Zusammenfassung
Numerische Methoden spielen in der Datenanalyse u. a. deswegen eine wichtige Rolle, weil nur in Spezialfällen geschlossene Formeln für die Parameterschätzung existieren, die zu einer bestmöglichen Passung eines statistischen Modells für beobachtete Daten führt. Der Einsatz numerischer Methoden bleibt dem Anwender aber verborgen, weil die typischerweise eingesetzten Funktionen zur Modellanpassung zwar intern auf solchen Methoden beruhen, sie die gewählten Algorithmen dem Anwender aber nicht unmittelbar offen legen.
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Notes
- 1.
- 2.
approxfun() gibt stattdessen eine Funktion zurück, die x-Koordinaten akzeptiert und y-Koordinaten ausgibt, so dass die ursprünglichen Daten interpoliert werden. approxfun() besitzt dieselben Argumente wie approx() bis auf die nicht benötigte Angabe n.
- 3.
splinefun() gibt stattdessen eine Funktion zurück, die x-Koordinaten akzeptiert und y-Koordinaten ausgibt, so dass die ursprünglichen Daten interpoliert werden. splinefun() besitzt dieselben Argumente wie spline() bis auf die nicht benötigte Angabe n.
- 4.
Für weitere Spline-Typen, etwa monotone splines, vgl. help(package="splines").
- 5.
Ein weitere Glätter ist in supsmu() implementiert. Das im Basisumfang enthaltene Paket KernSmooth (Wand, 2015) stellt mit locpoly() eine weitere Alternative bereit, deren optimale Bandbreite über dpill() aus demselben Paket berechnet werden kann.
- 6.
Unterschiedliche Varianten der Gauß-Quadratur stellt das Paket statmod (Smyth, Hu, Dunn, Phipson, & Chen, 2016) in der Funktion gauss.quad() bereit.
- 7.
Die hier selbst definierten Funktionen dienen nur als Illustration des allgemeinen Prinzips. Zu ihren Nachteilen gegenüber den R-eigenen Funktionen {d,p,q}norm() zählt, dass sie die übergebenen Argumente nicht auf zulässige Werte prüfen und zudem weit weniger genau sind. So funktioniert pGauss() nur für betragsmäßig kleine μ und kleine obere Integrationsgrenzen.
- 8.
Mit D() lässt sich die Ableitung bestimmter Funktionen auch symbolisch ermitteln.
- 9.
Einen deutlich erweiterten Funktionsumfang bietet das Paket fitdistrplus (Delignette-Muller & Dutang, 2015).
- 10.
Ein wrapper für den Spezialfall der Maximum-Likelihood-Schätzung von Parametern eines statistischen Modells ist die Funktion mle() aus dem im Basisumfang enthaltenen Paket stats4 . Sie schätzt auch die Kovarianzmatrix der Parameterschätzer.
Literatur
Adler, D., & Murdoch, D. (2016). rgl: 3D visualization device system (OpenGL) [Software]. http://CRAN.R-project.org/package=rgl (R package version 0.96.0)
Adler, J. (2012). R in a Nutshell (2. Aufl.). Sebastopol, CA: O’Reilly.
Agresti, A. (2007). An introduction to categorical data analysis (2. Aufl.). New York, NY: Wiley.
Aiken, L. S., & West, S. G. (1991). Multiple regression: Testing and interpreting interactions. Thousand Oaks, CA: SAGE.
Allaire, J. J., Cheng, J., Xie, Y., McPherson, J., Chang, W., Allen, J., … Hyndman, R. (2016). rmarkdown: Dynamic documents for R [Software]. http://rmarkdown.rstudio.com (R package version 1.1)
Allignol, A., & Latouche, A. (2016). CRAN task view: Survival analysis. http://CRAN.R-project.org/view=Survival (Version 2016-08-19)
Allison, P. D. (2008). Convergence failures in logistic regression. SAS Global Forum, 360, 1–11.
Andres, J. (1996). Das allgemeine lineare Modell. In E. Erdfelder, R. Mausfeld, T. Meiser, & G. Rudinger (Hrsg.), Handbuch Quantitative Methoden (S. 185–200). Weinheim: Beltz.
Arnold, J. B. (2016). ggthemes: Extra themes, scales and geoms for ‘ggplot2’ [Software]. https://CRAN.R-project.org/package=ggthemes (R package version 3.2.0)
Backhaus, K., Erichson, B., Plinke, W., & Weiber, R. (2015a). Multivariate Analysemethoden (14. Aufl.). Heidelberg: Springer.
Backhaus, K., Erichson, B., & Weiber, R. (2015b). Fortgeschrittene Multivariate Analysemethoden (3. Aufl.). Heidelberg: Springer.
Balasubramanian, N., & Johnson, S. G. (2013). cubature: Adaptive multivariate integration over hypercubes [Software]. http://CRAN.R-project.org/package=cubature (R package version 1.1-2)
Bates, D. (2004). Least squares calculations in R. R News, 4(1), 17–20. http://CRAN.R-project.org/doc/Rnews/
Bates, D., & Maechler, M. (2016). Matrix: Sparse and Dense Matrix Classes and Methods [Software]. http://CRAN.R-project.org/package=Matrix (R package version 1.2-7.1)
Bates, D., Maechler, M., Bolker, B., & Walker, S. (2015). Fitting linear mixed-effects models using lme4. Journal of Statistical Software, 67(1), 1–48. http://www.jstatsoft.org/article/view/v067i01/
Becker, R. A., Chambers, J. M., & Wilks, A. R. (1988). The new S language: A programming environment for data analysis and graphics. Pacific Grove, CA: Wadsworth & Brooks/Cole.
