Go to the MLX, M, PDF, or HTML version of this file. Go back to fan’s MEconTools Package, Matlab Code Examples Repository (bookdown site), or Math for Econ with Matlab Repository (bookdown site).
There is an estimation routine, each time the routine outputs a table with a single row, the single row contains estimation outputs including estiamtes, standard erros, initial parameters etc. We loop over different estimation routines, with different starting values etc, and rather than saving many tables, we want to save a joint table with all rows stacked together.
This simply means that we have a loop, during each iteration, generating a table, we want to stack things together. For this assume that the column names are the same.
rng("default");
tb_saveCoef_stack = [];
for row_idx=1:5
% a row of coefficent estimates
rng(123+row_idx);
it_num_cols = 4;
it_num_rows = 1;
mt_saveCoef = rand([it_num_rows, it_num_cols]);
% row to table
ar_st_col_names = ["FVAL", "EXITFLAG", "esti_iterations", "esti_funccount"];
tb_saveCoef = array2table(mt_saveCoef);
tb_saveCoef.Properties.VariableNames = ar_st_col_names;
% Stack all results
tb_saveCoef_stack = [tb_saveCoef_stack; tb_saveCoef];
end
% Add esti Counter as column
estimodelctr = (1:size(tb_saveCoef_stack,1))';
tb_saveCoef_stack = addvars(tb_saveCoef_stack, estimodelctr, 'Before', 1);
% Add a row name as a variable
cl_row_names_a = strcat('esti', string((1:size(tb_saveCoef_stack,1))));
tb_saveCoef_stack.Properties.RowNames = cl_row_names_a;
% display results
disp(tb_saveCoef_stack);
estimodelctr FVAL EXITFLAG esti_iterations esti_funccount
____________ _______ ________ _______________ ______________
esti1 1 0.10606 0.74547 0.57231 0.45824
esti2 2 0.50673 0.057531 0.62758 0.13255
esti3 3 0.10517 0.12814 0.087406 0.11548
esti4 4 0.52383 0.039963 0.18597 0.77279
esti5 5 0.86664 0.26314 0.13141 0.041593 Similar to the previous estimation problem, however, now during different iterations, the column names, i.e. the parameters been estiamted are different. For example, there are 10 parameters, sometimes we estimate 5 of the 10, sometimes 10 or the 10. Want to stack all results together similar to above.
This is accomplished in the following example with the outerjoin function.
for row_idx=1:5
% a row of coefficent estimates
rng(123+row_idx);
it_num_rows = 1;
if (row_idx <= 2)
it_num_cols = 4;
mt_saveCoef = rand([it_num_rows, it_num_cols]);
% row to table
ar_st_col_names = ["FVAL", "EXITFLAG", "esti_iterations", "esti_funccount"];
elseif (row_idx <= 4)
it_num_cols = 2;
mt_saveCoef = rand([it_num_rows, it_num_cols]);
% row to table
ar_st_col_names = ["FVAL", "EXITFLAG"];
else
it_num_cols = 3;
mt_saveCoef = rand([it_num_rows, it_num_cols]);
% row to table
ar_st_col_names = ["FVAL", "esti_iterations", "esti_funccount"];
end
tb_saveCoef = array2table(mt_saveCoef);
tb_saveCoef.Properties.VariableNames = ar_st_col_names;
tb_saveCoef = addvars(tb_saveCoef, row_idx, 'Before', 1);
% Stack all results
if(row_idx == 1)
tb_saveCoef_stack = tb_saveCoef;
else
tb_saveCoef_stack = outerjoin(tb_saveCoef_stack, tb_saveCoef, 'MergeKeys', true);
end
end
% Add esti Counter as column
estimodelctr = (1:size(tb_saveCoef_stack,1))';
tb_saveCoef_stack = addvars(tb_saveCoef_stack, estimodelctr, 'Before', 1);
% Add a row name as a variable
cl_row_names_a = strcat('esti', string((1:size(tb_saveCoef_stack,1))));
tb_saveCoef_stack.Properties.RowNames = cl_row_names_a;
% display results
disp(tb_saveCoef_stack);
estimodelctr row_idx FVAL EXITFLAG esti_iterations esti_funccount
____________ _______ _______ ________ _______________ ______________
esti1 1 1 0.10606 0.74547 0.57231 0.45824
esti2 2 2 0.50673 0.057531 0.62758 0.13255
esti3 3 3 0.10517 0.12814 NaN NaN
esti4 4 4 0.52383 0.039963 NaN NaN
esti5 5 5 0.86664 NaN 0.26314 0.13141 Same as above, but iterate/solve over loops with parfor
% Start cluster
delete(gcp('nocreate'));
myCluster = parcluster('local');
it_workers = 4;
myCluster.NumWorkers = it_workers;
parpool(it_workers);
Starting parallel pool (parpool) using the 'local' profile ...
Connected to the parallel pool (number of workers: 4).
% prepare storage
cl_stores = cell([4,1]);
% Loop over
parfor row_idx=1:4
% a row of coefficent estimates
rng(123+row_idx);
ar_st_col_names = ["FVAL", "EXITFLAG", "esti_iterations", "esti_funccount"];
it_num_rows = 1;
it_num_cols = 4;
mt_saveCoef = rand([it_num_rows, it_num_cols]);
tb_saveCoef = array2table(mt_saveCoef);
tb_saveCoef.Properties.VariableNames = ar_st_col_names;
tb_saveCoef = addvars(tb_saveCoef, row_idx, 'Before', 1);
% Stack all results
cl_stores{row_idx} = tb_saveCoef;
end
% delete cluster
delete(gcp('nocreate'));Stack tables stored in cells together:
% Combine
tb_saveCoef_stack = [];
for row_idx=1:4
tb_saveCoef_stack = [tb_saveCoef_stack; cl_stores{row_idx}];
end
% display results
disp(tb_saveCoef_stack);
Var1 FVAL EXITFLAG esti_iterations esti_funccount
____ _______ ________ _______________ ______________
1 0.48946 0.58215 0.2796 0.23945
2 0.28746 0.3907 0.12685 0.694
3 0.76682 0.48312 0.50655 0.24223
4 0.71522 0.15045 0.43025 0.4845 Now we will first column combine matrixes, model parameters and model outcomes, and then row combine matrixes from different simulations.
