secularEq

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

secularEq function

<dl><dt>a</dt>
<dd>matrix</dd>
<dt>b</dt>
<dd>matrix</dd></dl>

Arguments

Secular Equation — secularEq

<dl>

<dt>a</dt>
<dd>matrix</dd>


<dt>b</dt>
<dd>matrix</dd>

</dl>

secularEq: Secular Equation

Description

Usage

Value

Arguments