Bender, R., Augustin, T., & Blettner, M. (2005). Generating survival times to simulate Cox proportional hazards models. Statistics in Medicine, 24, 1713–1723.
Bernaards, C. A., & Jennrich, R. I. (2005). Gradient projection algorithms and software for arbitrary rotation criteria in factor analysis. Educational and Psychological Measurement, 65(5), 676–696. http://www.stat.ucla.edu/research/gpa/
Beyersmann, J., Allignol, A., & Schumacher, M. (2012). Competing risks and multistate models with R. New York, NY: Springer.
Bivand, R. S., Pebesma, E., & Gómez-Rubio, V. (2013). Applied spatial data analysis with R. New York, NY: Springer.
Bliese, P. (2016). multilevel: Multilevel Functions [Software]. http://CRAN.R-project.org/package=multilevel (R package version 2.6)
Bloomfield, V. A. (2014). Using R for numerical analysis in science and engineering. Boca Raton, FL: Chapman & Hall/CRC.
Boker, S., Neale, M., Maes, H., Wilde, M., Spiegel, M., Brick, T., … Fox, J. (2011). OpenMx: An open source extended structural equation modeling framework. Psychometrika, 66(2), 306–317. http://openmx.psyc.virginia.edu/
Borchers, H. W. (2016a). CRAN task view: Numerical mathematics. http://CRAN.R-project.org/view=NumericalMathematics (Version 2016-02-09)
Borchers, H. W. (2016b). pracma: Practical Numerical Math Functions [Software]. http://CRAN.R-project.org/package=pracma (R package version 1.9.5)
Borg, A., & Sariyar, M. (2016). RecordLinkage: Record linkage in R [Software]. https://CRAN.R-project.org/package=RecordLinkage (R package version 0.4-10)
Bortz, J., Lienert, G. A., & Boehnke, K. (2010). Verteilungsfreie Methoden in der Biostatistik (3. Aufl.). Heidelberg: Springer.
Bronstein, I. N., & Semendjajew, K. A. (2012). Springer Taschenbuch der Mathematik (3. Aufl.). Berlin: Springer.
Buerkner, P.-C. (2016). brms: Bayesian regression models using Stan [Software]. https://CRAN.R-project.org/package=brms (R package version 1.0.1)
Büning, H., & Trenkler, G. (1994). Nichtparametrische statistische Methoden (2. Aufl.). Berlin: Walter de Gruyter.
Canty, A., & Ripley, B. D. (2016). boot: Bootstrap R (S-Plus) Functions [Software]. http://CRAN.R-project.org/package=boot (R package version 1.3-18)
Carr, D., Lewin-Koh, N., & Maechler, M. (2015). hexbin: Hexagonal Binning Routines [Software]. http://CRAN.R-project.org/package=hexbin (R package version 1.27.1)
Chambers, J. M. (2008). Software for data analysis: Programming with R. New York, NY: Springer. http://statweb.stanford.edu/~jmc4/Rbook/
Champely, S., & De Rosario, H. (2016). pwr: Basic functions for power analysis [Software]. http://CRAN.R-project.org/package=pwr (R package version 1.2-0)
Chang, W. (2013). R graphics cookbook. Sebastopol, CA: O’Reilly. http://www.cookbook-r.com/
Chang, W., Cheng, J., Allaire, J. J., Xie, Y., & McPherson, J. (2016). shiny: Web application framework for R [Software]. http://CRAN.R-project.org/package=shiny (R package version 0.14.2)
Chang, W., & Luraschi, J. (2016). profvis: Interactive visualizations for profiling R code [Software]. https://rstudio.github.io/profvis/ (R package version 0.3.2)
Chernik, M. R., & LaBudde, R. A. (2011). An introduction to bootstrap methods with applications to R. Hoboken, NJ: Wiley.
Chihara, L., & Hesterberg, T. (2011). Mathematical statistics with resampling and R. Hoboken, NJ: Wiley. https://sites.google.com/site/chiharahesterberg/
Circle Systems. (2015). Stat/Transfer [Software]. http://www.stattransfer.com/ (Version 13)
Cowlishaw, M. F. (2008). Decimal arithmetic FAQ Part 1 – General questions. http://speleotrove.com/decimal/decifaq1.html
Dalgaard, P. (2007). New functions for multivariate analysis. R News, 7(2), 2–7. http://CRAN.R-project.org/doc/Rnews/
Dalgaard, P. (2008). Introductory statistics with R (2. Aufl.). London, UK: Springer. http://publicifsv.sund.ku.dk/~pd/ISwR.html
Davison, A. C., & Hinkley, D. V. (1997). Bootstrap methods and their applications. Cambridge, UK: Cambridge University Press.
De Rosario-Martinez, H. (2015). phia: Post-hoc interaction analysis [Software]. http://CRAN.R-project.org/package=phia (R package version 0.2-1)
Delignette-Muller, M. L., & Dutang, C. (2015). fitdistrplus: An R package for fitting distributions. Journal of Statistical Software, 64(4), 1–34. http://www.jstatsoft.org/v64/i04/
Dowle, M., Short, T., Lianoglou, S., & Srinivasan, A. (2015). data.table: Extension of data.frame [Software]. http://CRAN.R-project.org/package=data.table (R package version 1.9.6)
Duchateau, L., & Janssen, P. (2007). The frailty model. New York, NY: Springer.
Dutang, C. (2016). CRAN task view: Probability distributions. http://CRAN.R-project.org/view=Distributions (Version 2016-08-06)
Eddelbuettel, D. (2013). Seamless R and C++ integration with Rcpp. New York, NY: Springer.
