cops

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, ), 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, ), 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).