copstress

Calculates copstress for given MDS object

multivariate

Multidimensional scaling (MDS) methods that aim at pronouncing the clustered appearance of the configuration (Rusch, Mair & Hornik, 2021, <doi:10.1080/10618600.2020.1869027>). They achieve this by transforming proximities/distances with power functions and augment the fitting criterion with a clusteredness index, the OPTICS Cordillera (Rusch, Hornik & Mair, 2018, <doi:10.1080/10618600.2017.1349664>). There are two variants: One for finding the configuration directly (COPS-C) for ratio, power, interval and non-metric MDS (Borg & Groenen, 2005, ISBN:978-0-387-28981-6), and one for using the augmented fitting criterion to find optimal parameters (P-COPS). The package contains various functions, wrappers, methods and classes for fitting, plotting and displaying different MDS models in a COPS framework like ratio, interval and non-metric MDS for COPS-C and P-COPS with Torgerson scaling (Torgerson, 1958, ISBN:978-0471879459), scaling by majorizing a complex function (SMACOF; de Leeuw, 1977, <https://escholarship.org/uc/item/4ps3b5mj>), Sammon mapping (Sammon, 1969, <doi:10.1109/T-C.1969.222678>), elastic scaling (McGee, 1966, <doi:10.1111/j.2044-8317.1966.tb00367.x>), s-stress (Takane, Young & de Leeuw, 1977, <doi:10.1007/BF02293745>), r-stress (de Leeuw, Groenen & Mair, 2016, <https://rpubs.com/deleeuw/142619>), power stress (Buja & Swayne, 2002 <doi:10.1007/s00357-001-0031-0>), restricted power stress, approximate power stress, power elastic scaling, power Sammon mapping (for all Rusch, Mair & Hornik, 2021, <doi:10.1080/10618600.2020.1869027>). All of these models can also solely be fit as MDS with power transformations. The package further contains a function for pattern search optimization, the ``Adaptive Luus-Jaakola Algorithm'' (Rusch, Mair & Hornik, 2021,<doi:10.1080/10618600.2020.1869027>).

Thomas Rusch

cops

Cluster Optimized Proximity Scaling

Jan de Leeuw

Patrick Mair

copstress function

<dl><dt>obj</dt>
<dd>MDS object (supported are sammon, cmdscale, smacof, rstress, powermds)</dd>
<dt>stressweight</dt>
<dd>weight to be used for the fit measure; defaults to 1</dd>
<dt>cordweight</dt>
<dd>weight to be used for the cordillera; defaults to 0.5</dd>
<dt>q</dt>
<dd>the norm of the cordillera; defaults to 1</dd>
<dt>minpts</dt>
<dd>the minimum points to make up a cluster in OPTICS; defaults to 2</dd>
<dt>epsilon</dt>
<dd>the epsilon parameter of OPTICS, the neighbourhood that is checked; defaults to 10</dd>
<dt>rang</dt>
<dd>range of the distances (min distance minus max distance). If NULL (default) the cordillera will be normed to each configuration's maximum distance, so an absolute value of goodness-of-clusteredness.</dd>
<dt>verbose</dt>
<dd>numeric value hat prints information on the fitting process; &gt;2 is very verbose (copstress level), &gt;3 is extremely (up to MDS optimization level)</dd>
<dt>normed</dt>
<dd>should the cordillera be normed; defaults to TRUE</dd>
<dt>scale</dt>
<dd>should the configuration be scale adjusted.</dd>
<dt>init</dt>
<dd>a reference configuration when doing procrustes adjustment</dd>
<dt>...</dt>
<dd>additional arguments to be passed to the cordillera function</dd></dl>

Arguments

Calculates copstress for given MDS object — copstress

<dl>

<dt>obj</dt>
<dd>MDS object (supported are sammon, cmdscale, smacof, rstress, powermds)</dd>


<dt>stressweight</dt>
<dd>weight to be used for the fit measure; defaults to 1</dd>


<dt>cordweight</dt>
<dd>weight to be used for the cordillera; defaults to 0.5</dd>


<dt>q</dt>
<dd>the norm of the cordillera; defaults to 1</dd>


<dt>minpts</dt>
<dd>the minimum points to make up a cluster in OPTICS; defaults to 2</dd>


<dt>epsilon</dt>
<dd>the epsilon parameter of OPTICS, the neighbourhood that is checked; defaults to 10</dd>


<dt>rang</dt>
<dd>range of the distances (min distance minus max distance). If NULL (default) the cordillera will be normed to each configuration's maximum distance, so an absolute value of goodness-of-clusteredness.</dd>


<dt>verbose</dt>
<dd>numeric value hat prints information on the fitting process; &gt;2 is very verbose (copstress level), &gt;3 is extremely (up to MDS optimization level)</dd>


<dt>normed</dt>
<dd>should the cordillera be normed; defaults to TRUE</dd>


<dt>scale</dt>
<dd>should the configuration be scale adjusted.</dd>


<dt>init</dt>
<dd>a reference configuration when doing procrustes adjustment</dd>


<dt>...</dt>
<dd>additional arguments to be passed to the cordillera function</dd>

</dl>

copstress: Calculates copstress for given MDS object

Description

Usage

Value

Arguments