1. What is SimOutUtils?
2. File format
3. How to use the utilities
4. Examples
4.1. Core functionality
4.1.1. Plot simulation output
4.1.2. Get statistical summaries from one replication
4.1.3. Get and analyze statistical summaries from multiple replications
4.2. Distributional analysis of output
4.2.1. Distributional analysis tables
4.2.2. Visually analyze the distributional properties of a focal measure
4.2.3. LaTeX table with distributional analysis of all focal measures for one setup
4.2.4. LaTeX table with a distributional analysis of one focal measure for multiple setups
4.3. Comparison of model implementations
4.3.1. Compare the outputs of two or more model implementations
4.3.2. Compare focal measures of two model implementations
4.3.3. Compare focal measures of multiple model implementations
4.3.4. Pairwise comparison of model implementations
4.3.5. Plot the PDF and CDF of focal measures from one or more model implementations
4.3.6. Table with p-values from comparison of focal measures from model implementations
4.3.7. Multiple comparisons and comparison names
4.3.8. Comparison groups
5. Unit tests
6. License
7. References
A number of MATLAB/Octave functions for analyzing output data from simulation models, as well as for producing publication quality tables and figures. These utilities were originally developed to analyze the PPHPC model, and later generalized to be usable with stochastic simulation models with time series-like outputs.
These utilities are compatible with GNU Octave. However, note that a number of statistical tests provided by Octave return slightly different p-values from those returned by the equivalent MATLAB functions.
The following links list the available functions:
- Core functions
- Distributional analysis of output
- Comparison of model implementations
- Helper functions
- Third-party functions
If you use SimOutUtils, please cite reference [1].
The functions provided by SimOutUtils use the dlmread MATLAB/Octave function to open files containing simulation output. As such, these functions expect text files with numeric values delimited by a separator (automatically inferred by dlmread). The files should contain data values in tabular format, with one column per output and one row per iteration.
Clone or download the utilities to any folder. Then, either start
MATLAB/Octave directly in this folder, or cd into this folder and execute
the startup script:
startup
The examples use the following datasets:
These datasets correspond to the results presented in references [2], [3] and [4], respectively.
Unpack the datasets to any folder and put the complete path to these folders in
variables datafolder1, datafolder2 and datafolder3, respectively:
datafolder1 = 'path/to/dataset1';
datafolder2 = 'path/to/dataset2';
datafolder3 = 'path/to/dataset3';The datasets contain output from several implementations of the PPHPC agent-based model. PPHPC is a realization of prototypical predator-prey system with six outputs:
- Sheep population
- Wolves population
- Quantity of available grass
- Mean sheep energy
- Mean wolves energy
- Mean value of the grass countdown parameter
Dataset 1 contains output from the NetLogo implementation of PPHPC. It is used in the core functionality and distributional analysis of output examples. Dataset 2 contains output from the NetLogo implementation and from six variants of a parallel Java implementation, namely, ST, EQ, EX, ER and OD. These implementations and variants are aligned, i.e., they display the same dynamic behavior. Finally, dataset 3 contains aligned output from the NetLogo and Java EX implementations, and also output from two purposefully misaligned versions of the latter. Datasets 2 and 3 are used in the examples concerning the comparison of model implementations.
The datasets were collected under five different model sizes (100 x 100, 200 x 200, 400 x 400, 800 x 800 and 1600 x 1600) and two distinct parameterizations (v1 and v2).
Use the output_plot function to plot outputs from one replication of the PPHPC model:
output_plot([datafolder1 '/v1'], 'stats100v1r1.txt', 6);
The third parameter specifies the number of outputs. Alternatively, a cell array of strings can be passed in order to display personalized output names. Furthermore, outputs 4 to 6 are practically not visible, as they have a very different scale from outputs 1 to 3. The 'layout' option defines how many outputs to plot per figure, and can be used to solve this problem. As such, output_plot can be invoked in the following way:
outputs = {'SheepPop', 'WolfPop', 'GrassQty', 'SheepEnergy', 'WolfEnergy', 'GrassEnergy'};
output_plot([datafolder1 '/v1'], 'stats100v1r1.txt', outputs, 'layout', [3 3]);
The 'layout' option is one of the several key-value arguments accepted by output_plot. Another option is the 'Colors' parameter, which specifies the colors used for plotting individual outputs. It can be used, for example, to use the same colors for the outputs in both figures:
output_plot([datafolder1 '/v1'], 'stats100v1r1.txt', outputs, 'layout', [3 3], 'Colors', {'b', 'r', 'g', 'b', 'r', 'g'});
A number of these key-value arguments consist of LineSpecs for individual outputs (PatchSpecs in the case of type f plots, discussed further ahead). If there are more outputs than specs in the associated cell array, the given specs are repeated. As such, in the previous command we could have shortened the given 'Colors' cell array, i.e.:
output_plot([datafolder1 '/v1'], 'stats100v1r1.txt', outputs, 'layout', [3 3], 'Colors', {'b', 'r', 'g'});The output_plot function recognizes a number of LineSpecs and PatchSpecs, namely 'Colors', 'LineStyles', 'LineWidths', 'Markers', 'MarkerEdgeColors', 'MarkerFaceColors' and 'MarkerSizes'. There is also the 'EdgeColors' option, which is only recognized within the PatchSpecs context, i.e. for type f plots.