Eddelbuettel, D. (2016). CRAN task view: High-performance and parallel computing with R. http://CRAN.R-project.org/view=HighPerformanceComputing (Version 2016-08-18)
Eid, M., Gollwitzer, M., & Schmitt, M. (2015). Statistik und Forschungsmethoden (5. Aufl.). Weinheim: Beltz.
Faraway, J. J. (2014). Linear models with R (2. Aufl.). Boca Raton, FL: Chapman & Hall/CRC. http://www.maths.bath.ac.uk/~jjf23/LMR/
Faraway, J. J. (2016). Extending the linear model with R: generalized linear, mixed effects and nonparametric regression models (2. Aufl.). Boca Raton, FL: Chapman & Hall/CRC. http://www.maths.bath.ac.uk/~jjf23/ELM/
Faul, F., Erdfelder, E., Lang, A.-G., & Buchner, A. (2007). G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences. Behavior Research Methods, 39(2), 175–191. http://www.gpower.hhu.de/
Filzmoser, P., Fritz, H., & Kalcher, K. (2016). pcaPP: Robust PCA by Projection Pursuit [Software]. http://CRAN.R-project.org/package=pcaPP (R package version 1.9-61)
Filzmoser, P., & Gschwandtner, M. (2015). mvoutlier: Multivariate outlier detection based on robust methods [Software]. http://CRAN.R-project.org/package=mvoutlier (R package version 2.0.6)
Fischer, G. (2013). Lineare algebra (18. Aufl.). Wiesbaden: Vieweg+Teubner.
Fox, J. (2003). Effect displays in R for generalised linear models. Journal of Statistical Software, 8(15), 1–27. http://www.jstatsoft.org/v08/i15/
Fox, J. (2005). The R commander: A basic-statistics graphical user interface to R. Journal of Statistical Software, 14(9), 1–42. http://www.jstatsoft.org/v14/i09/
Fox, J. (2016a). CRAN task view: Statistics for the social sciences. http://CRAN.R-project.org/view=SocialSciences (Version 2016-08-18)
Fox, J. (2016b). polycor: Polychoric and Polyserial Correlations [Software]. http://CRAN.R-project.org/package=polycor (R package version 0.7-9)
Fox, J., Friendly, M., & Weisberg, S. (2013). Hypothesis tests for multivariate linear models using the car package. The R Journal, 5(1), 39–52. https://journal.r-project.org/archive/2013-1/
Fox, J., Nie, Z., & Byrnes, J. (2016). sem: Structural Equation Models [Software]. http://CRAN.R-project.org/package=sem (R package version 3.1-8)
Fox, J., & Weisberg, S. (2011). An R companion to applied regression (2. Aufl.). Thousand Oaks, CA: SAGE. http://socserv.socsci.mcmaster.ca/jfox/Books/Companion/
Fox, J., & Weisberg, S. (2016). car: Companion to Applied Regression [Software]. http://CRAN.R-project.org/package=car (R package version 2.1-3)
Friedman, J., Hastie, T., & Tibshirani, R. (2010). Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software, 33(1), 1–22. http://www.jstatsoft.org/v33/i01/
Gabry, J., & Goodrich, B. (2016). rstanarm: Bayesian applied regression modeling via Stan [Software]. https://CRAN.R-project.org/package=rstanarm (R package version 2.12.1)
Gałecki, A. T., & Burzykowski, T. (2013). Linear mixed-effects models using R: A step-by-step approach. New York, NY: Springer.
Gandrud, C. (2015). Reproducible research with R & RStudio (2. Aufl.). Boca Raton, FL: Chapman & Hall/CRC. http://christophergandrud.github.io/RepResR-RStudio/
Garnier, S. (2016). viridis: Default color maps from ‘matplotlib’ [Software]. https://CRAN.R-project.org/package=viridis (R package version 0.3.4)
Gentleman, R. C., Carey, V. J., Bates, D. M., Bolstad, B., Dettling, M., Dudoit, S., … Zhang, J. (2004). Bioconductor: Open software development for computational biology and bioinformatics. Genome Biology, 5, R80. http://genomebiology.com/2004/5/10/R80
Genz, A., & Bretz, F. (2009). Computation of multivariate normal and t probabilities (Lecture notes in statistics, Vol. 195). Heidelberg: Springer.
Genz, A., Bretz, F., Miwa, T., Mi, X., Leisch, F., Scheipl, F., & Hothorn, T. (2016). mvtnorm: Multivariate normal and t distributions [Software]. http://CRAN.R-project.org/package=mvtnorm (R package version 1.0-5)
Gesmann, M., & de Castillo, D. (2011). googleVis: Interface between R and the Google Visualisation API. The R Journal, 3(2), 40–44. http://journal.r-project.org/archive/2011-2/
Gilbert, P., & Varadhan, R. (2016). numDeriv: Accurate numerical derivatives [Software]. https://CRAN.R-project.org/package=numDeriv (R package version 2016.8-1)
Goldberg, D. (1991). What every computer scientist should know about floating-point arithmetic. ACM Computing Surveys, 23(1), 5–48. http://www.validlab.com/goldberg/paper.pdf
Good, P. I. (2004). Permutation, parametric, and bootstrap tests of hypotheses (3. Aufl.). New York, NY: Springer.
