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README.md

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[![Documentation](https://img.shields.io/badge/documentation-user_guide-brightgreen.svg)](docs/userguide.md)
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[![MIT Licence](https://img.shields.io/badge/license-MIT-yellowgreen.svg)](https://opensource.org/licenses/MIT/)
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[![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.931838.svg)](https://doi.org/10.5281/zenodo.931838)
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[![JOSS](http://joss.theoj.org/papers/10.21105/joss.00430/status.svg)](https://doi.org/10.21105/joss.00430)
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### Summary
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### References
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#### Practice
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* Fachada N, Rosa AC. (2018)
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micompm: A MATLAB/Octave toolbox for multivariate independent comparison of
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observations.
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*Journal of Open Source Software*. 3(23):430.
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https://doi.org/10.21105/joss.00430
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#### Theory
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* Fachada N, Lopes VV, Martins RC, Rosa AC. (2017)
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Model-independent comparison of simulation output. *Simulation Modelling
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Practice and Theory*. 72:131–149. http://dx.doi.org/10.1016/j.simpat.2016.12.013

docs/userguide.md

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### 1.1\. What is micompm?
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_micompm_ is a [MATLAB]/[Octave] port of the original [micompr] [R]
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[\[1\]][ref1] package for comparing multivariate samples associated with
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_micompm_ [\[1\]][ref1] is a [MATLAB]/[Octave] port of the original [micompr]
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[R] [\[2\]][ref2] package for comparing multivariate samples associated with
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different groups. It uses principal component analysis (PCA) to convert
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multivariate observations into a set of linearly uncorrelated statistical
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measures, which are then compared using a number of statistical methods. This
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all fields of science, although it requires some knowledge on design of
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experiments, statistical testing and multidimensional data analysis.
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If you use _micompm_, please cite reference [\[2\]][ref2].
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If you use _micompm_, please cite reference [\[1\]][ref1].
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<a name="basicconcepts"></a>
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“system” with k outputs to a “system” with one output. The proposed method
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would then be applied to samples composed of concatenated observations
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encompassing the existing outputs. This technique is described in detail in
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reference [\[2\]][ref2] in the context of comparing simulation outputs.
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reference [\[3\]][ref3] in the context of comparing simulation outputs.
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<a name="availablefunctions"></a>
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_P_-values smaller than the typical 0.05 or 0.01 thresholds may be considered
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statistically significant, casting doubt on the respective assumption. However,
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as discussed in reference [\[2\]][ref2], analysis of these these _p_-values is
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as discussed in reference [\[3\]][ref3], analysis of these these _p_-values is
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often not so clear-cut.
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<a name="multiplecomparisonsanddifferentoutputs"></a>
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## 3\. Tutorial
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The tutorial uses the following dataset, which corresponds to the results
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presented in reference [\[2\]][ref2]:
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presented in reference [\[3\]][ref3]:
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* [![DOI](https://zenodo.org/badge/doi/10.5281/zenodo.46848.svg)](http://dx.doi.org/10.5281/zenodo.46848)
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The dataset contains output from several implementations or variants of the
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[PPHPC] agent-based model. The [PPHPC] model, discussed in reference
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[\[3\]][ref3], is a realization of a prototypical predator-prey system with six
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[\[4\]][ref4], is a realization of a prototypical predator-prey system with six
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outputs:
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1. Sheep population
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simulation parameters.
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The first two implementations strictly follow the [PPHPC] conceptual model
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[\[3\]][ref3], and should generate statistically similar outputs. Variants 3
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[\[4\]][ref4], and should generate statistically similar outputs. Variants 3
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and 4 are purposefully misaligned, and should yield outputs with statistically
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significant differences from the first two implementations.
