3  What is a model?

Last modified on 26. November 2025 at 13:17:46

“A quote.” — Dan Meyer

Imagine you are standing on a globe but still believe it is flat. You are standing on solid ground, with boiling rocks a few kilometers below you. A few kilometers above, you cannot breathe anymore. You are not moving, but the Earth is moving at speeds of up to 828,000 km/h, depending on the reference point. Your reality is a serious misinterpretation.

3.1 General background

Table 3.1: Table of terms used in the statistical modelling. The terms in bold are used here. Depending on the scientific background, the usage of these terms can vary widely.
Symbol Name Application Description
\(y\) outcome, response, endpoint, dependent variable The right-hand side (abbr. RHS) of the model. Describing the values measured in an experiment or study.
\(x\) influencer, influential variable, risk factor, fixed effect, independent variable The left-hand side (abbr. LHS) of the model. Describing the influential variables in an experiment or study.
\(z\) random effect A factor that provides a description of an grouping variable, which is not part of the controlled experimental setting.
\(x\) explanator, explanatory variable Explanation The influencer is used to describe or explain the outcome.
\(x\) predictor, predictive variable Prediction The influencer is used to predict the outcome.
\(x\) focal explanator, focal predictor, focal variable Main effect In a model with multiple influencers, the focal variable is the variable of primary interest.
\(c\) covariate, covariable Continuous \(x\) The influencer is a numeric variable with continuous values.
\(f_A\) factor A, factorial variable, categorical variable Categorical \(x\) The influencer is discrete, functioning as a grouping variable, such as an experimental group or a treatment.
\(A.1\) to \(A.j\) levels, groups, treatment groups Factor \(f_A\) The discrete groups included in one factor A.

A sentence why we use \(y\) and not \(x\) for mean and other stuff.

1 What is a statistical model?

2 What do we mean by a statistical model?

3 What Is the Purpose of Statistical Modeling?

4 Where do statistical models come from? Revisiting the problem of specification

5 Statistical modelling

3.2 Theoretical background

Figure 3.1: foo
Figure 3.2: foo
Figure 3.3: foo
Figure 3.4: foo
Figure 3.5: foo
Figure 3.6: foo
Figure 3.7: foo
Figure 3.8: foo
Figure 3.9: foo 
[1] "#0D0887FF" "#6A00A8FF" "#B12A90FF" "#E16462FF" "#FCA636FF" "#F0F921FF"
[1] "#0D088780" "#6A00A880" "#B12A9080" "#E1646280" "#FCA63680" "#F0F92180"
Figure 3.10: foo

3.3 R packages used

3.4 Data

3.5 Alternatives

Further tutorials and R packages on XXX

3.6 Glossary

term

what does it mean.

3.7 The meaning of “Models of Reality” in this chapter.

  • itemize with max. 5-6 words

3.8 Summary

References

[1]
McCullagh P. What is a statistical model? The Annals of Statistics. 2002;30(5):1225-1310.
[2]
Appleton DR. What do we mean by a statistical model? Statistics in medicine. 1995;14(2):185-197.
[3]
Hand D. What is the purpose of statistical modeling? Harvard Data Science Review. 2019;1(1).
[4]
Spanos A. Where do statistical models come from? Revisiting the problem of specification. Lecture Notes-Monograph Series. Published online 2006:98-119.
[5]
Gilchrist W. Statistical Modelling. Wiley Chichester; 1984.