# 1 Matlab Table Summarize and Aggregate by Groups

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## 1.1 Group Table Rows and Sum within Group

There is a table where subsets of rows belong to different simulations, with exogenous fixed $$\rho$$ parameters. For each $$\rho$$ parameter combination, there are, stored as different rows, a number of model predictions and data moments, and corresponding difference. Find the total difference between model and data for subsets of rows based for each $$\rho$$ parameter set.

First, create a table where each $$\rho$$ group is identified jointly by $$\rho_a$$ and $$\rho_b$$, stored in the 3rd and 4th rows.

% Make N by 2 matrix of fieldname + value type
mt_st_variable_names_types = [...
["year", "double"];["category", "string"];...
["rhoa", "double"];["rhob", "double"]; ...
% Make table using fieldnames & value types from above
tb_agg_exa = table('Size',[0,size(mt_st_variable_names_types,1)],...
'VariableNames', mt_st_variable_names_types(:,1),...
'VariableTypes', mt_st_variable_names_types(:,2));
% Table with data inputs
tb_agg_exa = [tb_agg_exa;...
{1, 'C001', 0.50, 0.50, 5.5, 6.05}; {2, 'C002', 0.50, 0.50, 3.7, 4.4}; ...
{1, 'C001', 0.25, 0.30, 2.5, 3.65}; {2, 'C002', 0.25, 0.30, 0.1, 1.6}; ...
{3, 'C001', 0.25, 0.50, 0.01, 1.66}];
% Generate model and data difference
tb_agg_exa{:, "diff"} = tb_agg_exa{:, "numberWorkersSimu"} - tb_agg_exa{:, "numberWorkersData"};
% Display
disp(tb_agg_exa);

year    category    rhoa    rhob    numberWorkersSimu    numberWorkersData    diff
____    ________    ____    ____    _________________    _________________    _____

1       "C001"      0.5    0.5            5.5                 6.05           -0.55
2       "C002"      0.5    0.5            3.7                  4.4            -0.7
1       "C001"     0.25    0.3            2.5                 3.65           -1.15
2       "C002"     0.25    0.3            0.1                  1.6            -1.5
3       "C001"     0.25    0.5           0.01                 1.66           -1.65

Second, select the subset of columns that are relevant for aggregation.

% Select
tb_agg_exa = tb_agg_exa(:, ["rhoa", "rhob", "diff"]);
% Display
disp(tb_agg_exa);

rhoa    rhob    diff
____    ____    _____

0.5    0.5     -0.55
0.5    0.5      -0.7
0.25    0.3     -1.15
0.25    0.3      -1.5
0.25    0.5     -1.65

Third, group by unique combinations of rhoa, rhob, and aggregate. Then generate group ID.

% Sum within groupo
tb_groupby_agg_sum = groupsummary(tb_agg_exa, ["rhoa", "rhob"], "sum");
% Generate grouping ID
tb_groupby_agg_sum{:, "ID"} = (1:1:size(tb_groupby_agg_sum, 1))';
tb_groupby_agg_sum = movevars(tb_groupby_agg_sum, "ID", "Before", 1);
disp(tb_groupby_agg_sum);

ID    rhoa    rhob    GroupCount    sum_diff
__    ____    ____    __________    ________

1     0.25    0.3         2          -2.65
2     0.25    0.5         1          -1.65
3      0.5    0.5         2          -1.25