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The datasets were collected under five different model sizes (100 _x_ 100, 200
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_x_ 200, 400 _x_ 400, 800 _x_ 800 and 1600 _x_ 1600) and two distinct
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parameterizations (_v1_ and _v2_), as discussed in reference [\[2\]][ref2]. For
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parameterizations (_v1_ and _v2_), as discussed in reference [\[3\]][ref3]. For
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the remainder of this tutorial we will focus on model size 400 _x_ 400 and
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parameterization _v1_.
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```
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The second PC _p_-values are slightly significant (<0.05). However, as
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discussed in reference [\[2\]][ref2], a few significant _p_-values are to be
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discussed in reference [\[3\]][ref3], a few significant _p_-values are to be
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expected, and output misalignments are mostly reflected in the first PC
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_p_-values. As such, and considering that the _p_-values are generally
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non-significant, it is not possible to show that the implementations are
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in the univariate case for the first PC (the most important), but doubt is cast
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in a few less meaningful PCs, as shown by [Bartlett's] test _p_-values.
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Multivariate homogeneity of covariance matrices for the first two PCs is not
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confirmed by [Box's M] test. However, as discussed in reference [\[2\]][ref2],
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confirmed by [Box's M] test. However, as discussed in reference [\[3\]][ref3],
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this test is highly sensitive, and this assumption is not really critical when
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sample size is equal for both groups, which is the case in this comparison.
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Summarizing, these results indicate that the most critical parametric test
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## 4\. Limitations
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_micompm_ has the following limitations when compared with the original R
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[implementation][micompr] [\[1\]][ref1]:
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[implementation][micompr] [\[2\]][ref2]:
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* It does not support outputs with different lengths.
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* It does not directly provide _p_-values adjusted with the weighted Bonferroni
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<a name="ref1"></a>
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* [\[1\]][ref1] Fachada N, Rodrigues J, Lopes VV, Martins RC, Rosa AC. (2016) micompr: An R
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Package for Multivariate Independent Comparison of Observations. *The R Journal*
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8(2):405–420.
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https://journal.r-project.org/archive/2016-2/fachada-rodrigues-lopes-etal.pdf
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* [\[1\]][ref1] Fachada N, Rosa AC. (2018)
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micompm: A MATLAB/Octave toolbox for multivariate independent comparison of
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observations.
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*Journal of Open Source Software*. 3(23):430.
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https://doi.org/10.21105/joss.00430
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<a name="ref2"></a>
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* [\[2\]][ref2] Fachada N, Lopes VV, Martins RC, Rosa AC. (2017)
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* [\[2\]][ref2] Fachada N, Rodrigues J, Lopes VV, Martins RC, Rosa AC. (2016)
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micompr: An R Package for Multivariate Independent Comparison of Observations.
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*The R Journal* 8(2):405–420.
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https://journal.r-project.org/archive/2016-2/fachada-rodrigues-lopes-etal.pdf
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<a name="ref3"></a>
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* [\[3\]][ref3] Fachada N, Lopes VV, Martins RC, Rosa AC. (2017)
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Model-independent comparison of simulation output. *Simulation Modelling
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Practice and Theory*. 72:131–149. http://dx.doi.org/10.1016/j.simpat.2016.12.013
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([arXiv preprint](http://arxiv.org/abs/1509.09174))
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<a name="ref3"></a>
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<a name="ref4"></a>
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* [\[3\]][ref3] Fachada N, Lopes VV, Martins RC, Rosa AC. (2015) Towards a
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* [\[4\]][ref4] Fachada N, Lopes VV, Martins RC, Rosa AC. (2015) Towards a
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standard model for research in agent-based modeling and simulation. *PeerJ
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Computer Science* 1:e36. https://doi.org/10.7717/peerj-cs.36
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[ref1]: #ref1
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[ref2]: #ref2
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[ref3]: #ref3
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[ref4]: #ref4
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[NetLogo]: https://ccl.northwestern.edu/netlogo/
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[PPHPC]: https://github.com/fakenmc/pphpc
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[pphpc_netlogo]: https://github.com/fakenmc/pphpc/tree/netlogo

