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+setwd("C:/Users/DAVIS/Desktop/shell-novice-data/exe9/Intro_Biocomp_ND_317_Tutorial9/")
+
+##########QUESTION 1 ################
+#load ponzr csv data file
+Ponzr <- read.csv("ponzr1.csv", header=T)
+
+#make custom likelihood function that specifies model structure (parameters, observations)
+#-'unpack parameters'
+#-assign parameters to expected values (make a place to feed in variables)
+#-dnorm(x,mean,sd)
+like1 <- function(p,x,y){
+  B0=p[1]
+  B1=p[2]
+  sigma = exp(p[3])
+  expected = B0
+  
+  nll = -sum(dnorm(y, mean=expected, sd=sigma, log=TRUE))
+  return(nll)
+}
+
+#make second likelihood model
+like2 <- function(p,x,y){
+  B0=p[1]
+  B1=p[2]
+  sigma = exp(p[3])
+  expected = B0+B1*x
+  
+  nll = -sum(dnorm(y, mean=expected, sd=sigma, log=TRUE))
+  return(nll)
+}
+
+#change all WT to 0 and each mutation to 1 and split them up
+Ponzr1 <- Ponzr[which(Ponzr$mutation=="WT"),]
+Ponzr1[,1] <- 0
+Ponzr2 <- Ponzr[which(Ponzr$mutation=="M124K"),]
+Ponzr2[,1] <- 1
+Ponzr3 <- Ponzr[which(Ponzr$mutation=="V456D"),]
+Ponzr3[,1] <- 1
+Ponzr4 <- Ponzr[which(Ponzr$mutation=="I213N"),]
+Ponzr4[,1] <- 1
+
+Ponzr1_2 <- rbind(Ponzr1,Ponzr2)
+Ponzr1_3 <- rbind(Ponzr1,Ponzr3)
+Ponzr1_4 <- rbind(Ponzr1,Ponzr4)
+
+
+#optim function to look for maximum likelihood of our model
+#estimate parameters by minimizing the NLL
+#create a vector with initial guesses
+#minimize log likelihood
+
+#wt vs M124K
+Guess = c(1,1,1)
+fit1=optim(Guess, like1, x=Ponzr1$mutation, y=Ponzr1$ponzr1Counts)
+fit2=optim(Guess, like2, x=Ponzr2$mutation, y=Ponzr2$ponzr1Counts)
+fit1$value
+fit2$value
+D = 2*(fit1$value-fit2$value)
+pchisq(D, df=1, lower.tail=F)
+##Mutation M124K p-value=0.72, no effect of treatment
+
+#wt vs. V456D
+Guess = c(1,1,1)
+fit1=optim(Guess, like1, x=Ponzr1$mutation, y=Ponzr1$ponzr1Counts)
+fit2=optim(Guess, like2, x=Ponzr3$mutation, y=Ponzr3$ponzr1Counts)
+fit1$value
+fit2$value
+D = 2*(fit1$value-fit2$value)
+pchisq(D, df=1, lower.tail=F)
+##Mutation V456D p-value=0.0000056 effect of treatment
+
+#wt vs.I213N
+Guess = c(1,1,1)
+fit1=optim(Guess, like1, x=Ponzr1$mutation, y=Ponzr1$ponzr1Counts)
+fit2=optim(Guess, like2, x=Ponzr4$mutation, y=Ponzr4$ponzr1Counts)
+fit1$value
+fit2$value
+D = 2*(fit1$value-fit2$value)
+pchisq(D, df=1, lower.tail=F)
+##Mutation I213N p-value 0.88 no effect of treatment
+
+
+##Mutation M124K p-value=0.72, no effect of treatment
+##Mutation V456D p-value=0.0000056 effect of treatment
+##Mutation I213N p-value 0.88 no effect of treatment
+##Therefore, the V456D mutation significantly reduced the expression of ponzr1
+
+
+##########QUESTION 2 ################
+#load csv file for mmarinum
+Mmarinum <- read.csv("MmarinumGrowth.csv", header=T)
+
+#make custom likelihood function
+nllike <- function(p,x,y){
+  B0=p[1]
+  B1=p[2]
+  sigma = exp(p[3])
+  expected = B0*(x/(B1+x))
+  
+  nll = -sum(dnorm(x=y, mean=expected, sd=sigma, log=TRUE))
+  return(nll)
+}
+
+#optim function to find the max growth rate and half-saturatation constant
+Guess = c(1,1,1)
+fit=optim(Guess, nllike, x=Mmarinum$S, y=Mmarinum$u)
+print(cbind("umax is ", fit$par[1], " and Ks is ", fit$par[2]))
+
+##max growth rate (umax)=1.46
+##half sat constant=42.6
+##sigma=0.04
+
+
+
+#############QUESTION 3 #############
+#load data for decomposition of leaves
+leafDecomp <- read.csv("leafDecomp.csv", header = T)
+
+#create custom functions for the three models:
+#constant fit model(null model)
+constant <- function(p,x,y){
+  sigma = exp(p[1])
+  B0=p[2]
+  
+  expected = B0
+  
+  nll = -sum(dnorm(x=y, mean=expected, sd=sigma, log=TRUE))
+  return(nll)
+}
+
+#linear model
