# Data simulation for linear models in R

## Nov 1-12, 9AM-5 PM (daily)

**OUTLINE/AIMS/CONTENT: **Usually, when we fit linear models, we don't know the 'truth' about the data we analyse, and hope that the model uncovers this 'truth' (or at least reveals something related to it). However, this is not necessarily the case. The examples probably most well-known are lack of power (i.e., a model doesn't reveal significance despite the effect in question actually existing in reality) and type I errors (i.e., the model erroneously reveals an effect which actually does not exist). More generally, for each model we fit, we have to face the possibility that the results reflect the processes investigated only to some extent, but in parts also reflect problems with the model/the data. This becomes even more of an issue when the models used are recent developments with, in part, little known properties (such as GLMMs) and/or when the combination of model complexity and sample size pushes against the limits of what models can do (which is what quite frequently happens).

The primary aim of this course is to teach how to simulate data in a framework of linear models and using R. The cool thing about simulated data is that one knows exactly what is 'true' (because one has generated the data). Hence, one can then compare what a model reveals with truth. The perhaps most well-known use of simulated data is 'power analysis' (determining the probability of an analysis to reveal significance, given a certain effect and sample size, an alpha level, and a test). However, it can also be used to address questions such as 'Does the method do what I think it does?', 'Does the method do what people think it does?', 'Does bias in sampling translate into bias in the estimates?', 'How does an analysis behave when its assumptions are violated?', 'What is the probability that the model converges at all?', 'What is the expected width of confidence intervals', 'What is the precision of the estimated coefficients?', and many others.

The course has three main aims (in order of increasing importance):

- teaching how to simulate data and conduct power analyses in a wider sense (i.e., addressing the kinds of questions mentioned above). As part of this, participants will, for instance, learn how to simulate data sets with respect to various predictors (e.g., crossed and nested factors, correlating covariates), different response variables (e.g., Gaussian, binary, Poisson, negative binomial, beta, etc.), effects of fixed effects predictors and grouping variables (i.e., random intercepts and slopes), and non-linear effects of covariates. Participants will also get to know various functions for random sampling.
- teaching a bit about programming in R. In fact, it is somewhat in the nature of simulations that more or less the same set of operations needs to be done many times. In the course, participants will learn how to automate i) processes in R (using for- and while-loops and also lapply), ii) write code that evaluates conditions (e.g., if-constructs), iii) speed things up where possible, iv) store results, v) write one's own functions, vi) catch and deal with errors and warnings, vii) parallelize code execution, etc.; nothing really fancy, though, just the basics needed to program such simulations.
- enhancing the understanding of linear models and what the link between them and 'life' (in either direction) is. In fact, simulating data means that one needs clear hypotheses about life and an equally clear understanding of how these hypotheses translate into model coefficients (and eventually a response). So in case you are not quite sure whether you really understand the precise meaning of such things like interactions, link functions, error distributions, random intercepts and slopes, or what the idea behind an offset term is, the course might be useful for you.

The course will closely follow the course ’Linear models and their application in R’ (course number 34097) as we shall begin with simulating simple linear regression, and step up to simulating (effects of) factors, interactions, non-linear effects, data for GLMs (i.e., non-Gaussian response variables), and finally effects of grouping variables (i.e., random intercepts and slopes).

**STRUCTURE:** The course will consist of lectures/seminars, practical applications/examples, and extensive exercises. The exercises will by mandatory and an integral part of the course. That is, taking the course without working on the exercises is not an option as much of the material to be learned is put into the exercises. The exercises will take place during the regular course time (see below), and I'll be available in case participants encounter insurmountable obstacles.

**TARGETED AUDIENCE:** The targeted audience is not limited to students, but also faculty members, post docs, etc. are welcome to attend (basically everyone interested in the topics of the course).

**REQUIREMENTS:** The course requires a fairly good grasp on linear models as I teach them in the linear models course. Hence, participation is only permitted for people who participated in the course ’Linear models and their application in R’, either the most recent instance (GGNB course number 34097 in the summer semester 2021) or previous rounds. In addition, participants need to be familiar with the basics of R, also bring some level of interest in programming (but knowledge of a proper programming language is not required), and they shouldn't be too shy of a little bit of math. An additional requirement that needs extra time during the course is that, in preparation for each day, participants will need to go through a few handouts of the linear models course again.

**MATERIAL PROVIDED:** The course is accompanied with plenty of handouts which will be made available during it.

**WHEN & WHERE**: The course will take place during the two weeks from Nov. 1st to Nov. 12th, 2021, with lessons taking place each weekday from 9:00 (sharp) to at latest 17:00 (with several shorter and one longer break). An online format will be used and the number of participants is limited to 70.

**CREDITS: **Certificates of participation are accepted to fulfil credit requirements of the PhD programme Behavior and Cognition as well as the GGNB programmes (for GGNB, 4C are given). A regular attendance is required. Students of other PhD programmes should inquire with the heads of their study programmes regarding credits.

**LANGUAGE: **the course language will be English.

**SIGNING UP:** by sending an email to **statistics_teaching(at)dpz.eu**; **when registering, include your full name, affiliation, status (faculty member/PostDoc/PhD, Master) and study programme (if applicable)**. You can register between **September 1 and** **September 30, 2021**. People signing up later cannot be considered. Due to the priority regulations (see below), signing up does not imply that you can participate. Everyone who signed up will receive an email soon after Sept 30, stating whether s/he can participate.

**BEFORE YOU SIGN UP: please be aware that the course requires a more or less full time commitment for two entire weeks. Please sign up only if you will be definitely able to participate (given no major unexpected events). 'No shows' and late sign-outs will have reduced priority of access in future rounds of the course; GGNB and GAUSS doctoral students will be banned from all skills and methods courses and funding options for 12 months.**

**PRIORITY OF ACCESS:** there is a limited number of slots available, and in case more people sign up for the course than can participate, priority of access is given to first, members of the Leibniz ScienceCampus Primate Cognition, second, staff, members, and students of the University of Göttingen and the German Primate Center, and finally (third), to everyone else. Within each group, priority of access is given in the order in which people have signed up. Finally, in future rounds of the course people that have signed up for this round but then signed out again or just didn't appear might get lower priority.

# Contact

Dr. Roger Mundry Biostatistician +49-551-3851-478 Contact

# Registration

Registration period | Sept 1-Sept 30, 2021 |

registration by | email to statistics_teaching@dpz.eu |

required information | full name, affiliation, status (faculty member/PostDoc/PhD/Master), study programme (if applicable) |

**Note: The content and topics of the workshop require knowledge of the contents of the previous workshop "Linear Models and their application in R"**

**Note: The content and topics of the workshop require knowledge of the contents of the previous workshop "Linear Models and their application in R"**