Goulet, V., Dutang, C., Maechler, M., Firth, D., Shapira, M., & Stadelmann, M. (2015). expm: Matrix exponential [Software]. http://CRAN.R-project.org/package=expm (R package version 0.999-0)
Goyvaerts, J., & Levithan, S. (2012). Regular expressions cookbook. Sebastopol, CA: O’Reilly. http://www.regular-expressions.info/
Grolemund, G., & Wickham, H. (2011). Dates and Times Made Easy with lubridate. Journal of Statistical Software, 40(3), 1–25. http://www.jstatsoft.org/v40/i03/
Grothendieck, G., & Petzoldt, T. (2004). Date and Time Classes in R. R News, 4(1), 29–32. http://CRAN.R-project.org/doc/Rnews/
Harrell Jr, F. E. (2015). Regression modeling strategies (2. Aufl.). New York: Springer. http://biostat.mc.vanderbilt.edu/wiki/Main/RmS
Harrell Jr, F. E. (2016a). Hmisc: Harrell Miscellaneous [Software]. http://CRAN.R-project.org/package=Hmisc (R package version 4.0-0)
Harrell Jr, F. E. (2016b). rms: Regression Modeling Strategies [Software]. http://CRAN.R-project.org/package=rms (R package version 5.0-0)
Hastie, T., Tibshirani, R., & Friedman, J. (2009). The elements of statistical learning: data mining, inference, and prediction (2. Aufl.). New York: Springer. http://statweb.stanford.edu/~tibs/ElemStatLearn/
Heiberger, R. M., & Neuwirth, E. (2009). R through Excel. New York, NY: Springer.
Heinze, G., Ploner, M., Dunkler, D., & Southworth, H. (2013). logistf: Firth’s bias reduced logistic regression [Software]. http://CRAN.R-project.org/package=logistf (R package version 1.21)
Hendrickx, J. (2012). perturb: Tools for evaluating collinearity [Software]. http://CRAN.R-project.org/package=perturb (R package version 2.05)
Hesterberg, T. (2015). resample: Resampling functions [Software]. http://CRAN.R-project.org/package=resample (R package version 0.4)
Hewson, P. (2015). CRAN task view: Multivariate statistics. http://CRAN.R-project.org/view=Multivariate (Version 2015-07-01)
Hoffman, D. D. (2000). Visual intelligence: How we create what we see. New York, NY: W. W. Norton & Company.
Højsgaard, S., Halekoh, U., & Yan, J. (2006). The R package geepack for generalized estimating equations. Journal of Statistical Software, 15(2), 1–11. http://www.jstatsoft.org/v15/i02/
Honaker, J., King, G., & Blackwell, M. (2011). Amelia: II: A program for missing data. Journal of Statistical Software, 45(7), 1–47. http://www.jstatsoft.org/v45/i07/
Hornik, K. (2016). The R FAQ [Software-Handbuch]. http://CRAN.R-project.org/doc/FAQ/
Hosmer Jr, D. W., Lemeshow, S., & May, S. (2008). Applied survival analysis: Regression modeling of time to event data (2. Aufl.). New York, NY: Wiley.
Hothorn, T. (2016). CRAN task view: Machine learning & statistical learning. http://CRAN.R-project.org/view=MachineLearning (Version 2016-06-24)
Hothorn, T., Bretz, F., & Westfall, P. (2008). Simultaneous inference in general parametric models. Biometrical Journal, 50(3), 346–363.
Hothorn, T., & Everitt, B. S. (2014). A handbook of statistical analysis using R (3. Aufl.). Boca Raton, FL: Chapman & Hall/CRC.
Hothorn, T., & Everitt, B. S. (2015). HSAUR3: A handbook of statistical analyses using R (3rd ed.) [Software]. http://CRAN.R-project.org/package=HSAUR3 (R package version 1.0-5)
Hothorn, T., Hornik, K., van de Wiel, M. A., & Zeileis, A. (2008). Implementing a class of permutation tests: The coin package. Journal of Statistical Software, 28(8), 1–23. http://www.jstatsoft.org/v28/i08/
Huber, W., Carey, V. J., Gentleman, R., Anders, S., Carlson, M., Carvalho, B. S., … Morgan, M. (2015). Orchestrating high-throughput genomic analysis with Bioconductor. Nature Methods, 12, 115–121.
Hyndman, R. J. (2016). CRAN task view: Time series analysis. http://CRAN.R-project.org/view=TimeSeries (Version 2016-09-09)
Ihaka, R., & Gentleman, R. (1996). R: A language for data analysis and graphics. Journal of Computational and Graphical Statistics, 5(3), 299–314.
Ihaka, R., Murrell, P., Fisher, J. C., & Zeileis, A. (2015). colorspace: Color Space Manipulation [Software]. http://CRAN.R-project.org/package=colorspace (R package version 1.2-6)
James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning with applications in R. New York, NY: Springer. http://www-bcf.usc.edu/~gareth/ISL/
Johnson, P. E. (2016). rockchalk: Regression Estimation and Presentation [Software]. http://CRAN.R-project.org/package=rockchalk (R package version 1.8.101)
Johnson, S. G. (2014). The NLopt nonlinear-optimization package [Software]. http://ab-initio.mit.edu/nlopt/ (Version 2.4.2)
Kelley, K. (2016). MBESS [Software]. http://CRAN.R-project.org/package=MBESS (R package version 4.1.0)
Kirk, R. E. (2013). Experimental design – Procedures for the social sciences (4. Aufl.). Thousand Oaks, CA: SAGE. http://www.sagepub.com/kirk/
Klein, J. P., & Moeschberger, M. L. (2003). Survival analysis: Techniques for censored and truncated data (2. Aufl.). New York, NY: Springer.