+linear <- function(p,x,y){
+  sigma = exp(p[1])
+  B0=p[2]
+  B1=p[3]
+  
+  expected = B0 + B1*x
+  
+  nll = -sum(dnorm(x=y, mean=expected, sd=sigma, log=TRUE))
+  return(nll)
+}
+
+#quadratic model
+quadratic <- function(p,x,y){
+  sigma = exp(p[1])
+  B0=p[2]
+  B1=p[3]
+  B2=p[4]
+  
+  expected = B0 + B1*x + B2*x*x
+  
+  nll = -sum(dnorm(x=y, mean=expected, sd=sigma, log=TRUE))
+  return(nll)
+}
+
+#want to minimize parameters so we find max
+#likelihood to capture shape but with as few parameters
+#estimate parameters for each of the three likelihood functions
+#use mean of all decomposition values to set initial parameter guess for the constant model
+mean(leafDecomp$decomp)
+constantGuess = c(1,500)
+#use slope and intercept of data to inform initial guess for linear model
+plot(leafDecomp)
+linearGuess = c(1,200,10)
+#difficult to have initial guess, try B0=200, B1=10, B2=-0.2, sigma=1
+quadraticGuess = c(1,200,10,-0.2)
+
+#optimize each likelihood function with different number of parameters
+constantResult=optim(constantGuess, constant, x=leafDecomp$Ms, y=leafDecomp$decomp)
+linearResult=optim(linearGuess, linear, x=leafDecomp$Ms, y=leafDecomp$decomp)
+quadraticResult=optim(quadraticGuess, quadratic, x=leafDecomp$Ms, y=leafDecomp$decomp)
+
+constantResult$value
+linearResult$value
+quadraticResult$value
+
+constantResult$par
+linearResult$par
+quadraticResult$par
+
+#do t-tests on all combinations of min NLL for 3 models:
+D1_2 = 2*(constantResult$value - linearResult$value)
+D1_3 = 2*(constantResult$value - quadraticResult$value)
+D2_3 = 2*(linearResult$value - quadraticResult$value)
+
+#set df to 1 or 2 depending on difference in parameters between two models
+pchisq(D1_2, df=1, lower.tail=F)
+pchisq(D1_3, df=2, lower.tail=F)
+pchisq(D2_3, df=1, lower.tail=F)
+
+#p-values for likelihood ratio tests are all about 0
+#constant fit B0=589.7, sigma=164
+#linear fit B0=318, B1=6.3, sigma=54
+#quadratic fit B0=180, B1=15.7, B2=-0.11, sigma=10.7
+##therefore, quadratic model is the best since it has the smallest sigma, linear model is second best, null model is the worst
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diff --git a/Tutorial9_1.R b/Tutorial9_1.R
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+++ b/Tutorial9_1.R
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+########QUESTION 1#########
+
+#load ponzr csv data file
+ponzr1=read.csv("ponzr1.csv",header=TRUE)
+
+#make custom likelihood function that specifies model structure (parameters, observations)
+#-'unpack parameters'
+#-assign parameters to expected values (make a place to feed in variables)
+#-dnorm(x,mean,sd)
+nllike1=function(p,x,y){
+  B0=p[1]
+  B1=p[2]
+  sigma=exp(p[3])
+  
+  expected=B0+B1*x
+  
+  nll=-sum(dnorm(x=y,mean=expected,sd=sigma,log=TRUE))
+  return(nll)
+}
+
+#make second likelihood model
+nllike2=function(p,x,y){
+  B0=p[1]
+  B1=p[2]
+  sigma = exp(p[3])
+  expected = B0+B1*x
+  
+  nll = -sum(dnorm(x=y, mean=expected, sd=sigma, log=TRUE))
+  return(nll)
+}
+
+#change all WT to 0 and each mutation to 1 and split them up
+Ponzr1 = ponzr1[which(ponzr1$mutation=="WT"),]
+Ponzr1[,1] = 0
+Ponzr2 = ponzr1[which(ponzr1$mutation=="M124K"),]
+Ponzr2[,1] = 1
+Ponzr3 = ponzr1[which(ponzr1$mutation=="V456D"),]
+Ponzr3[,1] = 1
+Ponzr4 = ponzr1[which(ponzr1$mutation=="I213N"),]
+Ponzr4[,1] = 1
+
+
+#optim function to look for maximum likelihood of our model
+#estimate parameters by minimizing the NLL
+#create a vector with initial guesses
+#minimize log likelihood
+
+#wt vs M124K
+initialguess=c(1,1,1)
+fit1=optim(par=initialguess,fn=nllike1,x=Ponzr1$mutation,y=Ponzr1$ponzr1Counts)
