Small change to Week 7 lecture...

... plus added HW3 solution

Week 3 -- Temporal Models/Homework solution/HW3.r

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+library(TMB)
+
+setwd("/Users/jiecao/Desktop/hw3_soln")
+CPUE = FishData::download_catch_rates( survey="Eastern_Bering_Sea", species_set="Gadus chalcogrammus", error_tol=0.01, localdir=paste0(getwd(),"/") )
+B_t = tapply( CPUE[,'Wt'], INDEX=CPUE[,'Year'], FUN=mean )
+log_yt <- log(B_t)
+
+#Run TMB model 
+compile("gompertz.cpp")
+dyn.load(dynlib("gompertz"))
+
+N = length(log_yt)	
+data <- list(log_yt = log_yt,model_switch=1)
+parameters <- list(pop_par=c(1,0.5), log_sigma = -1,log_x0 = 4, log_xt = rep(mean(log_yt), N))
+
+#data <- list(log_yt = log_yt,model_switch=2)
+#parameters <- list(pop_par=c(0.6,100), log_sigma = -1,log_x0 = 4, log_xt = rep(mean(log_yt), N))
+
+obj <- MakeADFun(data, parameters, random = "log_xt", DLL = "gompertz")
+obj$hessian <- FALSE
+opt <- do.call("optim", obj)
+sd <- sdreport(obj)
+
+# extract fixed effects:
+fixed <- summary(sd, "fixed")
+# extract estimated process:
+log_xt <- summary(sd, "random")[, "Estimate"]
+log_xt_se <- summary(sd, "random")[, "Std. Error"]
+
+# simulation
+n_sim = 100
+sim <- replicate(n_sim, {
+simdata <- obj$simulate()
+obj2 <- MakeADFun(list(log_yt=c(simdata$log_yt[1:31],rep(NA,5)),model_switch=1), parameters, random = "log_xt", DLL = "gompertz", silent = TRUE)
+TMBhelper::Optimize( obj=obj2, newtonsteps=1)
+c( true = simdata$log_xt[32:36],
+   est = summary(sdreport(obj2), "random")[, "Estimate"][32:36],
+   sd = summary(sdreport(obj2), "random")[, "Std. Error"][32:36])
+})
+
+# calculate coverage 
+cal_coverage <- function (true, est, sd, interval){
+  low = est - qnorm(interval/2) * sd
+  high = est + qnorm(interval/2) * sd
+  return(true > low & true < high)
+}
+
+gom.matrix = matrix(NA,nrow=n_sim,ncol=5)
+for(i in 1:n_sim){
+  for(t in 1:5){
+    gom.matrix[i,t]=cal_coverage(sim[t,i],sim[t+5,i],sim[t+10,i],0.5)
+  }
+}
+apply(gom.matrix,2,sum)
+
+# ricker 
+parameters2 <- list(pop_par=c(0.6,100), log_sigma = -1,log_x0 = 4, log_xt = rep(mean(log_yt), N))
+sim2 <- replicate(n_sim, {
+simdata <- obj$simulate()
+obj3 <- MakeADFun(list(log_yt=c(simdata$log_yt[1:31],rep(NA,5)),model_switch=2), parameters2, random = "log_xt", DLL = "gompertz", silent = TRUE)
+TMBhelper::Optimize( obj=obj3, newtonsteps=1)
+c( true = simdata$log_xt[32:36],
+   est = summary(sdreport(obj3), "random")[, "Estimate"][32:36],
+   sd = summary(sdreport(obj3), "random")[, "Std. Error"][32:36])
+})
+
+ricker.matrix = matrix(NA,nrow=n_sim,ncol=5)
+for(i in 1:n_sim){
+  for(t in 1:5){
+    ricker.matrix[i,t]=cal_coverage(sim2[t,i],sim2[t+5,i],sim2[t+10,i],0.5)
+  }
+}
+apply(ricker.matrix,2,sum)

Week 3 -- Temporal Models/Homework solution/gompertz.cpp

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+
+// State-space Gompertz model
+#include <TMB.hpp>
+
+// Function for detecting NAs
+template<class Type>
+bool isNA(Type x){
+  return R_IsNA(asDouble(x));
+}
+
+template<class Type>
+Type objective_function<Type>::operator() () 
+{
+// data:
+DATA_VECTOR(log_yt);
+DATA_INTEGER(model_switch);
+
+// parameters:
+PARAMETER_VECTOR(pop_par); // population growth rate parameter //density dependence parameter
+PARAMETER(log_sigma); // log(process SD) = log(obs SD)
+PARAMETER(log_x0);
+PARAMETER_VECTOR(log_xt); // state
+
+// transform the parameters
+Type sigma = exp(log_sigma);
+
+// reports
+ADREPORT(sigma)
+
+int n = log_yt.size(); // get time series length
+Type nll = 0.0; // initialize negative log likelihood
+
+nll -= dnorm(log_xt[0], log_x0, sigma, true) ;
+
+Type m;
+
+// process model:
+for(int i = 1; i < n; i++){
+	if(model_switch == 1){
+		m = pop_par[0]+pop_par[1]*log_xt[i-1] ;    //Gompertz model
+	}
+    if(model_switch == 2){
+    	m = log_xt[i-1] + pop_par[0]*(1-exp(log_xt[i-1])/pop_par[1]) ;    //Ricker model
+    }
+    nll -= dnorm(log_xt[i], m, sigma, true); //likelihood for random effects
+}
+
+// observation model:
+for(int i = 0; i < n; i++){
+  if(!isNA(log_yt[i])){	
+  nll -= dnorm(log_yt[i], log_xt[i], sigma, true); //likelihood for observations
+  }
+ }
+
+SIMULATE{
+	log_xt[0] = rnorm(log_x0,sigma);
+	log_yt[0] = rnorm(log_xt[0],sigma);
+	for (int i = 1; i < n; i++){
+		log_xt[i] = rnorm(pop_par[0]+pop_par[1]*log_xt[i-1], sigma);
+		log_yt[i] = rnorm(log_xt[i], sigma);
+	}
+	REPORT(log_xt);
+	REPORT(log_yt);
+}
+
+return nll;
+}
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