Returning to the example, the third and sixth outputs of the last command (GrassQty and GrassEnergy, respectively) are still somewhat out of scale with the remaining outputs. This can be solved by specifying the 'scale' option:
outputs = {'SheepPop', 'WolfPop', 'GrassQty/4', 'SheepEnergy', 'WolfEnergy', '4*GrassEnergy'};
output_plot([datafolder1 '/v1'], 'stats100v1r1.txt', outputs, 'layout', [3 3], 'Colors', {'b', 'r', 'g'}, 'scale', [1 1 1/4 1 1 4]);
The plot looks good now. In order to plot outputs from multiple replications, we simply use wildcards to load more than one file:
output_plot([datafolder1 '/v1'], 'stats100v1r*.txt', outputs, 'layout', [3 3], 'Colors', {'b', 'r', 'g'}, 'scale', [1 1 1/4 1 1 4]);
When plotting multiple replications this way, the figures tend to look somewhat heavy and are slow to manipulate. We could alternatively plot only the output extremes (minimum and maximum of individual outputs at each iteration), and fill the space between with the output color. This can be accomplished by specifying the fill 'type':
output_plot([datafolder1 '/v1'], 'stats100v1r*.txt', outputs, 'type', 'f', 'layout', [3 3], 'Colors', {'b', 'r', 'g'}, 'scale', [1 1 1/4 1 1 4]);
Finally, it is also possible to visualize the moving average of each output over multiple replications by passing a positive integer as the 'type' option. This positive integer is the window size with which to smooth the output. A value of zero is equivalent to no smoothing, i.e. the function will simply plot the averaged outputs. A value of 10 offers a good balance between rough and overly smooth plots:
output_plot([datafolder1 '/v1'], 'stats100v1r*.txt', outputs, 'type', 10, 'layout', [3 3], 'Colors', {'b', 'r', 'g'}, 'scale', [1 1 1/4 1 1 4]);
The moving average type of plot is useful for empirically selecting a steady-state truncation point.
The following command plots only the first 3 outputs in black color, with different line styles:
output_plot([datafolder1 '/v1'], 'stats100v1r*.txt', outputs(1:3), 'type', 10, 'Colors', 'k', 'scale', [1 1 1/4], 'LineStyles', {'-','--',':'});
Figures generated with output_plot can be converted to LaTeX with the excellent matlab2tikz script. For the previous figure, the following commands would perform this conversion, assuming matlab2tikz is in MATLAB's path:
cleanfigure();
matlab2tikz('standalone', true, 'filename', 'simout_bw.tex');Compiling the simout_bw.tex file with LaTeX would produce the following
figure:
The stats_get function is the elementary building block of SimOutUtils for
analyzing simulation output. It is indirectly used by most package functions
(via the higher-level stats_gather function). The goal of stats_get is to
extract statistical summaries from simulation outputs from one file. It does
this through ancillary stats_get_* functions which perform the actual
extraction. The exact function to use (and consequently, the concrete
statistical summaries to extract) is specified in the simoututils_stats_get_
global variable, defined in the startup script when SimOutUtils is loaded.
The stats_get_pphpc function is the package default. This function returns six statistical summaries, namely the maximum (max), iteration where maximum occurs (argmax), minimum (min), iteration where minimum occurs (argmin), mean (mean), and standard deviation (std). The mean and std summaries are obtained during the (user-specified) steady-state stage of the output. These summaries were selected for the PPHPC model [2], but are appropriate for any model with tendentiously stable time series outputs.
The following instruction gets the statistical summaries of the first replication of the PPHPC model for size 100 and parameter set 1:
sdata = stats_get(1000, [datafolder1 '/v1/stats100v1r1.txt'], 6)The first argument is dependent on the actual stats_get_* being used. In this
case, we are using the package default stats_get_pphpc function, which
requires the user to specify the steady-state truncation point (i.e., 1000). The
last argument specifies the number of outputs. The function returns a n x m
matrix of focal measures, with n=6 statistical summaries and m=6 outputs:
sdata =
1.0e+03 *
2.5160 0.5260 8.6390 0.0190 0.0331 0.0035
0.1530 3.3130 0.0120 0.0690 0.2550 0.1590
0.3050 0.0180 3.6530 0.0045 0.0122 0.0007
0.0070 0.0860 0.1590 0 0.0150 0.0100
1.1854 0.3880 6.2211 0.0164 0.0244 0.0021
0.1211 0.0487 0.2731 0.0007 0.0016 0.0002
In order to use alternative statistical summaries, the user should specify
another function by setting the appropriate function handle in the
simoututils_stats_get_ global variable:
simoututils_stats_get_ = @stats_get_iters;The previous instruction configures stats_get_iters as the stats_get_*
function to use. The statistical summaries fetched by this function are simply
the output values at user-specified iterations. Invoking stats_get again, the
first argument now specifies the iterations at which to get output values:
sdata = stats_get([10 100 1000], [datafolder1 '/v1/stats100v1r1.txt'], 6)The returned n x m matrix of focal measure now has n=3 statistical summaries and m=6 outputs:
sdata =
1.0e+03 *
0.3180 0.2160 8.5940 0.0115 0.0139 0.0007
1.9110 0.0240 4.9280 0.0160 0.0246 0.0028
1.0060 0.4690 6.6110 0.0170 0.0207 0.0018
To permanently use another stats_get_* function as default, edit the startup
script and change the value of the simoututils_stats_get_ global variable as
desired. For the remainder of this discussion it is assumed that the
stats_get_pphpc function is being used.
The stats_gather function extracts statistical summaries from simulation outputs from multiple files. The following instruction obtains statistical summaries for 30 runs of the PPHPC model for size 100 and parameter set 1:
s100v1 = stats_gather('100v1', [datafolder1 '/v1'], 'stats100v1r*.txt', 6, 1000);The fourth parameter, 6, corresponds to the number of outputs of the PPHPC model. Instead of the number of outputs, the function alternatively accepts a cell array of strings containing the output names, which can be useful for tables and figures. The fifth and last parameter, 1000 , corresponds to the iteration after which the outputs are in steady-state. The stats_gather function returns a struct with several fields, of which the following are important to this discussion:
namecontains the name with which the data was tagged, '100v1' in this case;outputsis a cell array containing the output names (which default to 'o1', 'o2', etc.);sdatais a 30 x 36 matrix, with 30 observations (from 30 files) and 36 focal measures (six statistical summaries for each of the six outputs).
Next, we analyze the focal measures (i.e., statistical summaries for each output):
[m, v, cit, ciw, sw, sk] = stats_analyze(s100v1.sdata', 0.05);The 0.05 value in the second parameter is the significance level for the
confidence intervals and the Shapiro-Wilk test. The variables returned by the
stats_analyze function have 36 rows, one per focal measure. The m (mean),
v (variance), sw (p-value of the Shapiro-Wilk test) and sk (skewness)
variables have only one column, i.e. one value per focal measure, while the
cit (t-confidence interval) and ciw (Willink confidence interval
[5]) variables have two columns, which correspond to the lower and
upper limits of the respective intervals.