Kleinman, K., & Horton, N. J. (2014). SAS and R: Data management, statistical analysis, and graphics (2. Aufl.). Boca Raton, FL: Chapman Hall/CRC. http://nhorton.people.amherst.edu/sasr2/
Kolde, R. (2015). pheatmap: Pretty heatmaps [Software]. https://CRAN.R-project.org/package=pheatmap (R package version 1.0.8)
Kruschke, J. K. (2015). Doing Bayesian data analysis: A tutorial with R, JAGS, and Stan (2. Aufl.). Amsterdam: Academic Press.
Kuhn, M. (2016). caret: Classification and regression training [Software]. http://CRAN.R-project.org/package=caret (R package version 6.0-71)
Kuhn, M., & Johnson, K. (2013). Applied predictive modeling. New York, NY: Springer. http://appliedpredictivemodeling.com/
Leeper, T., Chamberlain, S., Mair, P., Ram, K., & Gandrud, C. (2016). CRAN task view: Web technologies and services. http://CRAN.R-project.org/view=WebTechnologies (Version 2016-08-18)
Leisch, F., & Gruen, B. (2016). CRAN task view: Cluster analysis & finite mixture models. http://CRAN.R-project.org/view=Cluster (Version 2016-08-18)
Lemon, J. (2006). Plotrix: a package in the red light district of R. R News, 6(4), 8–12.
Ligges, U. (2002). R Help Desk: Automation of mathematical annotation in plots. R News, 2(3), 32–34. http://CRAN.R-project.org/doc/Rnews/
Ligges, U. (2003). R Help Desk: Package management. R News, 3(3), 37–39. http://CRAN.R-project.org/doc/Rnews/
Ligges, U. (2016). Programmieren mit R (4. Aufl.). Berlin: Springer Spektrum.
Ligges, U., & Fox, J. (2008). R Help Desk: How can I avoid this loop or make it faster? R News, 8(1), 46–50. http://CRAN.R-project.org/doc/Rnews/
Long, J. D. (2012). Longitudinal data analysis for the behavioral sciences using R. Thousand Oaks, CA: SAGE. https://studysites.sagepub.com/long/
Lumley, T. (2009). leaps: Regression subset selection (using Fortran code by Alan Miller) [Software]. http://CRAN.R-project.org/package=leaps (R package version 2.9)
Maechler, M. (2016). CRAN task view: Robust statistical methods. http://CRAN.R-project.org/view=Robust (Version 2016-08-29)
Maindonald, J., & Braun, W. J. (2010). Data analysis and graphics using R: An example-based approach (3. Aufl.). Cambridge, UK: Cambridge University Press. http://maths-people.anu.edu.au/~johnm/r-book/daagur3.html
Maindonald, J., & Braun, W. J. (2015). DAAG: Data Analysis And Graphics data and functions [Software]. http://CRAN.R-project.org/package=DAAG (R package version 1.22)
Mair, P. (2016). CRAN task view: Psychometric models and methods. http://CRAN.R-project.org/view=Psychometrics (Version 2016-08-18)
Mardia, K. V., Kent, J. T., & Bibby, J. M. (1980). Multivariate Analysis. London, UK: Academic Press.
Maronna, R. A., Martin, R. D., & Yohai, V. J. (2006). Robust Statistics: Theory and Methods. New York, NY: Wiley.
Maxwell, S. E., & Delaney, H. D. (2004). Designing experiments and analyzing data: A model comparison perspective (2. Aufl.). Mahwah, NJ: Lawrence Erlbaum.
Mazerolle, M. J. (2016). AICcmodavg: Model selection and multimodel inference based on (Q)AIC(c) [Software]. http://CRAN.R-project.org/package=AICcmodavg (R package version 2.0-4)
McElreath, R. (2015). Statistical rethinking: A Bayesian course with examples in R and Stan. Boca Raton, FL: Chapman & Hall/CRC.
McFarlane, J. (2016). pandoc: A universal document converter [Software]. http://pandoc.org/ (Version 1.18)
Mersmann, O. (2015). microbenchmark: Sub microsecond accurate timing functions [Software]. http://CRAN.R-project.org/package=microbenchmark (R package version 1.4-2.1)
Meyer, D., & Hornik, K. (2009). Generalized and customizable sets in R. Journal of Statistical Software, 31(2), 1–27. http://www.jstatsoft.org/v31/i02/
Meyer, D., Zeileis, A., & Hornik, K. (2016). vcd: Visualizing Categorical Data [Software]. http://CRAN.R-project.org/package=vcd (R package version 1.4-3)
Meyer, S., & Held, L. (2014). Power-law models for infectious disease spread. The Annals of Applied Statistics, 8(3), 1612–1639.
Microsoft. (2016). checkpoint: Install packages from snapshots on the checkpoint server for producibility [Software]. https://CRAN.R-project.org/package=checkpoint (R package version 0.3.18)
Microsoft. (2016a). Microsoft R Open [Software]. http://mran.revolutionanalytics.com/open/ (3.3.1)
Microsoft. (2016b). R Tools for Visual Studio [Software]. https://www.visualstudio.com/vs/rtvs/ (Version 0.5)
Miller, A. J. (2002). Subset selection in regression (2. Aufl.). Boca Raton, FL: Chapman & Hall/CRC.
Muenchen, R. A. (2011). R for SAS and SPSS users (2. Aufl.). New York, NY: Springer. http://r4stats.com/
Muenchen, R. A., & Hilbe, J. M. (2010). R for Stata users. New York, NY: Springer. http://r4stats.com/
Murrell, P. (2011). R Graphics (2. Aufl.). Boca Raton, FL: Chapman & Hall/CRC. http://www.stat.auckland.ac.nz/~paul/RG2e/
Nash, J. C. (2014a). Nonlinear parameter optimization using R tools. Chichester, UK: Wiley.