A model takes a N parameters, solve the model over M sets of parameters. Each time when the model is solved, a P by Q table of results is generated. Each column is a different statistics (mean, std, etc.), and each row is a different outcome variable (consumption, asset choices, etc.). Stack these P by Q Tables together, and add in information about the N parameters, each of the tables been stacked initially had the same column and row names.
The resulting table should have P times M rows, for M sets of model simulations each with P rows of results. And there should be N + Q columns, storing the N parameters as well as the Q columns of different outcomes.
rng(123);
% Generate A P by Q matrix of random parameter Values
it_param_groups_m = 5;
it_params_n = 2;
it_outcomes_p = 3;
it_stats_q = 3;
% Parameter Matrix and Names
ar_param_names = strcat('param_', string(1:it_params_n));
mt_param_m_by_n = round(rand([it_param_groups_m, it_params_n])*5, 2);
% Loop over the parameters
for it_cur_param_group=1:1:it_param_groups_m
% Current Parameters
ar_param = mt_param_m_by_n(it_cur_param_group,:);
% Some Model is simulated
mt_model_simu = normrnd(mean(ar_param), std(ar_param), [it_outcomes_p, it_stats_q]);
% Model Results are Saved As Table With Column and Row Information
tb_model_simu = array2table(mt_model_simu);
cl_col_names = strcat('stats_', string((1:size(mt_model_simu,2))));
cl_row_names = strcat('outvar_', string((1:size(mt_model_simu,1))));
tb_model_simu.Properties.VariableNames = cl_col_names;
tb_model_simu.Properties.RowNames = cl_row_names;
% Convert Row Variable Names to a Column String
outvar = string(tb_model_simu.Properties.RowNames);
tb_model_simu = addvars(tb_model_simu, outvar, 'Before', 1);
% Parameter Information Table that Shares Row Names as Simu Results
mt_param_info = zeros([it_outcomes_p,it_params_n]) + ar_param;
tb_param_info = array2table(mt_param_info);
tb_param_info.Properties.VariableNames = ar_param_names;
tb_param_info.Properties.RowNames = cl_row_names;
% Combine Parameter Information and Simulation Contents
tb_model_simu_w_info = [tb_param_info tb_model_simu];
% Update Row Names based on total row available
ar_rows_allsimu = (1:it_stats_q)' + (it_cur_param_group-1)*it_stats_q;
tb_model_simu_w_info.Properties.RowNames = strcat('row=', string(ar_rows_allsimu));
% Show One Example Table before Stacking
if (it_cur_param_group == round(it_param_groups_m/2))
disp(tb_model_simu);
disp(tb_param_info);
disp(tb_model_simu_w_info);
end
% Stack all results
if(it_cur_param_group == 1)
tb_model_allsimu_w_info = tb_model_simu_w_info;
else
tb_model_allsimu_w_info = [tb_model_allsimu_w_info; tb_model_simu_w_info];
end
end
outvar stats_1 stats_2 stats_3
__________ ________ _______ _______
outvar_1 "outvar_1" 0.056853 2.1703 2.1098
outvar_2 "outvar_2" 3.1545 2.0634 0.7798
outvar_3 "outvar_3" -0.49033 2.2566 1.7896
param_1 param_2
_______ _______
outvar_1 1.13 3.42
outvar_2 1.13 3.42
outvar_3 1.13 3.42
param_1 param_2 outvar stats_1 stats_2 stats_3
_______ _______ __________ ________ _______ _______
row=7 1.13 3.42 "outvar_1" 0.056853 2.1703 2.1098
row=8 1.13 3.42 "outvar_2" 3.1545 2.0634 0.7798
row=9 1.13 3.42 "outvar_3" -0.49033 2.2566 1.7896 Show all Simulation Joint Table Outputs:
disp(tb_model_allsimu_w_info);
param_1 param_2 outvar stats_1 stats_2 stats_3
_______ _______ __________ ________ _______ _______
row=1 3.48 2.12 "outvar_1" 2.2665 1.1885 1.924
row=2 3.48 2.12 "outvar_2" 3.3427 2.4647 2.3548
row=3 3.48 2.12 "outvar_3" 2.6714 3.6132 2.918
row=4 1.43 4.9 "outvar_1" 3.3859 5.3759 1.5816
row=5 1.43 4.9 "outvar_2" 3.9499 3.8698 2.2693
row=6 1.43 4.9 "outvar_3" 5.7745 4.6871 1.7334
row=7 1.13 3.42 "outvar_1" 0.056853 2.1703 2.1098
row=8 1.13 3.42 "outvar_2" 3.1545 2.0634 0.7798
row=9 1.13 3.42 "outvar_3" -0.49033 2.2566 1.7896
row=10 2.76 2.4 "outvar_1" 2.9611 2.6847 2.4986
row=11 2.76 2.4 "outvar_2" 2.9333 2.3457 3.0629
row=12 2.76 2.4 "outvar_3" 2.5814 2.4372 2.4806
row=13 3.6 1.96 "outvar_1" 2.7199 3.3129 3.0577
row=14 3.6 1.96 "outvar_2" 3.9804 1.4529 2.9285
row=15 3.6 1.96 "outvar_3" 2.8445 4.4117 2.6576