While the data returned by the stats_analyze is in a format adequate for further processing and/or analysis, it is not very human readable. For this purpose, we can use the stats_table_per_setup function to output an informative plain text table:
stats_table_per_setup(s100v1, 0.05, 0)-----------------------------------------------------------------------------------------
| Output | Stat. | Mean | Variance | 95.0% Conf. interval | SW test |
|------------|----------|------------|------------|---------------------------|---------|
| o1 | max | 2517 | 6699 | [ 2486, 2547] | 0.8287 |
| | argmax | 145.2 | 91.36 | [ 141.7, 148.8] | 0.8255 |
| | min | 317 | 204.9 | [ 311.7, 322.3] | 0.8227 |
| | argmin | 6.8 | 6.51 | [ 5.847, 7.753] | 0.0326 |
| | mean | 1186 | 65.54 | [ 1183, 1189] | 0.9663 |
| | std | 107.9 | 223.9 | [ 102.3, 113.5] | 0.3534 |
|------------|----------|------------|------------|---------------------------|---------|
| o2 | max | 530.5 | 435.8 | [ 522.7, 538.3] | 0.0026 |
| | argmax | 2058 | 8.845e+05 | [ 1707, 2409] | 0.1654 |
| | min | 19.9 | 58.58 | [ 17.04, 22.76] | 0.6423 |
| | argmin | 71.93 | 105.7 | [ 68.1, 75.77] | 0.1912 |
| | mean | 390.5 | 6.518 | [ 389.5, 391.4] | 0.1380 |
| | std | 44.93 | 25.6 | [ 43.04, 46.82] | 0.0737 |
|------------|----------|------------|------------|---------------------------|---------|
| o3 | max | 8624 | 4097 | [ 8600, 8647] | 0.3778 |
| | argmax | 11.7 | 0.2862 | [ 11.5, 11.9] | 0.0000 |
| | min | 3745 | 1.66e+04 | [ 3697, 3793] | 0.5270 |
| | argmin | 148.2 | 94.14 | [ 144.5, 151.8] | 0.6463 |
| | mean | 6216 | 285.7 | [ 6210, 6222] | 0.6502 |
| | std | 247.3 | 1128 | [ 234.7, 259.8] | 0.0824 |
|------------|----------|------------|------------|---------------------------|---------|
| o4 | max | 19.74 | 0.5092 | [ 19.47, 20] | 0.1594 |
| | argmax | 53.07 | 36.96 | [ 50.8, 55.34] | 0.3321 |
| | min | 4.461 | 0.01765 | [ 4.412, 4.511] | 0.9519 |
| | argmin | 0 | 0 | [ 0, 0] | NaN |
| | mean | 16.38 | 0.003763 | [ 16.36, 16.41] | 0.9614 |
| | std | 0.653 | 0.004133 | [ 0.629, 0.677] | 0.4578 |
|------------|----------|------------|------------|---------------------------|---------|
| o5 | max | 41.86 | 41.39 | [ 39.46, 44.26] | 0.0761 |
| | argmax | 135.7 | 1075 | [ 123.4, 147.9] | 0.0021 |
| | min | 11.31 | 0.9338 | [ 10.95, 11.67] | 0.1280 |
| | argmin | 24.33 | 142.7 | [ 19.87, 28.79] | 0.0000 |
| | mean | 24.61 | 0.02589 | [ 24.55, 24.67] | 0.6280 |
| | std | 1.673 | 0.01815 | [ 1.623, 1.723] | 0.0457 |
|------------|----------|------------|------------|---------------------------|---------|
| o6 | max | 3.455 | 0.005314 | [ 3.428, 3.482] | 0.5257 |
| | argmax | 148.9 | 109.8 | [ 145, 152.8] | 0.5714 |
| | min | 0.7595 | 0.001429 | [ 0.7454, 0.7736] | 0.2921 |
| | argmin | 10.33 | 0.2989 | [ 10.13, 10.54] | 0.0000 |
| | mean | 2.081 | 8.627e-05 | [ 2.078, 2.085] | 0.6190 |
| | std | 0.1371 | 0.0003382 | [ 0.1302, 0.144] | 0.0794 |
-----------------------------------------------------------------------------------------
The last parameter, 0, specifies plain text output. This function can also output a publication quality LaTeX table by setting the last argument to 1:
stats_table_per_setup(s100v1, 0.05, 1)
The produced LaTeX table requires the siunitx, multirow, booktabs and ulem packages to compile.
The dist_plot_per_fm function offers a simple way of assessing the distributional properties of a focal measure for different model configurations (i.e., different model sizes, different parameter set, etc). For each configuration the function shows an approximate probability density function (PDF), a histogram, and a QQ-plot. The dist_plot_per_fm function works with the data returned by stats_gather.
For example, let us assess the distributional properties of the PPHPC focal measure given by the argmin of the grass quantity output for parameter set 2 and a number of different model sizes:
% Get statistical summaries for different model sizes, parameter set 2
outputs = {'SheepPop', 'WolfPop', 'GrassQty', 'SheepEn', 'WolfEn', 'GrassEn'};
s100v2 = stats_gather('100v2', [datafolder1 '/v2'], 'stats100v2r*.txt', outputs, 2000);
s200v2 = stats_gather('200v2', [datafolder1 '/v2'], 'stats200v2r*.txt', outputs, 2000);
s400v2 = stats_gather('400v2', [datafolder1 '/v2'], 'stats400v2r*.txt', outputs, 2000);
s800v2 = stats_gather('800v2', [datafolder1 '/v2'], 'stats800v2r*.txt', outputs, 2000);
s1600v2 = stats_gather('1600v2', [datafolder1 '/v2'], 'stats1600v2r*.txt', outputs, 2000);
% Group them into a cell array
sv2 = {s100v2, s200v2, s400v2, s800v2, s1600v2};The argmin of the grass quantity output is the third statistical summary of the fourth output, as indicated in the second and third arguments of dist_plot_per_fm:
% Plot distributional properties
dist_plot_per_fm(sv2, 3, 4);
Note that in this example we explicitly specified the output names when calling the stats_gather function. Also, for parameter set 2, we set the steady-state truncation point to iteration 2000.
