added in class-example code

Week 3 -- Temporal Models/Lab/In-class exercise/Gompertz_exercise.R

@@ -0,0 +1,54 @@
+
+setwd( "C:/Users/James.Thorson/Desktop/Project_git/2018_FSH556/Week 3 -- Temporal Models/Lab/In-class exercise" )
+
+######################
+# Modify to add sampling variance to measurement error
+######################
+
+# Modify to decompose measurement error into sampling and additional error
+sd_B_t = sqrt( tapply( CPUE[,'Wt'], INDEX=CPUE[,'Year'], FUN=var ) / tapply( CPUE[,'Wt'], INDEX=CPUE[,'Year'], FUN=length ) )
+CV_b_t = sd_B_t / B_t
+SD_log_b_t = sqrt(log( CV_b_t^2 + 1 ))
+
+# Compile model
+Version = "gompertz_2"
+compile( paste0(Version,".cpp") )
+
+# Build inputs
+Data = list( "nt"=length(B_t), "log_b_t"=log(B_t), "SD_log_b_t"=SD_log_b_t )
+Parameters = list( "log_d0"=0, "log_sigmaP"=1, "log_sigmaM"=1, "alpha"=0, "rho"=0, "log_d_t"=rep(0,Data$nt) )
+Random = c("log_d_t")
+if( Use_REML==TRUE ) Random = union( Random, c("log_d0","alpha","rho") )
+
+# Build object
+dyn.load( dynlib("gompertz_2") )
+Obj = MakeADFun(data=Data, parameters=Parameters, random=Random, DLL="gompertz_2")  #
+Opt2 = TMBhelper::Optimize( obj=Obj )
+
+# Plot again
+for( z in 1:2 ){
+  png( file=paste0("pollock_",z,"-with_measurement_error.png"), width=8, height=5, res=200, units="in" )
+    par( mar=c(3,3,1,1), mgp=c(2,0.5,0), tck=-0.02 )
+    plot( x=1:Data$nt, y=Data$log_b_t, col="blue", cex=1.2, xlab="Time", ylab="Value", pch=20 )
+    if(z>=2){
+      points( x=1:Data$nt, y=as.list(Opt2$SD,"Estimate")$log_d_t, col="red" )
+      for( t in 1:Data$nt) lines( x=rep(t,2), y=as.list(Opt2$SD,"Estimate")$log_d_t[t]+c(-1.96,1.96)*as.list(Opt2$SD,"Std. Error")$log_d_t[t], col="red" )
+    }
+  dev.off()
+}
+
+write.csv( cbind(Opt2$diagnostics, summary(Opt$SD,"fixed")[,'Std. Error']), file=paste0(getwd(),"/pollock_2.csv") )
+
+###############
+# Fix SigmaM at zero
+###############
+
+Map = list()
+Map$log_sigmaM = factor(NA)
+Parameters$log_sigmaM = log(1e-10)
+Obj = MakeADFun(data=Data, parameters=Parameters, random=Random, map=Map, DLL="gompertz_2")  #
+Opt3 = TMBhelper::Optimize( obj=Obj )
+Report = Obj$report()
+
+# Compare AIC
+c(Opt2$AIC, Opt3$AIC)

Week 3 -- Temporal Models/Lab/In-class exercise/gompertz_2.cpp

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+#include <TMB.hpp>
+template<class Type>
+Type objective_function<Type>::operator() ()
+{
+  // Data
+  DATA_INTEGER( nt );
+  DATA_VECTOR( log_b_t );
+  DATA_VECTOR( SD_log_b_t );
+
+  // Parameters
+  PARAMETER( log_d0 );
+  PARAMETER( log_sigmaP );
+  PARAMETER( log_sigmaM );
+  PARAMETER( alpha );
+  PARAMETER( rho );
+  PARAMETER_VECTOR( log_d_t );
+
+  // Objective funcction
+  Type jnll = 0;
+
+  // Reporting
+  Type sigmaP = exp(log_sigmaP);
+  vector<Type> sigmaM_t(nt);
+  for( int t=0; t<nt; t++){
+    sigmaM_t(t) = pow( pow(exp(log_sigmaM),2) + pow(SD_log_b_t(t),2), 0.5 );
+  }
+
+  // Probability of random coefficients
+  jnll -= dnorm( log_d_t(0), log_d0, exp(log_sigmaP), true );
+  for( int t=1; t<nt; t++){
+    jnll -= dnorm( log_d_t(t), alpha + rho*log_d_t(t-1), sigmaP, true );
+  }
+
+  // Probability of data conditional on fixed and random effect values
+  for( int t=0; t<nt; t++){
+    jnll -= dnorm( log_b_t(t), log_d_t(t), sigmaM_t(t), true );
+  }
+
+  REPORT( sigmaP );
+  REPORT( sigmaM_t );
+  REPORT( log_d_t );
+
+  ADREPORT( sigmaP );
+  ADREPORT( sigmaM_t );
+
+  return jnll;
+}

Week 3 -- Temporal Models/Lab/In-class exercise/pollock_2.csv

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+"","Param","starting_value","Lower","MLE","Upper","final_gradient","summary(Opt$SD, ""fixed"")[, ""Std. Error""]"
+"log_d0","log_d0",0,-Inf,4.2042152454022,Inf,1.92605013971382e-07,0.260513687545267
+"log_sigmaP","log_sigmaP",1,-Inf,-1.52772207486349,Inf,-4.45955622083714e-07,0.117851155182634
+"log_sigmaM","log_sigmaM",1,-Inf,-12.602926982783,Inf,2.75469399300347e-10,26029.8440043728
+"alpha","alpha",0,-Inf,2.12296833291583,Inf,1.01415665495722e-06,0.6652356191063
+"rho","rho",0,-Inf,0.534989073577766,Inf,4.91719614775057e-06,0.145993116527693

Week 3 -- Temporal Models/Lab/In-class exercise/pollock_3.csv

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+"","Param","starting_value","Lower","MLE","Upper","final_gradient","summary(Opt$SD, ""fixed"")[, ""Std. Error""]"
+"log_d0","log_d0",0,-Inf,4.2042152330218,Inf,5.70944991666547e-08,0.252015718084337
+"log_sigmaP","log_sigmaP",1,-Inf,-1.52772206019661,Inf,4.02960706804333e-08,0.156722880918147
+"alpha","alpha",0,-Inf,2.12296839434053,Inf,-1.14044039858778e-07,0.753630593218351
+"rho","rho",0,-Inf,0.534989059737808,Inf,-5.77914213419342e-07,0.165465200289098