* Accurate Floating Point Sums and Products* (

**PreciseSums**)

Most of the time floating point arithmetic does approximately the right thing. When adding sums or having products of numbers that greatly differ in magnitude, the floating point arithmetic may be incorrect. This package implements the Kahan (1965) sum <doi:10.1145/363707.363723>, Neumaier (1974) sum <doi:10.1002/zamm.19740540106>, pairwise-sum (adapted from ‘NumPy’, See Castaldo (2008) <doi:10.1137/070679946> for a discussion of accuracy), and arbitrary precision sum (adapted from the fsum in ‘Python’ ; Shewchuk (1997) <http://…/robustr.pdf> ). In addition, products are changed to long double precision for accuracy, or changed into a log-sum for accuracy.

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**Metrics for Continuous Efficiency****dief**)

An implementation of the metrics dief@t and dief@k to measure the diefficiency (or continuous efficiency) of incremental approaches, see Acosta, M., Vidal, M. E., & Sure-Vetter, Y. (2017) <doi:10.1007/978-3-319-68204-4_1>. The metrics dief@t and dief@k allow for measuring the diefficiency during an elapsed time period t or while k answers are produced, respectively. dief@t and dief@k rely on the computation of the area under the curve of answer traces, and thus capturing the answer rate concentration over a time interval.

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**Model Response Styles in Partial Credit Models****PCMRS**)

Implementation of PCMRS (Partial Credit Model with Response Styles) as proposed in by Tutz, Schauberger and Berger (2016) <https://…/> . PCMRS is an extension of the regular partial credit model. PCMRS allows for an additional person parameter that characterizes the response style of the person. By taking the response style into account, the estimates of the item parameters are less biased than in partial credit models.

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**Likelihood Exploration****likelihoodExplore**)

Provides likelihood functions as defined by Fisher (1922) <doi:10.1098/rsta.1922.0009> and a function that creates likelihood functions from density functions. The functions are meant to aid in education of likelihood based methods.

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**Tools for Working with Image Pixels****pixels**)

Provides tools to show and draw image pixels using ‘HTML’ widgets and ‘Shiny’ applications. It can be used to visualize the ‘MNIST’ dataset for handwritten digit recognition or to create new image recognition datasets.

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**Approximately Optimal Fine Balance Matching with Multiple Groups****approxmatch**)

Tools for constructing a matched design with multiple comparison groups. Further specifications of refined covariate balance restriction and exact match on covariate can be imposed. Matches are approximately optimal in the sense that the cost of the solution is at most twice the optimal cost, Crama and Spieksma (1992) <doi:10.1016/0377-2217(92)90078-N>.