In reference [2], a number of tables containing a detailed distributional analysis of all PPHPC focal measures are provided as supplemental information. Each table displays a distributional analysis for one setup, i.e., for one size/parameter set combination. The dist_table_per_setup function produces these tables, accepting a single parameter which corresponds to the output of stats_gather. For example, to get a table with the distributional analysis of all PPHPC focal measures for model size 1600, parameter set 2, only two commands are required:
outputs = {'$P^s_i$', '$P^w_i$', '$P^c_i$', '$\bar{E}^s_i$', '$\bar{E}^w_i$', '$\bar{C}_i$'};
s1600v2 = stats_gather('1600v2', [datafolder1 '/v2'], 'stats1600v2r*.txt', outputs, 2000);
dist_table_per_setup(s1600v2)
We specify the output names in LaTeX math mode so they appear in the produced table as they appear in the article.
A distributional analysis of a focal measure for multiple setups is often useful for evaluating how its distributional properties vary with different model configurations/setups. The dist_table_per_fm function fits this purpose. However, this function returns a partial table, which can have additional columns (specified with the 'pre' parameter) prior to the distributional data itself, as well as additional rows, such as headers, footers, similar partial tables for other focal measures, and so on.
Using the PPHPC model as an example, let us generate a table with the distributional analysis of the steady-state mean of the sheep population, for all tested model sizes and both parameter sets. Model sizes are specified as columns, while parameter sets are obtained with two separate partial tables, which together form the final table:
% Get stats data for parameter set 1, all sizes
s100v1 = stats_gather('100v1', [datafolder1 '/v1'], 'stats100v1r*.txt', outputs, 1000);
s200v1 = stats_gather('200v1', [datafolder1 '/v1'], 'stats200v1r*.txt', outputs, 1000);
s400v1 = stats_gather('400v1', [datafolder1 '/v1'], 'stats400v1r*.txt', outputs, 1000);
s800v1 = stats_gather('800v1', [datafolder1 '/v1'], 'stats800v1r*.txt', outputs, 1000);
s1600v1 = stats_gather('1600v1', [datafolder1 '/v1'], 'stats1600v1r*.txt', outputs, 1000);
datas1 = {s100v1, s200v1, s400v1, s800v1, s1600v1};
% Get stats data for parameter set 2, all sizes
s100v2 = stats_gather('100v2', [datafolder1 '/v2'], 'stats100v2r*.txt', outputs, 2000);
s200v2 = stats_gather('200v2', [datafolder1 '/v2'], 'stats200v2r*.txt', outputs, 2000);
s400v2 = stats_gather('400v2', [datafolder1 '/v2'], 'stats400v2r*.txt', outputs, 2000);
s800v2 = stats_gather('800v2', [datafolder1 '/v2'], 'stats800v2r*.txt', outputs, 2000);
s1600v2 = stats_gather('1600v2', [datafolder1 '/v2'], 'stats1600v2r*.txt', outputs, 2000);
datas2 = {s100v2, s200v2, s400v2, s800v2, s1600v2};
% Specify the focal measure: steady-state mean of the sheep population
out = 1; % Sheep population
ssumm = 5; % Steady-state mean
% Table headers
t = sprintf('\n\\begin{table}[ht]');
t = sprintf('%s\n\\centering', t);
t = sprintf('%s\\begin{tabular}{ccrrrrrr}\n', t);
t = sprintf('%s\\toprule\n', t);
t = sprintf('%sSet & Stat. & 100 & 200 & 400 & 800 & 1600\\\\\n', t);
t = sprintf('%s\\midrule\n\\multirow{4}{*}{v1} ', t);
% First partial table, for parameter set 1
t = sprintf('%s%s', t, dist_table_per_fm(datas1, out, ssumm, 1));
% A midrule to separate the partial tables
t = sprintf('%s\\midrule\n\\multirow{4}{*}{v2}', t);
% Second partial table, for parameter set 2
t = sprintf('%s%s', t, dist_table_per_fm(datas2, out, ssumm, 1));
% Table footers and caption
t = sprintf('%s\\bottomrule\n', t);
t = sprintf('%s\n\\end{tabular}', t);
t = sprintf('%s\n\\caption{Distributional analysis of sheep population steady-state mean for different model sizes and parameter sets.}\n', t);
t = sprintf('%s\n\\end{table}\n', t);
% Show the table
t
The output_compare_plot function can be used to graphically compare outputs from two or more model implementations. Multiple replications from each implementation are averaged, and an optional moving average filter can be used to smooth the per implementation output plots. It works in a similar fashion to output_plot, but is oriented towards multiple model implementations.
In the following example we compare the outputs of the NetLogo, Java EX (no agent shuffling) and Java EX (different parameter), using dataset 3.
% Specify output names
outputs = {'SheepPop', 'WolfPop', 'GrassQty', 'SheepEnergy', 'WolfEnergy', 'GrassEnergy'};
% Compare outputs
output_compare_plot({'NetLogo','Java-NS', 'Java-DIFF'}, ...
{[datafolder3 '/nl_ok'], [datafolder3 '/j_ex_noshuff'], [datafolder3 '/j_ex_diff']}, ...
{'stats400v1*.txt', 'stats400v1*.txt', 'stats400v1*.txt'}, outputs, ...
'ws', 10, 'Colors', {'b','k','g'}, 'LineWidths', {2,1,3});
The stats_compare function is used for comparing focal measures from two or more model implementations. For this purpose, it applies statistical tests to data obtained with the stats_gather function. Currently, stats_compare and the remaining functions for model comparison are limited to comparing samples of the same size.