Nash, J. C. (2014b). On best practice optimization methods in R. Journal of Statistical Software, 60(2), 1–14. http://www.jstatsoft.org/v60/i02/
Nash, J. C., & Ravi, V. (2011). Unifying optimization algorithms to aid software system users: Optimx for R. Journal of Statistical Software, 43(9), 1–14. http://www.jstatsoft.org/v43/i09/
Neuwirth, E. (2014). RColorBrewer: ColorBrewer palettes [Software]. http://CRAN.R-project.org/package=RColorBrewer (Version 1.1-2)
Neuwirth, E. (2016). RExcel [Software]. http://rcom.univie.ac.at/ (Version 3.2.16)
Oksanen, J., Blanchet, F. G., Kindt, R., Legendre, P., Minchin, P. R., O’Hara, R. B., … Wagner, H. (2016). vegan: Community Ecology Package [Software]. http://CRAN.R-project.org/package=vegan (R package version 2.4-1)
OpenAnalytics BVBA. (2015). Architect [Software]. http://www.openanalytics.eu/architect/ (Version 0.9.8)
Park, J. H. (2016). CRAN task view: Bayesian inference. http://CRAN.R-project.org/view=Bayesian (Version 2016-09-19)
Pau, G., Fuchs, F., Sklyar, O., Boutros, M., & Huber, W. (2010). EBImage – an R package for image processing with applications to cellular phenotypes. Bioinformatics, 26(7), 979–981. http://www.bioconductor.org/packages/devel/bioc/html/EBImage.html
Peters, A., & Hothorn, T. (2015). ipred: Improved predictors [Software]. http://CRAN.R-project.org/package=ipred (R package version 0.9-5)
Pinheiro, J. C., & Bates, D. M. (2000). Mixed-effects models in S and S-PLUS. New York, NY: Springer.
Pinheiro, J. C., Bates, D. M., DebRoy, S., Sarkar, D., & R Core Team. (2016). nlme: Linear and Nonlinear Mixed Effects Models [Software]. http://CRAN.R-project.org/package=nlme (R package version 3.1-128)
Plate, T., & Heiberger, R. (2016). abind: Combine multi-dimensional arrays [Software]. http://CRAN.R-project.org/package=abind (R package version 1.4-5)
Ploner, M., & Heinze, G. (2015). coxphf: Cox regression with Firth’s penalized likelihood [Software]. http://CRAN.R-project.org/package=coxphf (R package version 1.11)
Polzehl, J., & Tabelow, K. (2007). Adaptive Smoothing of Digital images: The R Package adimpro. Journal of Statistical Software, 19(1), 1–17. http://www.jstatsoft.org/v19/i01/
Poncet, P. (2012). modeest: Mode estimation [Software]. http://CRAN.R-project.org/package=modeest (R package version 2.1)
R Core Team. (2014). R: A language and environment for statistical computing [Software-Handbuch]. Vienna, Austria. http://www.r-project.org/
R Core Team. (2016a). foreign: Read data stored by Minitab, S, SAS, SPSS, Stata, Systat, dBase, …[Software]. http://CRAN.R-project.org/package=foreign (R package version 0.8-67)
R Core Team. (2016b). R: Data Import/Export [Software-Handbuch]. Vienna, Austria. http://CRAN.R-project.org/doc/manuals/R-data.html
R Core Team. (2016c). R: Installation and Administration [Software-Handbuch]. Vienna, Austria. http://CRAN.R-project.org/doc/manuals/R-admin.html
R Core Team. (2016d). Writing R Extensions [Software-Handbuch]. Vienna. http://cran.r-project.org/doc/manuals/R-exts.html
R Foundation for Statistical Computing. (2014). R: Regulatory compliance and validation issues – A guidance document for the use of R in regulated clinical trial environments [Software-Handbuch]. Vienna, Austria. http://www.r-project.org/doc/R-FDA.pdf
R Special Interest Group on Databases, Wickham, H., & Müller, K. (2016). DBI: R database interface [Software]. http://CRAN.R-project.org/package=DBI (R package version 0.5-1)
Revelle, W. (2016). psych: Procedures for Psychological, Psychometric, and Personality Research [Software]. http://CRAN.R-project.org/package=psych (R package version 1.6.9)
Ripley, B. D. (2016). RODBC: ODBC Database Access [Software]. http://CRAN.R-project.org/package=RODBC (R package version 1.3-14)
Ripley, B. D., & Murdoch, D. (2016). R for Windows FAQ. http://CRAN.R-project.org/bin/windows/base/rw-FAQ.html
Ritz, C., & Streibig, J. C. (2009). Nonlinear regression with R. New York, NY: Springer.
