What we have covered so far...

Aims for semester 2

1. Discuss analysis of experimental designs using linear model.

   • Models with multiple nominal categorical variables.
   • Overall effects as well as comparisons between levels.
   • Categorical interactions

2. Recap assumption and diagnostics

3. Discuss ways to conduct inferential tests with violated assumptions (bootstrapping)

4. Extend to linear models to include other types of dependent variale (binary, categorical)

5. Discuss a number of important modelling and inference topics

   • Missing data
   • Multiple comparisons
   • Power analysis

6. Draw all of this together and emphasize the skills we have been developing in the context of reproducible analysis and science.

Key concepts from semester 1

1. Basic structure of the linear model:

$$y_i = b_0 + b_1x_1 + b_2x_2 ...b_kx_k + \epsilon_i$$

• And in R:

lm(y ~ x1 + x2 + x3, data = tibble)

• From which we have:
  • Individual tests of $\beta$ coefficients
  • $F$-tests of overall model
  • $R^2$ estimating variance accounted for

Key concepts from semester 1

1. Assumptions

• Linearity: The relationship between $y$ and $x$ is linear.

• Independence of errors: The error terms should be independent from one another.

• Normality: The errors $\epsilon$ are normally distributed

• Equal variances ("Homoscedasticity"): The scale of the variability of the errors $\epsilon$ is constant at all values of $x$.

Key concepts from semester 1

1. Interactions

• We have looked at interactions between two numeric/continuous variables, and between a categorical and numeric variable.

• When the effect of one variable changes as a function of another.

  • We can explore these visually
  • Calculate simple slopes (the effect of $x$ at a specific value of $z$)

Key concepts from semester 1

1. Model comparisons

• When we have two nested models, we can compute an incremental $f$-test that tells us the improvement in the model for the inclusion of a (set) of variables.

Semester plan

• Weeks 1 to 5

  • Recap experimental designs and the types of data they produce
  • Discuss analysis for different types of design, linking linear models to ANOVA.
  • Introduce categorical interactions
  • Discuss assumptions and multiple comparisons

• Weeks 7 to 11

  • Bootstrapping
  • Binary logistic regression
  • Multinomial regression & generalized linear model
  • Missing data (conceptual)
  • Power Analysis
  • Reproducibility

Weekly material

1. Lectures

2. Lecture exercises

3. Practical exercises

4. Reading

Weekly support

• "Live R" and Q&A

• Lab drop-in (new format)

• Office hours (new time for Tom)

• Study groups (still live, not used in S1)

• Discussion boards (new format)

Assessments

• Weekly quizzes (10 more in weeks 1 5, 7 to 11)

• Report 2

  • Second half of the semester.
  • Format near identical to semester 1