In this example we compare the NetLogo and Java EX implementations of the PPHPC model for model size 400, parameter set 1 (as described in reference [3]). Replications of the Java EX variant were performed with 12 threads. First, we need to obtain the focal measures (i.e., statistical summaries of simulation outputs) with the stats_gather function:
% Get stats data for NetLogo implementation, parameter set 1, all sizes
snl400v1 = stats_gather('NL', [datafolder2 '/simout/NL'], 'stats400v1r*.txt', 6, 1000);
% Get stats data for the Java implementation, EX strategy (12 threads), parameter set 1, all sizes
sjex400v1 = stats_gather('JEX', [datafolder2 '/simout/EX'], 'stats400v1pEXt12r*.txt', 6, 1000);The fourth parameter, 6, corresponds to the number of model outputs, while the last, 1000, is the steady-state truncation point. We can now perform the comparison using the stats_compare function:
% Perform comparison
[ps, h_all] = stats_compare(0.01, {'p', 'np', 'p', 'np', 'p', 'p'}, 'none', snl400v1, sjex400v1)The first parameter specifies the significance level for the statistical tests. The second parameter specifies the tests to apply on individual statistical summaries for each output. In this case we are performing the t-test to all summaries, except argmax and argmin, to which the Mann-Whitney test [6] is applied instead. The options 'p' and 'np' stand for parametric and non-parametric, respectively. The third parameter specifies the p-value adjustment method for comparing multiple focal measures. No correction is performed in this case.
The stats_compare function return ps, a matrix of p-values for the
requested tests (rows correspond to outputs, columns to statistical summaries),
and h_all, containing the number of tests failed for the specified
significance level.
ps =
0.1784 0.8491 0.4536 1.0000 0.9560 0.1666
0.0991 0.4727 0.5335 0.0752 0.7231 0.1859
0.2515 0.3006 0.2312 0.0852 0.8890 0.1683
0.4685 0.8496 0.9354 1.0000 0.8421 0.4394
0.7973 0.8796 0.0009 0.3534 0.2200 0.5757
0.2443 0.0750 0.1719 1.0000 0.9009 0.1680
h_all =
1
The stats_compare function also allows to compare focal measure from more than two model implementations. If more than two stats_gather structs are passed as arguments, the stats_compare function automatically uses n-sample statistical tests, namely ANOVA [7] as a parametric test, and Kruskal-Wallis [8] as a non-parametric test. In the following, we compare all Java variants of the PPHPC model for size 800, parameter set 2:
% Get stats data for Java implementation, ST strategy
sjst800v2 = stats_gather('ST', [datafolder2 '/simout/ST'], 'stats800v2pSTr*.txt', 6, 2000);
% Get stats data for the Java implementation, EQ strategy (12 threads)
sjeq800v2 = stats_gather('EQ', [datafolder2 '/simout/EQ'], 'stats800v2pEQt12r*.txt', 6, 2000);
% Get stats data for the Java implementation, EX strategy (12 threads)
sjex800v2 = stats_gather('EX', [datafolder2 '/simout/EX'], 'stats800v2pEXt12r*.txt', 6, 2000);
% Get stats data for the Java implementation, ER strategy (12 threads)
sjer800v2 = stats_gather('ER', [datafolder2 '/simout/ER'], 'stats800v2pERt12r*.txt', 6, 2000);
% Get stats data for the Java implementation, OD strategy (12 threads, b = 500)
sjod800v2 = stats_gather('OD', [datafolder2 '/simout/OD'], 'stats800v2pODb500t12r*.txt', 6, 2000);
% Perform comparison
ps = stats_compare(0.05, {'p', 'np', 'p', 'np', 'p', 'p'}, 'none', sjst800v2, sjeq800v2, sjex800v2, sjer800v2, sjod800v2)ps =
0.8735 0.5325 1.0000 1.0000 0.7132 0.7257
0.4476 0.9051 0.3624 0.5947 0.7011 0.6554
0.4227 0.6240 0.8860 0.2442 0.5945 0.6785
0.0124 0.5474 0.6447 0.5238 0.7038 0.6182
0.8888 0.9622 0.1410 0.1900 0.7182 0.6825
0.9306 0.6286 0.4479 0.8377 0.5785 0.6785
When comparing multiple model implementations, if one or more are misaligned, the stats_compare function will detected a misalignment, but will not provide information regarding which implementations are misaligned. The stats_compare_pw function performs pairwise comparisons of multiple model implementations and outputs a table of failed tests for each pair of implementations, allowing to detect which ones are misaligned. The following instruction outputs this table for the data used in the previous example:
% Output table of pairwise failed tests for significance level 0.05
stats_compare_pw(0.05, {'p', 'np', 'p', 'np', 'p', 'p'}, 'none', sjst800v2, sjeq800v2, sjex800v2, sjer800v2, sjod800v2) -----------------------------------------------------------------------
| ST | EQ | EX | ER | OD |
------------------------------------------------------------------------------------
| ST | 0 | 1 | 1 | 1 | 2 |
| EQ | 1 | 0 | 0 | 0 | 1 |
| EX | 1 | 0 | 0 | 0 | 0 |
| ER | 1 | 0 | 0 | 0 | 1 |
| OD | 2 | 1 | 0 | 1 | 0 |
------------------------------------------------------------------------------------
Since each pairwise comparison involves the comparison of multiple focal measures, it can be useful to correct the p-values to account for multiple comparisons, e.g., using the Bonferroni procedure:
% Output table of pairwise failed tests for significance level 0.05 with Bonferroni correction
stats_compare_pw(0.05, {'p', 'np', 'p', 'np', 'p', 'p'}, 'bonferroni', sjst800v2, sjeq800v2, sjex800v2, sjer800v2, sjod800v2) -----------------------------------------------------------------------
| ST | EQ | EX | ER | OD |
------------------------------------------------------------------------------------
| ST | 0 | 0 | 0 | 0 | 0 |
| EQ | 0 | 0 | 0 | 0 | 0 |
| EX | 0 | 0 | 0 | 0 | 0 |
| ER | 0 | 0 | 0 | 0 | 0 |
| OD | 0 | 0 | 0 | 0 | 0 |
------------------------------------------------------------------------------------
No single test fails after the Bonferroni correction is applied to the p-values, strengthening the conclusion that the compared model implementations are aligned.