Robin, X., Turck, N., Hainard, A., Tiberti, N., Lisacek, F., Sanchez, J.-C., & Müller, M. (2011). pROC: an open-source package for R and S+ to analyze and compare ROC curves. BMC Bioinformatics, 12, 77. http://web.expasy.org/pROC/
Rödiger, S., Friedrichsmeier, T., Prasenjit, K., & Michalke, M. (2011). RKWard: A Comprehensive Graphical User Interface and Integrated Development Environment for Statistical Analysis with R. Journal of Statistical Software, 49(9), 1–34. http://www.jstatsoft.org/v49/i09/
Rosseel, Y. (2012). lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 48(2), 1–36. http://www.jstatsoft.org/v48/i02/
Rossini, A. J., Maechler, M., Sparapani, R. A., Eglen, S., Spinu, V., & Heiberger, R. M. (2016). ESS: Emacs Speaks Statistics [Software]. http://ess.r-project.org/ (Version 16.04)
Rousseeuw, P. J., Croux, C., Todorov, V., Ruckstuhl, A., Salibian-Barrera, M., Verbeke, T., & Maechler, M. (2016). robustbase: Basic Robust Statistics [Software]. http://CRAN.R-project.org/package=robustbase (R package version 0.92-6)
Rousseeuw, P. J., & van Zomeren, B. C. (1990). Unmasking Multivariate Outliers and Leverage Points. Journal of the American Statistical Association, 85(411), 633–639. http://www.jstor.org/stable/2289995
RStudio Inc. (2016a). ggvis: Interactive grammar of graphics [Software]. http://CRAN.R-project.org/package=ggvis (R package version 0.4.3)
RStudio Inc. (2016b). RStudio [Software]. http://www.rstudio.org/ (Version 1.0.39)
Shumway, R. H., & Stoffer, D. S. (2016). Time Series Analysis and Its Applications (4. Aufl.). New York, NY: Springer. http://www.stat.pitt.edu/stoffer/tsa4/
Sievert, C., Parmer, C., Hocking, T., Chamberlain, S., Ram, K., Corvellec, M., & Despouy, P. (2016). plotly: Create interactive web graphics via Plotly’s JavaScript graphing library [Software]. https://CRAN.R-project.org/package=plotly (R package version 4.5.2)
Signorell, A. (2016). DescTools: Tools for descriptive statistics. http://CRAN.R-project.org/package=DescTools (R package version 0.99.17)
Smyth, G., Hu, Y., Dunn, P., Phipson, B., & Chen, Y. (2016). statmod: Statistical modeling [Software]. https://CRAN.R-project.org/package=statmod (R package version 1.4.26)
Soetaert, K. (2015). rootSolve: Nonlinear root finding, equilibrium and steady-state analysis of ordinary differential equations [Software]. https://CRAN.R-project.org/package=rootSolve (R package version 1.6.6)
Soetaert, K., & Petzoldt, T. (2015). CRAN task view: Differential equations. http://CRAN.R-project.org/view=DifferentialEquations (Version 2015-07-03)
Spector, P. (2008). Data manipulation with R. New York, NY: Springer.
Strang, G. (2003). Lineare Algebra. Berlin: Springer.
Su, Y.-S., Gelman, A., Hill, J., & Yajima, M. (2011). Multiple imputation with diagnostics (mi) in R: Opening windows into the black box. Journal of Statistical Software, 45(2), 1–67. http://www.jstatsoft.org/v45/i02/
Templ, M. (2016). CRAN task view: Official statistics & survey methodology. http://CRAN.R-project.org/view=OfficialStatistics (Version 2016-06-28)
Therneau, T. (2016). survival: Survival analysis [Software]. http://CRAN.R-project.org/package=survival (R package version 2.39-5)
Theussl, S., & Borchers, H. W. (2016). CRAN task view: Optimization and mathematical programming. http://CRAN.R-project.org/view=Optimization (Version 2016-06-06)
TIBCO Software Inc. (2016). TIBCO enterprise runtime for R (TERR) [Software]. http://spotfire.tibco.com/ (Version 4.1)
Tingley, D., Yamamoto, T., Keele, L., & Imai, K. (2015). mediation: R Package for Causal Mediation Analysis [Software]. http://CRAN.R-project.org/package=mediation (R package version 4.4.5)
Unwin, A. (2015). Graphical data analysis with R. Boca Raton, FL: Chapman & Hall/CRC. http://www.gradaanwr.net/
Urbanek, S., & Horner, J. (2015). Cairo: R graphics device using cairo graphics library for creating high-quality bitmap (PNG, JPEG, TIFF), vector (PDF, SVG, PostScript) and display (X11 and Win32) output [Software]. http://CRAN.R-project.org/package=Cairo (R package version 1.5-9)
Ushey, K., McPherson, J., Cheng, J., Atkins, A., & Allaire, J. (2016). packrat: A dependency management system for projects and their R package pendencies [Software]. https://CRAN.R-project.org/package=packrat (R package version 0.4.8-1)
van Buuren, S. (2012). Flexible imputation of missing data. Boca Raton, FL: Chapman & Hall/CRC.
