# Advanced Statistical Methods 2023 (course handbook)

## Introduction to the module

Throughout this course, we will cover three major statistical procedures a) Generalized linear models, b) Structural Equation Modelling, and c) Mixed-effects models. Specific techniques will include logistic regression, path models, confirmatory factor analysis, and multilevel models for cross-sectional and longitudinal data. We will focus on the rationale and principles behind these modelling approaches and on practical work that will showcase when and how to use these models. The complete work will be integrated with the R statistical environment. Each lecture will provide students with a theoretical introduction to statistical techniques, data that can be analysed, and commented R code. Lectures will be recorded and uploaded to the dedicated Blackboard environment. The materials for the course will be hosted on the Blackboard module’s page and the following webpages:

https://nemanjavaci.netlify.app/advanced-stats-course/

https://github.com/nvaci.

## Learning activities during the module:

Each lecture will consist of a theoretical introduction and practical work. The theoretical part of the session will motivate, explain in the context of other models, and exemplify the utilisation of each model in the R statistical environment using simulated data. The practical part of the session will focus on modelling the real-world data and it will be supported and led by students. Students will learn how to manipulate, visualise, and analyse the data in R statistical environment. Specific focus will be spent on the interpretation of estimated coefficients, modifications of the model structure and critique of the proposed model. The lectures will aim to provide learning activities on three different levels:

a) Theoretical aspect - discussion on why and when would we want to use a certain statistical model.

b) Mathematical aspect - the mathematical basis of the model and how can we transform the data and parameters.

c) Practical aspect - using R to analyse the data and build the statistical models.

## Assessment methods:

The assessment will focus on the application of statistical methods to the existing data. The 10% mark will be allocated to the homework during the module. 90% of the mark will be assessed by the final essay exam. Students will be set with a series of research questions that will require recognition of the optimal statistical procedure, explanation of the motivation behind it, application of the statistical models in the R statistical environment, and interpretation of the results.

## Module learning outcomes

By the end of this module students will know how to build regression models on normally and non-normally distributed data - by specifying link functions and conditional distributions; use Structural Equation Modelling framework to fit path models and confirmatory factor analysis, as well as to combine these models; be able to recognise clustering of the data points and based on the understanding of the data and research question, propose and build multilevel/mixed-effect regression models with various random structure specification.

## The module content by week:

Week 1: Outline of the course and statistical models

Week 2: Generalized linear models (logistic and Poisson regression)

Week 3 and 4: Structural equation modelling (Path models and Confirmatory Factor Analysis)

Week 5: Mixed-effect modelling

Week 6: Practice!

Week 7: Nonlinear modelling or Bayesian stats (not assessed for the exam!)

Week 8: Practice again!

## Literature:

Gelman, A., & Hill, J. (2006). Data analysis using regression and multilevel/hierarchical models. Cambridge university press.

McElreath, R. (2018). Statistical rethinking: A Bayesian course with examples in R and Stan. Chapman and Hall/CRC.

Hayes, A. (2018). Introduction to Mediation, Moderation, and Conditional Process Analysis: A Regression-Based Approach

Principles and Practice of Structural Equation Modeling by Rex B. Kline

## Recommended preliminary and further reading:

Navarro, D. R for Psychological Sciences (https://psyr.djnavarro.net/)

DeBruine, L. M., & Barr, D. J. (2021). Understanding Mixed-Effects Models Through Data Simulation. Advances in Methods and Practices in Psychological Science, 4(1), 2515245920965119.

Wang, Y. A., & Rhemtulla, M. (2021). Power analysis for parameter estimation in structural equation modeling: A discussion and tutorial. Advances in Methods and Practices in Psychological Science, 4(1), 2515245920918253.

Lafit, G., Adolf, J., Dejonckheere, E., Myin-Germeys, I., Viechtbauer, W., & Ceulemans, E. (2020). Selection of the number of participants in intensive longitudinal studies: A user-friendly Shiny app and tutorial to perform power analysis in multilevel regression models that account for temporal dependencies.

Summary songs by Rafael Moral (https://www.youtube.com/user/rafamoral2007)