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function oo = model_comparison(ModelNames,ModelPriors,oo,options_,fname)
% function oo = model_comparison(ModelNames,ModelPriors,oo,options_,fname)
% Conducts Bayesian model comparison. This function computes Odds ratios and
% estimates a posterior density over a collection of models.
%
% INPUTS
% ModelNames [string] m*1 cell array of string.
% ModelPriors [double] m*1 vector of prior probabilities
% oo [struct] Dynare results structure
% options_ [struct] Dynare options structure
% fname [string] name of the current mod-file
%
% OUTPUTS
% oo [struct] Dynare results structure containing the
% results in a field PosteriorOddsTable
%
% ALGORITHM
% See e.g. Koop (2003): Bayesian Econometrics
%
% SPECIAL REQUIREMENTS
% none
% Copyright (C) 2007-2018 Dynare Team
%
% This file is part of Dynare.
%
% Dynare is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% Dynare is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
NumberOfModels = size(ModelNames,2);
skipline(2)
if isempty(ModelPriors)
prior_flag = 0;% empty_prior=0
ModelPriors = ones(NumberOfModels,1)/NumberOfModels;
else % The prior density has to sum up to one.
prior_flag = 1;
improper = abs(sum(ModelPriors)-1)>1e-6;
if improper
if ~all(ModelPriors==1)
disp('model_comparison:: The user supplied prior distribution over models is improper...')
disp('model_comparison:: The distribution is automatically rescaled!')
end
ModelPriors=ModelPriors/sum(ModelPriors);
end
end
% The marginal densities are based on Laplace approxiations (default) or
% modified harmonic mean estimators.
if isfield(options_,'mc_marginal_density')
type = options_.mc_marginal_density;
if strcmp(type,'laplace') || strcmp(type,'Laplace')
type = 'LaplaceApproximation';
title = 'Model Comparison (based on Laplace approximation)';
elseif strcmp(type,'modifiedharmonicmean') || strcmp(type,'ModifiedHarmonicMean')
type = 'ModifiedHarmonicMean';
title = 'Model Comparison (based on Modified Harmonic Mean Estimator)';
end
else
type = 'LaplaceApproximation';
title = 'Model Comparison (based on Laplace approximation)';
end
% Get the estimated logged marginal densities.
MarginalLogDensity = zeros(NumberOfModels,1);
ShortModelNames = get_short_names(ModelNames);
iname = strmatch(fname,ShortModelNames,'exact');
for i=1:NumberOfModels
if i==iname
mstruct.oo_ = oo;
else
if strcmpi(ModelNames{i}(end-3:end),'.mod') || strcmpi(ModelNames{i}(end-3:end),'.dyn')
mstruct = load([ModelNames{i}(1:end-4) '_results.mat' ],'oo_');
else
mstruct = load([ModelNames{i} '_results.mat' ],'oo_');
end
end
try
eval(['MarginalLogDensity(i) = mstruct.oo_.MarginalDensity.' type ';'])
catch
if strcmpi(type,'LaplaceApproximation')
if isfield(mstruct.oo_,'mle_mode')
disp(['MODEL_COMPARISON: Model comparison is a Bayesian approach and does not support models estimated with ML'])
else
disp(['MODEL_COMPARISON: I cant''t find the Laplace approximation associated to model ' ModelNames{i}])
end
return
elseif strcmpi(type,'ModifiedHarmonicMean')
if isfield(mstruct.oo_,'mle_mode')
disp(['MODEL_COMPARISON: Model comparison is a Bayesian approach and does not support models estimated with ML'])
else
disp(['MODEL_COMPARISON: I cant''t find the modified harmonic mean estimate associated to model ' ModelNames{i}])
end
return
end
end
end
% In order to avoid overflow, we divide the numerator and the denominator
% of the Posterior Odds Ratio by the largest Marginal Posterior Density
lmpd = log(ModelPriors)+MarginalLogDensity;
[maxval,k] = max(lmpd);
elmpd = exp(lmpd-maxval);
% Now I display the posterior probabilities.
headers = vertcat('Model', ShortModelNames);
if prior_flag
labels = {'Priors'; 'Log Marginal Density'; 'Bayes Ratio'; 'Posterior Model Probability'};
field_labels={'Prior','Log_Marginal_Density','Bayes_Ratio', 'Posterior_Model_Probability'};
values = [ModelPriors';MarginalLogDensity';exp(lmpd-lmpd(1))'; elmpd'/sum(elmpd)];
else
labels = {'Priors'; 'Log Marginal Density'; 'Bayes Ratio'; 'Posterior Odds Ratio'; 'Posterior Model Probability'};
field_labels={'Prior','Log_Marginal_Density','Bayes_Ratio','Posterior_Odds_Ratio','Posterior_Model_Probability'};
values = [ModelPriors';MarginalLogDensity'; exp(MarginalLogDensity-MarginalLogDensity(1))'; exp(lmpd-lmpd(1))'; elmpd'/sum(elmpd)];
end
for model_iter = 1:NumberOfModels
for var_iter = 1:length(labels)
oo.Model_Comparison.(headers{1+model_iter}).(field_labels{var_iter}) = values(var_iter, model_iter);
end
end
dyntable(options_, title, headers, labels, values, 0, 15, 6);
if options_.TeX
M_temp.fname = fname;
M_temp.dname = fname;
headers_tex = {};
for ii = 1:length(headers)
headers_tex = vertcat(headers_tex, strrep(headers{ii}, '_', '\_'));
end
labels_tex = {};
for ii = 1:length(labels)
labels_tex = vertcat(labels_tex, strrep(labels{ii},' ', '\ '));
end
dyn_latex_table(M_temp, options_, title, ['model_comparison', type], headers_tex, labels_tex, values, 0, 16, 6);
end
function name = get_model_name_without_path(modelname)
idx = strfind(modelname,'\');
if isempty(idx)
idx = strfind(modelname,'/');
end
if isempty(idx)
name = modelname;
return
end
name = modelname(idx(end)+1:end);
function name = get_model_name_without_extension(modelname)
idx = strfind(modelname,'.mod');
if isempty(idx)
idx = strfind(modelname,'.dyn');
end
if isempty(idx)
name = modelname;
return
end
name = modelname(1:end-4);
function modellist = get_short_names(modelnames)
n = length(modelnames);
modellist = cell(n, 1);
for i=1:n
name = get_model_name_without_extension(modelnames{i});
name = get_model_name_without_path(name);
modellist(i) = {name};
end
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