+fit2=optim(par=initialguess,fn=nllike2,x=Ponzr2$mutation,y=Ponzr2$ponzr1Counts)
+fit1$value
+fit2$value
+#run t-test
+D=2*(fit1$value-fit2$value)
+pchisq(q=D,df=1,lower.tail=FALSE)
+
+#wt vs. V456D
+initialguess = c(0,0,0)
+fit1=optim(initialguess, nllike1, x=Ponzr1$mutation, y=Ponzr1$ponzr1Counts)
+fit2=optim(initialguess, nllike2, x=Ponzr3$mutation, y=Ponzr3$ponzr1Counts)
+fit1$value
+fit2$value
+D = 2*(fit1$value-fit2$value)
+pchisq(q=D, df=1, lower.tail=FALSE)
+
+#wt vs.I213N
+Guess = c(1,1,1)
+fit1=optim(Guess, nllike1, x=Ponzr1$mutation, y=Ponzr1$ponzr1Counts)
+fit2=optim(Guess, nllike2, x=Ponzr4$mutation, y=Ponzr4$ponzr1Counts)
+fit1$value
+fit2$value
+D = 2*(fit1$value-fit2$value)
+pchisq(D, df=1, lower.tail=F)
+
+
+##Mutation M124K p-value=0.72, no effect of treatment
+##Mutation V456D p-value=0.0000056 effect of treatment
+##Mutation I213N p-value 0.88 no effect of treatment
+##Therefore, the V456D mutation significantly reduced the expression of ponzr1
+
+
+
+#### QUESTION 2 ################
+#load csv file for mmarinum
+Mmarinum = read.csv("MmarinumGrowth.csv", header=TRUE)
+
+#make custom likelihood function
+nllike1 <- function(p,x,y){
+  B0=p[1]
+  B1=p[2]
+  sigma = exp(p[3])
+  expected = B0*(x/(B1+x))
+  
+  nll = -sum(dnorm(x=y, mean=expected, sd=sigma, log=TRUE))
+  return(nll)
+}
+#optim function to find the max growth rate and half-saturatation constant
+initialguess = c(1,1,1)
+fit=optim(initialguess, nllike1, x=Mmarinum$S, y=Mmarinum$u)
+print(cbind("umax:", fit$par[1], "Ks:", fit$par[2]))
+
+##max growth rate (umax)=1.46
+##half sat constant=42.6
+##sigma=0.04
+
+
+
+###QUESTION 3 ########
+#load data for decomposition of leaves
+leafs= read.csv("leafDecomp.csv", header = TRUE)
+
+#create custom functions for the three models:
+#constant fit model(null model)
+constant = function(p,x,y){
+  sigma = exp(p[1])
+  a=p[2]
+  
+  expected = a
+
+nll = -sum(dnorm(x=y, mean=expected, sd=sigma, log=TRUE))
+return(nll)
+}
+
+#linear model
+linear = function(p,x,y){
+  sigma = exp(p[1]) 
+  a=p[2]
+  b=p[3]
+ 
+  expected = a + b*x
+  
+  nll = -sum(dnorm(x=y, mean=expected, sd=sigma, log=TRUE))
+  return(nll)
+}
+
+#quadratic model
+quadratic = function(p,x,y){
+  sigma = exp(p[1])
+  a=p[2]
+  b=p[3]
+  c=p[4]
+  
+  expected = a + b*x + c*x*x
+  
+  nll = -sum(dnorm(x=y, mean=expected, sd=sigma, log=TRUE))
+  return(nll)
+}
+
+#want to minimize parameters so we find max
+#likelihood to capture shape but with as few parameters
+#start with initial guess
+constantguess = c(1,1)
+linearguess = c(1,1,1)
+quadraticguess = c(1,1,1,1)
+
+#optimize each likelihood function with different number of parameters
+constantOpt=optim(constantguess, constant, x=leafs$Ms, y=leafs$decomp)
+linearOpt=optim(linearguess, linear, x=leafs$Ms, y=leafs$decomp)
+quadraticOpt=optim(quadraticguess, quadratic, x=leafs$Ms, y=leafs$decomp)
+
+print(constantOpt)
+print(linearOpt)
+print(quadraticOpt)
+
+constantOpt$value
+linearOpt$value
+quadraticOpt$value
+
+#do t-tests on all combinations of min NLL for 3 models:
+D1_2 = 2*(constantOpt$value-linearOpt$value)
+D1_3 = 2*(constantOpt$value-quadraticOpt$value)
+D2_3 = 2*(quadraticOpt$value-linearOpt$value)
+#set df to 1 or 2 depending on difference in parameters between two models
+pchisq(D1_2, df=1, lower.tail=FALSE)
+pchisq(D1_3, df=2, lower.tail=FALSE)
+pchisq(D2_3, df=1, lower.tail=F)
+
+
+#p-values for likelihood ratio tests are all about 0
+#contant fit B0=589.7, sigma=164
+#linear fit B0=318, B1=6.3, sigma=54
+#quadratic fit B0=180, B1=15.7, B2=-0.11, signma=10.7
+
+##quadratic model is the best, linear model is second best, null model is the worst
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