# Thomas Rusch

#### 5 packages on CRAN

Cluster optimized proximity scaling (COPS) refers to multidimensional scaling (MDS) methods that aim at pronouncing the clustered appearance of the configuration. 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 for given parameters (COPS-C) for ratio, 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>) and power elastic scaling, power Sammon mapping and approximated power stress (Rusch, Mair & Hornik, 2015, <https://bach-s59.wu.ac.at/4888/>). 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-Jakola Algorithm" (Rusch, Mair & Hornik, 2015, <https://bach-s59.wu.ac.at/4888/>).

Functions for calculating the OPTICS Cordillera. The OPTICS Cordillera measures the amount of 'clusteredness' in a numeric data matrix within a distance-density based framework for a given minimum number of points comprising a cluster, as described in Rusch, Hornik, Mair (2017) <doi:10.1080/10618600.2017.1349664>. There is an R native version and a version that uses 'ELKI', with methods for printing, summarizing, and plotting the result. There also is an interface to the reference implementation of OPTICS in 'ELKI'.

Implementation of the Tukey, Mandel, Johnson-Graybill, LBI, Tusell and modified Tukey non-additivity tests.

Fits Rasch models (RM), linear logistic test models (LLTM), rating scale model (RSM), linear rating scale models (LRSM), partial credit models (PCM), and linear partial credit models (LPCM). Missing values are allowed in the data matrix. Additional features are the ML estimation of the person parameters, Andersen's LR-test, item-specific Wald test, Martin-Loef-Test, nonparametric Monte-Carlo Tests, itemfit and personfit statistics including infit and outfit measures, ICC and other plots, automated stepwise item elimination, simulation module for various binary data matrices.

Graphical and computational methods that can be used to assess the stability of results from supervised statistical learning.