In this example we have two PPHPC implementations which produce equivalent results (NLOK and JEXOK), and two other which display slightly different behavior (JEXNS and JEXDIFF), as discussed in reference [4]. The following code loads simulation output data from these four implementations, and plots, using the stats_compare_plot function, the PDF and CDF of the respective focal measures. Plots for each focal measure are overlaid, allowing the modeler to observe distributional output differences between the various implementations.
% Specify output names
outputs = {'SheepPop', 'WolfPop', 'GrassQty', 'SheepEnergy', 'WolfEnergy', 'GrassEnergy'};
% Determine focal measures of four PPHPC implementations
snl800v2 = stats_gather('NL', [datafolder3 '/nl_ok'], 'stats800v2*.txt', outputs, 2000);
sjexok800v2 = stats_gather('JEXOK', [datafolder3 '/j_ex_ok'], 'stats800v2*.txt', outputs, 2000);
sjexns800v2 = stats_gather('JEXNS', [datafolder3 '/j_ex_noshuff'], 'stats800v2*.txt', outputs, 2000);
sjexdiff800v2 = stats_gather('JEXDIFF', [datafolder3 '/j_ex_diff'], 'stats800v2*.txt', outputs, 2000);
% Plot PDF and CDF of focal measures
stats_compare_plot(snl800v2, sjexok800v2, sjexns800v2, sjexdiff800v2);Sheep population
Wolf population
Quantity of available grass
Mean sheep energy
Mean wolves energy
Mean value of the countdown parameter in all cells
The stats_compare_table function produces publication quality tables of p-values in LaTeX. This function accepts four parameters:
tests- Type of statistical tests to perform (parametric or non-parametric).adjust- Adjustment to p-values for comparison of multiple focal measures: 'holm', 'hochberg', 'hommel', 'bonferroni', 'BH', 'BY', 'sidak' or 'none'.pthresh- Minimum value of p-values before truncation (e.g., if this value is set to 0.001 and a certain p-value is less than that, the table will display "< 0.001".tformat- Specifies if outputs appear in the header (0) or in the first column (1).varargin- Variable number of cell arrays containing the following two items defining a comparison:- Item 1 can take one of three formats: a) zero, 0, which is an indication not to print any type of comparison name; b) a string describing the comparison name; or, c) a cell array of two strings, the first describing a comparison group name, and the second describing a comparison name.
- Item 2, a cell array of statistical summaries (given by the stats_gather function) of the implementations to be compared.
The following command uses data from a previous example and outputs a table of p-values returned by the non-parametric, multi-sample Kruskal-Wallis test for individual focal measures:
s800v2 = {sjst800v2, sjeq800v2, sjex800v2, sjer800v2, sjod800v2};
stats_compare_table('np', 'none', 0.001, 0, {0, s800v2})
As we are only performing one comparison (for model size 800, parameter set 2), the third argument is set to 0. For multiple comparisons, it is preferable to set this parameter to 1, as it puts comparisons along columns and outputs along rows. The first item in the final argument is set to 0, such that the comparison name is not printed (which makes sense when the table only contains a single comparison).
In Table 1 of reference [4], three comparisons, I, II, and III, are performed. The comparison name can be specified in item 1 of the variable argument cell arrays, as shown in the following code:
% Specify output names
outputs = {'$P^s$', '$P^w$', '$P^c$', '$\overline{E}^s$', '$\overline{E}^w$', '$\overline{C}$'};
% Determine focal measures
snl400v1 = stats_gather('NL', [datafolder3 '/nl_ok'], 'stats400v1*.txt', outputs, 1000);
sjexok400v1 = stats_gather('JEXOK', [datafolder3 '/j_ex_ok'], 'stats400v1*.txt', outputs, 1000);
sjexns400v1 = stats_gather('JEXNS', [datafolder3 '/j_ex_noshuff'], 'stats400v1*.txt', outputs, 1000);
sjexdiff400v1 = stats_gather('JEXDIFF', [datafolder3 '/j_ex_diff'], 'stats400v1*.txt', outputs, 1000);
% Comparisons to perform, specify name in item 1
cmp1 = {'I', {snl400v1, sjexok400v1}};
cmp2 = {'II', {snl400v1, sjexns400v1 }};
cmp3 = {'III', {snl400v1, sjexdiff400v1}};
% Output comparison table
stats_compare_table({'p', 'np', 'p', 'np', 'p', 'p'}, 'none', 0.000001, 0, cmp1, cmp2, cmp3)
Here we specify comparison names, I, II, and II, which will be printed in the table. Note that each comparison tests two model implementations. As such the resulting p-values come from two-sample tests, i.e., from the parametric t-test and from the non-parametric Mann-Whitney test.