van Buuren, S., & Groothuis-Oudshoorn, K. (2011). MICE: Multivariate Imputation by Chained Equations in R. Journal of Statistical Software, 45(3), 1–67. http://www.jstatsoft.org/v45/i03/
van der Loo, M. P. J. (2014). The stringdist package for approximate string matching. The R Journal, 6,111–122. http://CRAN.R-project.org/package=stringdist
Venables, W. N. (2016). codingMatrices: Alternative factor coding matrices for linear model formulae [Software]. https://CRAN.R-project.org/package=codingMatrices (R package version 0.2.1)
Venables, W. N., & Ripley, B. D. (2002). Modern applied statistics with S (4. Aufl.). New York, NY: Springer. http://www.stats.ox.ac.uk/pub/MASS4/
Venables, W. N., Smith, D. M., Gentleman, R., Ihaka, R., Maechler, M., & R Core Team. (2016). An introduction to R [Software-Handbuch]. Vienna. http://CRAN.R-project.org/doc/manuals/R-intro.html
Wahlbrink, S. (2016). Eclipse Plug-In for R: StatET [Software]. http://www.walware.de/goto/statet (Version 3.5.1)
Walker, A. (2015). openxlsx: Read, write and edit XLSX files [Software]. http://CRAN.R-project.org/package=openxlsx (R package version 3.0.0)
Wand, M. (2015). KernSmooth: Functions for kernel smoothing for Wand & Jones (1995) [Software]. http://CRAN.R-project.org/package=KernSmooth (R package version 2.23-15j)
West, B. T., Welch, K. B., & Gałecki, A. T. (2014). Linear mixed models: A Practical guide using statistical software (2. Aufl.). Boca Raton, FL: Chapman & Hall/CRC. http://www-personal.umich.edu/~agalecki/
Wickham, H. (2014). Advanced R programming. Boca Raton, FL: Chapman & Hall/CRC. http://adv-r.had.co.nz/
Wickham, H. (2015). R packages. Sebastopol, CA: O’Reilly. http://r-pkgs.had.co.nz/
Wickham, H. (2016a). devtools: Tools to make developing R code easier [Software]. http://CRAN.R-project.org/package=devtools (R package version 1.12.0)
Wickham, H. (2016b). readxl: Read Excel files [Software]. http://CRAN.R-project.org/package=readxl (R package version 0.1.1)
Wickham, H. (2016c). stringr: Simple, consistent wrappers for common string operations [Software]. http://CRAN.R-project.org/package=stringr (R package version 1.1.0)
Wickham, H. (2016d). tidyr: Easily tidy data with spread and gather functions [Software]. http://CRAN.R-project.org/package=tidyr (R package version 0.6.0)
Wickham, H. (2016e). tidyverse: Easily install and load ‘tidyverse’ packages [Software]. https://CRAN.R-project.org/package=tidyverse (R package version 1.0.0)
Wickham, H., Cook, D., Hofmann, H., & Buja, A. (2011). tourr: An R package for exploring multivariate data with projections. Journal of Statistical Software, 40(2), 1–18. http://www.jstatsoft.org/v40/i02/
Wickham, H., & Francois, R. (2016a). dplyr: A grammar of data manipulation [Software]. http://CRAN.R-project.org/package=dplyr (R package version 0.5.0)
Wickham, H., & Francois, R. (2016b). readr: Read tabular data [Software]. http://CRAN.R-project.org/package=readr (R package version 1.0.0)
Wickham, H., & Grolemund, G. (2016). R for data science. Sebastopol, CA: O’Reilly. http://r4ds.had.co.nz/
Wickham, H., James, D. A., Falcon, S., SQLite Authors, Healy, L., & RStudio Inc. (2014). RSQLite: SQLite interface for R [Software]. http://CRAN.R-project.org/package=RSQLite (R package version 1.0.0)
Wickham, H., & Miller, E. (2016). haven: Import SPSS, Stata and SAS files [Software]. http://CRAN.R-project.org/package=haven (R package version 1.0.0)
Wickham, H., & Sievert, C. (2016). ggplot2: Elegant graphics for data analysis (2. Aufl.). New York, NY: Springer. http://github.com/hadley/ggplot2-book
Wilke, C. O. (2016). cowplot: Streamlined plot theme and plot annotations for ggplot2 [Software]. https://CRAN.R-project.org/package=cowplot (R package version 0.6.3)
Wilkinson, G. N., & Rogers, C. E. (1973). Symbolic description of factorial models for analysis of variance. Applied Statistics, 22, 392–399.
Wilkinson, L. (2005). The Grammar of Graphics (2. Aufl.). New York, NY: Springer.
Wirtz, M., & Caspar, F. (2002). Beurteilerübereinstimmung und Beurteilerreliabilität. Göttingen: Hogrefe.
Wood, S. N. (2006). Generalized additive models: An introduction with R. Boca Raton, FL: Chapman & Hall/CRC.
Würtz, D., Chalabi, Y., & Maechler, M. (2015). timeDate: Rmetrics – Chronological and Calendar Objects [Software]. http://CRAN.R-project.org/package=timeDate (R package version 3012.100)
Xie, Y. (2015). Dynamic documents with R and knitr (2. Aufl.). Boca Raton, FL: Chapman & Hall/CRC.
Xie, Y. (2016). knitr: A general-purpose package for dynamic report generation in R [Software]. http://CRAN.R-project.org/package=knitr (R package version 1.14)
Yan, J., & Fine, J. P. (2004). Estimating equations for association structures. Statistics in Medicine, 23(6), 859–874.
Yee, T. W. (2010). The VGAM package for categorical data analysis. Journal of Statistical Software, 32(10), 1–34. http://www.jstatsoft.org/v32/i10/
Zeileis, A. (2004). Econometric computing with HC and HAC covariance matrix estimators. Journal of Statistical Software, 11(10), 1–17. http://www.jstatsoft.org/v11/i10/
Zeileis, A. (2005). CRAN task views. R News, 5(1), 39–40. http://CRAN.R-project.org/doc/Rnews/
Zeileis, A., & Hothorn, T. (2002). Diagnostic checking in regression relationships. R News, 2(3), 7–10. http://CRAN.R-project.org/doc/Rnews/
Zeileis, A., Kleiber, C., & Jackman, S. (2008). Regression models for count data in R. Journal of Statistical Software, 27(8), 1–25. http://www.jstatsoft.org/v27/i08/
Zelterman, D. (2015). Applied multivariate statistics with R. Cham: Springer.
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Wollschläger, D. (2017). Numerische Methoden. In: Grundlagen der Datenanalyse mit R. Statistik und ihre Anwendungen. Springer Spektrum, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53670-4_16
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