Specifying covariance structures in glmmTMB

C++ code for multivariate distributions for different covariance structures:
#include <[TMB.hpp](http://kaskr.github.io/adcomp/TMB_8hpp.html)>
template<class Type>
Type objective_function<Type>::operator() ()
{
  [PARAMETER](http://kaskr.github.io/adcomp/group__macros.html#ga70b2d449f7c53e87abee7d5fb71dc4c0)(dummy_par)         
  // Load namespace which contains the multivariate distributions
  using namespace [density](http://kaskr.github.io/adcomp/namespacedensity.html);

  Type res;                    // Dummy variable to which results will be asigned

  // Example: MVNORM_t  -----------------------------------------------------------
  [matrix<Type>](http://kaskr.github.io/adcomp/structmatrix.html) Sigma(3,3);
  Sigma.fill(0.1);                   // Fill the whole matrix
  Sigma.diagonal() *= 10.0;          // Multiply diagonal by 10 to positive definite Sigma
  vector<Type> x0(3);                // Point of evaluation
  x0.fill(0.0);                      // Initialize x0 to be zero
  [MVNORM_t<Type>](http://kaskr.github.io/adcomp/classdensity_1_1MVNORM__t.html) N_0_Sigma(Sigma);   // N_0_Sigma is now a Distribution  
  res = N_0_Sigma(x0);               // Evaluates (neg. log) density at x
  res = [MVNORM](http://kaskr.github.io/adcomp/namespacedensity.html#a0721aacc998f4cbd0290626073c19763)(Sigma)(x0);           // Shorthand form of the above two lines
  N_0_Sigma.[cov](http://kaskr.github.io/adcomp/classdensity_1_1MVNORM__t.html#a1d284b3f3adac475399ae1e5428cb202)();                   // Returns covariance matrix (Sigma in this case)
  [REPORT](http://kaskr.github.io/adcomp/group__macros.html#gac2d7888f4e0385930448f992de53079b)(N_0_Sigma.[cov](http://kaskr.github.io/adcomp/classdensity_1_1MVNORM__t.html#a1d284b3f3adac475399ae1e5428cb202)());           // Report back to R
  [REPORT](http://kaskr.github.io/adcomp/group__macros.html#gac2d7888f4e0385930448f992de53079b)([MVNORM_t<Type>](http://kaskr.github.io/adcomp/classdensity_1_1MVNORM__t.html)(Sigma).cov()); // Should return the same matrix as line above

  // Example: UNSTRUCTURED_CORR_t  -----------------------------------------------------

   // First: read docs for UNSTRUCTURED_CORR_t
  vector<Type> Lx(6);                             // Free parameters to be estimated 
  Lx.fill(2.5);
  [UNSTRUCTURED_CORR_t<Type>](http://kaskr.github.io/adcomp/classdensity_1_1UNSTRUCTURED__CORR__t.html) nll(Lx);
  vector<Type> x1(4);
  x1.fill(2.0);
  res = nll(x1  );
  [REPORT](http://kaskr.github.io/adcomp/group__macros.html#gac2d7888f4e0385930448f992de53079b)(nll.[cov](http://kaskr.github.io/adcomp/classdensity_1_1MVNORM__t.html#a1d284b3f3adac475399ae1e5428cb202)());

  // Example: AR1_t  -----------------------------------------------------

  // Univariate case
  int n = 10;                   // Number of time steps
  vector<Type> x2(n);           // Evaluation point, i.e. the time series       
  x2.fill(1.0);
  Type phi = 0.5;                               // Autocorrelation
  [N01<Type>](http://kaskr.github.io/adcomp/classdensity_1_1N01.html) nllN01;             // Distribution to be used at each time step
  [AR1_t<N01<Type>](http://kaskr.github.io/adcomp/classdensity_1_1AR1__t.html) > nll2(phi,nllN01);  // Create AR(1) process with N(0,1) distribution
  [REPORT](http://kaskr.github.io/adcomp/group__macros.html#gac2d7888f4e0385930448f992de53079b)(nll2(x2));                             // Evaluate neg. log density
  AR1(phi)(x2);                 // Equivalent to line above

  // Scale variances
  vector<Type> sds2(n);         // Vector of standard deviations (SD)
  sds2.fill(2.0);               // Set SD's  
  [REPORT](http://kaskr.github.io/adcomp/group__macros.html#gac2d7888f4e0385930448f992de53079b)([VECSCALE](http://kaskr.github.io/adcomp/namespacedensity.html#ad4883b13b683e6b9e1e27846b74e4680)(nll2,sds2)(x2));   // Evaluate neg. log density
  [REPORT](http://kaskr.github.io/adcomp/group__macros.html#gac2d7888f4e0385930448f992de53079b)([VECSCALE](http://kaskr.github.io/adcomp/namespacedensity.html#ad4883b13b683e6b9e1e27846b74e4680)(AR1(phi),sds2)(x2)); // Equivalent to line above   

  // Multivariate AR(1) process where the innovation vector is correlated
  int p=2;                      // dim(x)
  [array<Type>](http://kaskr.github.io/adcomp/structarray.html) x(p,n);           // Evaluation point       
  x.fill(1.0);
  [REPORT](http://kaskr.github.io/adcomp/group__macros.html#gac2d7888f4e0385930448f992de53079b)(x);                                    // Reported back to R so that we can see layout of x
  vector<Type> unconstrained_params(p*(p-1)/2);
  unconstrained_params.fill(0.01);      // Low correlaiton, but this is not directly the correlation  
  [REPORT](http://kaskr.github.io/adcomp/group__macros.html#gac2d7888f4e0385930448f992de53079b)(AR1(phi,[UNSTRUCTURED_CORR](http://kaskr.github.io/adcomp/namespacedensity.html#aec3874ac89bc3a5d5d4d245db46b09e4)(unconstrained_params))(x)); // nll 
  // Find nll for univariate time series. 
  // Do not add to nll for system of time series due to intra series correlation.
  [REPORT](http://kaskr.github.io/adcomp/group__macros.html#gac2d7888f4e0385930448f992de53079b)(AR1(phi)(x.[transpose](http://kaskr.github.io/adcomp/structarray.html#a9f0df57cc5403f71194f2159ec80bd66)().col(0)));       // First time series
  [REPORT](http://kaskr.github.io/adcomp/group__macros.html#gac2d7888f4e0385930448f992de53079b)(AR1(phi)(x.[transpose](http://kaskr.github.io/adcomp/structarray.html#a9f0df57cc5403f71194f2159ec80bd66)().col(1)));       // Second time series

  return Type(0.0);
}
Reference to make matrix with Eigen in C++: http://eigen.tuxfamily.org/dox/group__TutorialMatrixClass.html
coraliewilliams / glmmTMB

Specifying covariance structures in glmmTMB #2