In Table 8 of reference [3], ten comparisons are performed. Each comparison is associated with a model size and parameter set, and tests for differences between six model implementations. Comparisons are divided in two groups, according to the parameter set used. This is accomplished by passing a cell array of two strings (comparison group and comparison name) to the first item of each comparison. The following code outputs this table:
% Specify output names
outputs = {'$P_i^s$', '$P_i^w$', '$P_i^c$', '$\overline{E}^s_i$', '$\overline{E}^w_i$', '$\overline{C}_i$'};
% Determine focal measures for NetLogo replications
snl100v1 = stats_gather('NL', [datafolder2 '/simout/NL'], 'stats100v1*.txt', outputs, 1000);
snl200v1 = stats_gather('NL', [datafolder2 '/simout/NL'], 'stats200v1*.txt', outputs, 1000);
snl400v1 = stats_gather('NL', [datafolder2 '/simout/NL'], 'stats400v1*.txt', outputs, 1000);
snl800v1 = stats_gather('NL', [datafolder2 '/simout/NL'], 'stats800v1*.txt', outputs, 1000);
snl1600v1 = stats_gather('NL', [datafolder2 '/simout/NL'], 'stats1600v1*.txt', outputs, 1000);
snl100v2 = stats_gather('NL', [datafolder2 '/simout/NL'], 'stats100v2*.txt', outputs, 2000);
snl200v2 = stats_gather('NL', [datafolder2 '/simout/NL'], 'stats200v2*.txt', outputs, 2000);
snl400v2 = stats_gather('NL', [datafolder2 '/simout/NL'], 'stats400v2*.txt', outputs, 2000);
snl800v2 = stats_gather('NL', [datafolder2 '/simout/NL'], 'stats800v2*.txt', outputs, 2000);
snl1600v2 = stats_gather('NL', [datafolder2 '/simout/NL'], 'stats1600v2*.txt', outputs, 2000);
% Determine focal measures for Java ST replications
sjst100v1 = stats_gather('ST', [datafolder2 '/simout/ST'], 'stats100v1*.txt', outputs, 1000);
sjst200v1 = stats_gather('ST', [datafolder2 '/simout/ST'], 'stats200v1*.txt', outputs, 1000);
sjst400v1 = stats_gather('ST', [datafolder2 '/simout/ST'], 'stats400v1*.txt', outputs, 1000);
sjst800v1 = stats_gather('ST', [datafolder2 '/simout/ST'], 'stats800v1*.txt', outputs, 1000);
sjst1600v1 = stats_gather('ST', [datafolder2 '/simout/ST'], 'stats1600v1*.txt', outputs, 1000);
sjst100v2 = stats_gather('ST', [datafolder2 '/simout/ST'], 'stats100v2*.txt', outputs, 2000);
sjst200v2 = stats_gather('ST', [datafolder2 '/simout/ST'], 'stats200v2*.txt', outputs, 2000);
sjst400v2 = stats_gather('ST', [datafolder2 '/simout/ST'], 'stats400v2*.txt', outputs, 2000);
sjst800v2 = stats_gather('ST', [datafolder2 '/simout/ST'], 'stats800v2*.txt', outputs, 2000);
sjst1600v2 = stats_gather('ST', [datafolder2 '/simout/ST'], 'stats1600v2*.txt', outputs, 2000);
% Determine focal measures for Java EQ replications, 12 threads
sjeq100v1 = stats_gather('EQ', [datafolder2 '/simout/EQ'], 'stats100v1pEQt12r*.txt', outputs, 1000);
sjeq200v1 = stats_gather('EQ', [datafolder2 '/simout/EQ'], 'stats200v1pEQt12r*.txt', outputs, 1000);
sjeq400v1 = stats_gather('EQ', [datafolder2 '/simout/EQ'], 'stats400v1pEQt12r*.txt', outputs, 1000);
sjeq800v1 = stats_gather('EQ', [datafolder2 '/simout/EQ'], 'stats800v1pEQt12r*.txt', outputs, 1000);
sjeq1600v1 = stats_gather('EQ', [datafolder2 '/simout/EQ'], 'stats1600v1pEQt12r*.txt', outputs, 1000);
sjeq100v2 = stats_gather('EQ', [datafolder2 '/simout/EQ'], 'stats100v2pEQt12r*.txt', outputs, 2000);
sjeq200v2 = stats_gather('EQ', [datafolder2 '/simout/EQ'], 'stats200v2pEQt12r*.txt', outputs, 2000);
sjeq400v2 = stats_gather('EQ', [datafolder2 '/simout/EQ'], 'stats400v2pEQt12r*.txt', outputs, 2000);
sjeq800v2 = stats_gather('EQ', [datafolder2 '/simout/EQ'], 'stats800v2pEQt12r*.txt', outputs, 2000);
sjeq1600v2 = stats_gather('EQ', [datafolder2 '/simout/EQ'], 'stats1600v2pEQt12r*.txt', outputs, 2000);
% Determine focal measures for Java EX replications, 12 threads
sjex100v1 = stats_gather('EX', [datafolder2 '/simout/EX'], 'stats100v1pEXt12r*.txt', outputs, 1000);
sjex200v1 = stats_gather('EX', [datafolder2 '/simout/EX'], 'stats200v1pEXt12r*.txt', outputs, 1000);
sjex400v1 = stats_gather('EX', [datafolder2 '/simout/EX'], 'stats400v1pEXt12r*.txt', outputs, 1000);
sjex800v1 = stats_gather('EX', [datafolder2 '/simout/EX'], 'stats800v1pEXt12r*.txt', outputs, 1000);
sjex1600v1 = stats_gather('EX', [datafolder2 '/simout/EX'], 'stats1600v1pEXt12r*.txt', outputs, 1000);
sjex100v2 = stats_gather('EX', [datafolder2 '/simout/EX'], 'stats100v2pEXt12r*.txt', outputs, 2000);
sjex200v2 = stats_gather('EX', [datafolder2 '/simout/EX'], 'stats200v2pEXt12r*.txt', outputs, 2000);
sjex400v2 = stats_gather('EX', [datafolder2 '/simout/EX'], 'stats400v2pEXt12r*.txt', outputs, 2000);
sjex800v2 = stats_gather('EX', [datafolder2 '/simout/EX'], 'stats800v2pEXt12r*.txt', outputs, 2000);
sjex1600v2 = stats_gather('EX', [datafolder2 '/simout/EX'], 'stats1600v2pEXt12r*.txt', outputs, 2000);
% Determine focal measures for Java ER replications, 12 threads
sjer100v1 = stats_gather('ER', [datafolder2 '/simout/ER'], 'stats100v1pERt12r*.txt', outputs, 1000);