docs/userguide.mdpp

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### What is micompm?
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_micompm_ is a [MATLAB]/[Octave] port of the original [micompr] [R]
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[\[1\]][ref1] package for comparing multivariate samples associated with
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_micompm_ [\[1\]][ref1] is a [MATLAB]/[Octave] port of the original [micompr]
16+
[R] [\[2\]][ref2] package for comparing multivariate samples associated with
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different groups. It uses principal component analysis (PCA) to convert
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multivariate observations into a set of linearly uncorrelated statistical
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measures, which are then compared using a number of statistical methods. This
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all fields of science, although it requires some knowledge on design of
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experiments, statistical testing and multidimensional data analysis.
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If you use _micompm_, please cite reference [\[2\]][ref2].
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If you use _micompm_, please cite reference [\[1\]][ref1].
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### Basic concepts
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“system” with k outputs to a “system” with one output. The proposed method
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would then be applied to samples composed of concatenated observations
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encompassing the existing outputs. This technique is described in detail in
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reference [\[2\]][ref2] in the context of comparing simulation outputs.
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reference [\[3\]][ref3] in the context of comparing simulation outputs.
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### Available functions
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_P_-values smaller than the typical 0.05 or 0.01 thresholds may be considered
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statistically significant, casting doubt on the respective assumption. However,
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as discussed in reference [\[2\]][ref2], analysis of these these _p_-values is
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as discussed in reference [\[3\]][ref3], analysis of these these _p_-values is
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often not so clear-cut.
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### Multiple comparisons and different outputs
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## Tutorial
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The tutorial uses the following dataset, which corresponds to the results
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presented in reference [\[2\]][ref2]:
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presented in reference [\[3\]][ref3]:
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* [![DOI](https://zenodo.org/badge/doi/10.5281/zenodo.46848.svg)](http://dx.doi.org/10.5281/zenodo.46848)
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The dataset contains output from several implementations or variants of the
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[PPHPC] agent-based model. The [PPHPC] model, discussed in reference
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[\[3\]][ref3], is a realization of a prototypical predator-prey system with six
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[\[4\]][ref4], is a realization of a prototypical predator-prey system with six
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outputs:
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1. Sheep population
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simulation parameters.
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The first two implementations strictly follow the [PPHPC] conceptual model
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[\[3\]][ref3], and should generate statistically similar outputs. Variants 3
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[\[4\]][ref4], and should generate statistically similar outputs. Variants 3
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and 4 are purposefully misaligned, and should yield outputs with statistically
289289
significant differences from the first two implementations.
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The datasets were collected under five different model sizes (100 _x_ 100, 200
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_x_ 200, 400 _x_ 400, 800 _x_ 800 and 1600 _x_ 1600) and two distinct
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parameterizations (_v1_ and _v2_), as discussed in reference [\[2\]][ref2]. For
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parameterizations (_v1_ and _v2_), as discussed in reference [\[3\]][ref3]. For
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the remainder of this tutorial we will focus on model size 400 _x_ 400 and
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parameterization _v1_.
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```
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The second PC _p_-values are slightly significant (<0.05). However, as
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discussed in reference [\[2\]][ref2], a few significant _p_-values are to be
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discussed in reference [\[3\]][ref3], a few significant _p_-values are to be
397397
expected, and output misalignments are mostly reflected in the first PC
398398
_p_-values. As such, and considering that the _p_-values are generally
399399
non-significant, it is not possible to show that the implementations are
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530530
in the univariate case for the first PC (the most important), but doubt is cast
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in a few less meaningful PCs, as shown by [Bartlett's] test _p_-values.
532532
Multivariate homogeneity of covariance matrices for the first two PCs is not
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confirmed by [Box's M] test. However, as discussed in reference [\[2\]][ref2],
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confirmed by [Box's M] test. However, as discussed in reference [\[3\]][ref3],
534534
this test is highly sensitive, and this assumption is not really critical when
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sample size is equal for both groups, which is the case in this comparison.
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Summarizing, these results indicate that the most critical parametric test
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## Limitations
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_micompm_ has the following limitations when compared with the original R
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[implementation][micompr] [\[1\]][ref1]:
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[implementation][micompr] [\[2\]][ref2]:
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* It does not support outputs with different lengths.
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* It does not directly provide _p_-values adjusted with the weighted Bonferroni
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<a name="ref1"></a>
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* [\[1\]][ref1] Fachada N, Rodrigues J, Lopes VV, Martins RC, Rosa AC. (2016) micompr: An R
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Package for Multivariate Independent Comparison of Observations. *The R Journal*
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8(2):405–420.
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https://journal.r-project.org/archive/2016-2/fachada-rodrigues-lopes-etal.pdf
701+
* [\[1\]][ref1] Fachada N, Rosa AC. (2018)
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micompm: A MATLAB/Octave toolbox for multivariate independent comparison of
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observations.
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*Journal of Open Source Software*. 3(23):430.
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https://doi.org/10.21105/joss.00430
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<a name="ref2"></a>
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* [\[2\]][ref2] Fachada N, Lopes VV, Martins RC, Rosa AC. (2017)
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* [\[2\]][ref2] Fachada N, Rodrigues J, Lopes VV, Martins RC, Rosa AC. (2016)
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micompr: An R Package for Multivariate Independent Comparison of Observations.
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*The R Journal* 8(2):405–420.
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https://journal.r-project.org/archive/2016-2/fachada-rodrigues-lopes-etal.pdf
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<a name="ref3"></a>
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* [\[3\]][ref3] Fachada N, Lopes VV, Martins RC, Rosa AC. (2017)
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Model-independent comparison of simulation output. *Simulation Modelling
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Practice and Theory*. 72:131–149. http://dx.doi.org/10.1016/j.simpat.2016.12.013
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([arXiv preprint](http://arxiv.org/abs/1509.09174))
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<a name="ref3"></a>
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<a name="ref4"></a>
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* [\[3\]][ref3] Fachada N, Lopes VV, Martins RC, Rosa AC. (2015) Towards a
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* [\[4\]][ref4] Fachada N, Lopes VV, Martins RC, Rosa AC. (2015) Towards a
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standard model for research in agent-based modeling and simulation. *PeerJ
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Computer Science* 1:e36. https://doi.org/10.7717/peerj-cs.36
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[ref1]: #ref1
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[ref2]: #ref2
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[ref3]: #ref3
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[ref4]: #ref4
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[NetLogo]: https://ccl.northwestern.edu/netlogo/
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[PPHPC]: https://github.com/fakenmc/pphpc
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[pphpc_netlogo]: https://github.com/fakenmc/pphpc/tree/netlogo
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