2)
dev.off()

# Checking the assumptions of normality for all of the models:
setEPS()
postscript("/Users/amyhurford/Desktop/Figure4.eps")
par(mfrow = c(4,2),mar = c(2,4,2,2))
qqnorm(logCases, main="", ylab = "Constant - Cases", xlab = "Theoretical quantiles")
qqline(logCases)
qqnorm(log(Mx$Cases/Mx$Duration), main="", ylab = "Constant - Rate", xlab = "Theoretical quantiles")
qqline(logRate)
qqnorm(resCase_TR,main="", ylab = "TR - Cases", xlab = "Theoretical quantiles")
qqline(resCase_TR)
qqnorm(resRate_TR, main="", ylab = "TR - Rate", xlab = "Theoretical quantiles")
qqline(resRate_TR)
qqnorm(resCase_Species,main="", ylab = "Species - Cases", xlab = "Theoretical quantiles")
qqline(resCase_Species)
qqnorm(resRate_Species, main="", ylab = "Species - Rate", xlab = "Theoretical quantiles")
qqline(resRate_Species)
qqnorm(resCase_Int, main="", ylab = "Int - Cases", xlab = "Theoretical quantiles")
qqline(resCase_Int)
qqnorm(resRate_Int, main="", ylab = "Int - Rate", xlab = "Theoretical quantiles")
qqline(resRate_Int)
dev.off()

# Code to make the interaction boxplot for Cases
setEPS()
postscript("/Users/amyhurford/Desktop/Figure2.eps")
par(mfrow = c(4,4), mar = c(3.5, 2, 2, 2), mgp = c(2, 1, 0))
#bymed1 <- with(MxAcin, reorder(Transmission, Cases..patient., median))
boxplot(log(MxAcin$Cases)~MxAcin$Transmission, las=2, ylab = "log CASES", main = "Acinobacter")
#bymed1 <- with(MxCdiff, reorder(Transmission, Cases..patient., median))
boxplot(log(MxCdiff$Cases) ~ MxCdiff$Transmission, las=2, main = "C. difficle")
#bymed1 <- with(MxEcoli, reorder(Transmission, Cases..patient., median))
boxplot(log(MxEcoli$Cases) ~ MxEcoli$Transmission, las=2, main = "E. coli")
#bymed1 <- with(MxEnterob, reorder(Transmission, Cases..patient., median))
boxplot(log(MxEnterob$Cases) ~ MxEnterob$Transmission, las=2, main = "Enterobacter")
#bymed1 <- with(MxEnteroc, reorder(Transmission, Cases..patient., median))
boxplot(log(MxEnteroc$Cases) ~ MxEnteroc$Transmission, las=2, ylab = "log CASES", main = "Enterococci")
#bymed1 <- with(MxHepB, reorder(Transmission, Cases..patient., median))
boxplot(log(MxHepB$Cases) ~ MxHepB$Transmission, las=2, main = "Hep. B")
#bymed1 <- with(MxHepC, reorder(Transmission, Cases..patient., median))
boxplot(log(MxHepC$Cases) ~ MxHepC$Transmission, las=2, main = "Hep. C")
#bymed1 <- with(MxKlebs, reorder(Transmission, Cases..patient., median))
boxplot(log(MxKlebs$Cases) ~ MxKlebs$Transmission, las=2, main = "Klebsiella")
#bymed1 <- with(MxLegion, reorder(Transmission, Cases..patient., median))
boxplot(log(MxLegion$Cases) ~ MxLegion$Transmission, las=2, main = "Legionella",ylab = "log CASES")
#bymed1 <- with(MxPseudo, reorder(Transmission, Cases..patient., median))
boxplot(log(MxPseudo$Cases) ~ MxPseudo$Transmission, las=2, main = "Pseudomonas")
#bymed1 <- with(MxSalm, reorder(Transmission, Cases..patient., median))
boxplot(log(MxSalm$Cases) ~ MxSalm$Transmission, las=2, main  = "Salmonella")
#bymed1 <- with(MxSerr, reorder(Transmission, Cases..patient., median))
boxplot(log(MxSerr$Cases) ~ MxSerr$Transmission, las=2, main = "Serratia")
#bymed1 <- with(MxStaph, reorder(Transmission, Cases..patient., median))
boxplot(log(MxStaph$Cases) ~ MxStaph$Transmission, las=2, main = "Staphylococcus", ylab = "log CASES")
#bymed1 <- with(MxStrep, reorder(Transmission, Cases..patient., median))
boxplot(log(MxStrep$Cases) ~ MxStrep$Transmission, las=2, main = "Streptococcus")
dev.off()