sjer200v1 = stats_gather('ER', [datafolder2 '/simout/ER'], 'stats200v1pERt12r*.txt', outputs, 1000);
sjer400v1 = stats_gather('ER', [datafolder2 '/simout/ER'], 'stats400v1pERt12r*.txt', outputs, 1000);
sjer800v1 = stats_gather('ER', [datafolder2 '/simout/ER'], 'stats800v1pERt12r*.txt', outputs, 1000);
sjer1600v1 = stats_gather('ER', [datafolder2 '/simout/ER'], 'stats1600v1pERt12r*.txt', outputs, 1000);
sjer100v2 = stats_gather('ER', [datafolder2 '/simout/ER'], 'stats100v2pERt12r*.txt', outputs, 2000);
sjer200v2 = stats_gather('ER', [datafolder2 '/simout/ER'], 'stats200v2pERt12r*.txt', outputs, 2000);
sjer400v2 = stats_gather('ER', [datafolder2 '/simout/ER'], 'stats400v2pERt12r*.txt', outputs, 2000);
sjer800v2 = stats_gather('ER', [datafolder2 '/simout/ER'], 'stats800v2pERt12r*.txt', outputs, 2000);
sjer1600v2 = stats_gather('ER', [datafolder2 '/simout/ER'], 'stats1600v2pERt12r*.txt', outputs, 2000);
% Determine focal measures for Java OD replications, 12 threads, b = 500
sjod100v1 = stats_gather('OD', [datafolder2 '/simout/OD'], 'stats100v1pODb500t12r*.txt', outputs, 1000);
sjod200v1 = stats_gather('OD', [datafolder2 '/simout/OD'], 'stats200v1pODb500t12r*.txt', outputs, 1000);
sjod400v1 = stats_gather('OD', [datafolder2 '/simout/OD'], 'stats400v1pODb500t12r*.txt', outputs, 1000);
sjod800v1 = stats_gather('OD', [datafolder2 '/simout/OD'], 'stats800v1pODb500t12r*.txt', outputs, 1000);
sjod1600v1 = stats_gather('OD', [datafolder2 '/simout/OD'], 'stats1600v1pODb500t12r*.txt', outputs, 1000);
sjod100v2 = stats_gather('OD', [datafolder2 '/simout/OD'], 'stats100v2pODb500t12r*.txt', outputs, 2000);
sjod200v2 = stats_gather('OD', [datafolder2 '/simout/OD'], 'stats200v2pODb500t12r*.txt', outputs, 2000);
sjod400v2 = stats_gather('OD', [datafolder2 '/simout/OD'], 'stats400v2pODb500t12r*.txt', outputs, 2000);
sjod800v2 = stats_gather('OD', [datafolder2 '/simout/OD'], 'stats800v2pODb500t12r*.txt', outputs, 2000);
sjod1600v2 = stats_gather('OD', [datafolder2 '/simout/OD'], 'stats1600v2pODb500t12r*.txt', outputs, 2000);
% Group same size/param.set focal measures into comparisons to be performed
s100v1 = {snl100v1, sjst100v1, sjeq100v1, sjex100v1, sjer100v1, sjod100v1};
s200v1 = {snl200v1, sjst200v1, sjeq200v1, sjex200v1, sjer200v1, sjod200v1};
s400v1 = {snl400v1, sjst400v1, sjeq400v1, sjex400v1, sjer400v1, sjod400v1};
s800v1 = {snl800v1, sjst800v1, sjeq800v1, sjex800v1, sjer800v1, sjod800v1};
s1600v1 = {snl1600v1, sjst1600v1, sjeq1600v1, sjex1600v1, sjer1600v1, sjod1600v1};
s100v2 = {snl100v2, sjst100v2, sjeq100v2, sjex100v2, sjer100v2, sjod100v2};
s200v2 = {snl200v2, sjst200v2, sjeq200v2, sjex200v2, sjer200v2, sjod200v2};
s400v2 = {snl400v2, sjst400v2, sjeq400v2, sjex400v2, sjer400v2, sjod400v2};
s800v2 = {snl800v2, sjst800v2, sjeq800v2, sjex800v2, sjer800v2, sjod800v2};
s1600v2 = {snl1600v2, sjst1600v2, sjeq1600v2, sjex1600v2, sjer1600v2, sjod1600v2};
% Comparisons to perform
cmp1 = {{'Param. set 1', '100'}, s100v1};
cmp2 = {{'Param. set 1', '200'}, s200v1};
cmp3 = {{'Param. set 1', '400'}, s400v1};
cmp4 = {{'Param. set 1', '800'}, s800v1};
cmp5 = {{'Param. set 1', '1600'}, s1600v1};
cmp6 = {{'Param. set 2', '100'}, s100v2};
cmp7 = {{'Param. set 2', '200'}, s200v2};
cmp8 = {{'Param. set 2', '400'}, s400v2};
cmp9 = {{'Param. set 2', '800'}, s800v2};
cmp10 = {{'Param. set 2', '1600'}, s1600v2};
% Output comparison table
stats_compare_table('np', 'none', 1e-6, 1, cmp1, cmp2, cmp3, cmp4, cmp5, cmp6, cmp7, cmp8, cmp9, cmp10)
We set the tformat parameter to 1, as this is more appropriate when many
comparisons are performed.
The SimOutUtils unit tests require the MOxUnit framework. Set the
appropriate path to this framework as specified in the respective instructions,
cd into the tests folder and execute the following instruction:
moxunit_runtests
The tests can take a few minutes to run.
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[3] Fachada N, Lopes VV, Martins RC, Rosa AC. (2017) Parallelization strategies for spatial agent-based models. International Journal of Parallel Programming. 45(3):449–481. http://dx.doi.org/10.1007/s10766-015-0399-9 (arXiv preprint)
[4] Fachada N, Lopes VV, Martins RC, Rosa AC. (2017) Model-independent comparison of simulation output. Simulation Modelling Practice and Theory. 72:131–149. http://dx.doi.org/10.1016/j.simpat.2016.12.013 (arXiv preprint)
[5] Willink R. (2005) A Confidence Interval and Test for the Mean of an Asymmetric Distribution. Communications in Statistics - Theory and Methods 34 (4): 753–766. https://doi.org/10.1081%2FSTA-200054419
[6] Gibbons JD, Chakraborti S. (2010) Nonparametric statistical inference. Chapman and Hall/CRC
[7] Montgomery DC, Runger GC. (2014) Applied statistics and probability for engineers. John Wiley & Sons
[8] Kruskal WH, Wallis WA. (1952) Use of Ranks in One-Criterion Variance Analysis. Journal of the American Statistical Association 47 (260): 583–621