# And code to make the interaction boxplot for Rate
setEPS()
postscript("/Users/amyhurford/Desktop/Figure3.eps")
par(mfrow = c(4,4), mar = c(3.5, 2, 2, 2), mgp = c(2, 1, 0))
#bymed2 <- with(MxAcin, reorder(Transmission, Cases..patient./Duration..days., median))
boxplot(log(MxAcin$Cases/MxAcin$Duration) ~ MxAcin$Transmission, las=2, ylab = "log RATE", main = "Acinobacter")
#bymed2 <- with(MxCdiff, reorder(Transmission, Cases..patient./Duration..days., median))
boxplot(log(MxCdiff$Cases/MxCdiff$Duration) ~ MxCdiff$Transmission, las=2, main = "C. difficle")
#bymed2 <- with(MxEcoli, reorder(Transmission, Cases..patient./Duration..days., median))
boxplot(log(MxEcoli$Cases/MxEcoli$Duration) ~ MxEcoli$Transmission, las=2, main = "E. coli")
#bymed2 <- with(MxEnterob, reorder(Transmission, Cases..patient./Duration..days., median))
boxplot(log(MxEnterob$Cases/MxEnterob$Duration) ~ MxEnterob$Transmission, las=2, main = "Enterobacter")
#bymed2 <- with(MxEnteroc, reorder(Transmission, Cases..patient./Duration..days., median))
boxplot(log(MxEnteroc$Cases/MxEnteroc$Duration) ~ MxEnteroc$Transmission, las=2, ylab = "log RATE", main = "Enterococci")
#bymed2 <- with(MxHepB, reorder(Transmission, Cases..patient./Duration..days., median))
boxplot(log(MxHepB$Cases/MxHepB$Duration) ~ MxHepB$Transmission, las=2, main = "Hep. B")
#bymed2 <- with(MxHepC, reorder(Transmission, Cases..patient./Duration..days., median))
boxplot(log(MxHepC$Cases/MxHepC$Duration) ~ MxHepC$Transmission, las=2, main = "Hep. C")
#bymed2 <- with(MxKlebs, reorder(Transmission, Cases..patient./Duration..days., median))
boxplot(log(MxKlebs$Cases/MxKlebs$Duration) ~ MxKlebs$Transmission, las=2, main = "Klebsiella")
#bymed2 <- with(MxLegion, reorder(Transmission, Cases..patient./Duration..days., median))
boxplot(log(MxLegion$Cases/MxLegion$Duration) ~ MxLegion$Transmission, las=2, main = "Legionella",ylab = "log RATE")
#bymed2 <- with(MxPseudo, reorder(Transmission, Cases..patient./Duration..days., median))
boxplot(log(MxPseudo$Cases/MxPseudo$Duration) ~ MxPseudo$Transmission, las=2, main = "Pseudomonas")
#bymed2 <- with(MxSalm, reorder(Transmission, Cases..patient./Duration..days., median))
boxplot(log(MxSalm$Cases/MxSalm$Duration) ~ MxSalm$Transmission, las=2, main  = "Salmonella")
#bymed2 <- with(MxSerr, reorder(Transmission, Cases..patient./Duration..days., median))
boxplot(log(MxSerr$Cases/MxSerr$Duration) ~ MxSerr$Transmission, las=2, main = "Serratia")
#bymed2 <- with(MxStaph, reorder(Transmission, Cases..patient./Duration..days., median))
boxplot(log(MxStaph$Cases/MxStaph$Duration) ~ MxStaph$Transmission, las=2, main = "Staphylococcus", ylab = "log RATE")
#bymed2 <- with(MxStrep, reorder(Transmission, Cases..patient./Duration..days., median))
boxplot(log(MxStrep$Cases/MxStrep$Duration) ~ MxStrep$Transmission, las=2, main = "Streptococcus")
dev.off()

# Supplementary analysis - Appears in discussion
# Frequency of outbreaks from different species
#Species
Species = c("Staph", "Pseudo", "Klebs", "Acin", "Enteroc", "Enterob", "Strep", "Serr", "Hep B", "Hep C", "Salm", "Legion")
Hurford = c(268, 144, 79, 169, 116, 62, 87,116,85,85,78,55,39,15)
Gastmeier = c(223, 129, 115, 105, 67, 66, 63,94,70,56,56,48)
Chi_S2 = sum((Gastmeier - mean(Gastmeier))^2/mean(Gastmeier))
qchisq(0.001,11, lower.tail=FALSE)

setEPS()
postscript("/Users/amyhurford/Desktop/AdditionalFig.eps",width=15,height=7)
par(mgp=c(4,1,0),mar = c(8, 5, 3, 3), mfrow = c(1,1))
plotCI(1:69, exp(sorted_coeffs2[1:69,1]), ui=exp(sorted_coeffs2[1:69,3]), li=exp(sorted_coeffs2[1:69,2]), xaxt="n", ylab = "Log mean number of cases per day", las=2)
axis(1,1:69, labels = coef_labs2, las=2)
dev.off()