Statistics

The purpose of this course is to familiarise students with the basic concepts of Bayesian theory. It is designed to provide an introduction to the principles, methods, and applications of Bayesian statistics. Bayesian statistics offers a powerful framework for data analysis and inference, allowing for the incorporation of prior knowledge and uncertainty in a coherent and systematic manner. Throughout this course, we will cover key concepts such as Bayes' theorem, prior and posterior distributions, likelihood functions, and the fundamental differences between Bayesian and frequentist approaches. You will learn to formulate and estimate statistical models, update beliefs using new data, and make informed decisions based on the posterior probabilities generated through Bayesian inference.  By the end of this course, you will possess the necessary skills to perform Bayesian data analysis, interpret results, and apply Bayesian methods in various contexts. 

Prerequisites

Some familiarity with using Stata is recommended. You may wish to take the module 'Introduction to Stata' before begin this module.

Sessions

How to Book

Bookings can be made via the Modules List where you will also find the module dates. Click on the module you want and you will be taken to a booking screen. As soon as you book, you will receive an automated email confirming your place. Please note, some modules (though not all) have multiple iterations in the Michaelmas and Lent Term.

This module introduces the statistical techniques of Exploratory and Confirmatory Factor Analyses. Exploratory Factor Analysis (EFA) is used to uncover the latent structure (dimensions) of a set of variables. It reduces the attribute space from a larger number of variables to a smaller number of factors. Confirmatory Factor Analysis (CFA) examines whether collected data correspond to a model of what the data are meant to measure. STATA will be introduced as a powerful tool to conduct confirmatory factor analysis. A brief introduction will be given to confirmatory factor analysis and structural equation modelling.

• Session 1: Exploratory Factor Analysis Introduction
• Session 2: Factor Analysis Applications
• Session 3: CFA and Path Analysis with STATA
• Session 4: Introduction to SEM and programming

Prerequisites

• Students are expected to be familiar with basic statistical concepts such as variance, correlation and regression
• The course also assumes familiarity with using the essential features of Stata

Software

Stata

Assessment

There may be a practical exercise at the end of the module.

Textbook(s)

• Bartholomew, D. J., Steele, F., & Moustaki, I. (2008). Analysis of Multivariate Social Science Data (2nd ed ed.). New York, NY: Chapman & Hall/CRC Press.
• Long, J. S. (1983). Confirmatory Factor Analysis: A Preface to LISREL. SAGE Publications.
• Kim, J. O., & Mueller, C. W. (1978). Factor Analysis: Statistical Methods and Practical Issues. SAGE Publications.
• LP., S., Hamilton, L. C., & Corporation, S. (2011). Stata Structural Equation Modeling Reference Manual-Release 12. StataCorp LP.

In addition, there are chapters on Exploratory and Confirmatory Factor Analysis in the Electronic Statistics Textbook (EST).

Sessions

How to Book

Bookings can be made via the Modules List where you will also find the module dates. Click on the module you want and you will be taken to a booking screen. As soon as you book, you will receive an automated email confirming your place. Please note, some modules (though not all) have multiple iterations in the Michaelmas and Lent Term.

Propensity score matching (PSM) is a technique that simulates an experimental study in an observational data set in order to estimate a causal effect. In an experimental study, subjects are randomly allocated to “treatment” and “control” groups; if the randomisation is done correctly, there should be no differences in the background characteristics of the treated and non-treated groups, so any differences in the outcome between the two groups may be attributed to a causal effect of the treatment. An observational survey, by contrast, will contain some people who have been subject to the “treatment” and some people who have not, but they will not have not been randomly allocated to those groups. The characteristics of people in the treatment and control groups may differ, so differences in the outcome cannot be attributed to the treatment. PSM attempts to mimic the experimental situation trial by creating two groups from the sample, whose background characteristics are virtually identical. People in the treatment group are “matched” with similar people in the control group. The difference between the treatment and control groups in this case should may therefore more plausibly be attributed to the treatment itself. PSM is widely applied in many disciplines, including sociology, criminology, economics, politics, and epidemiology. The module covers the basic theory of PSM, the steps in the implementation (e.g. variable choice for matching and types of matching algorithms), and assessment of matching quality. We will also work through practical exercises using Stata, in which students will learn how to apply the technique to the analysis of real data and how to interpret the results.

Prerequisites

Students wishing to take this module should have either successfully completed Doing Multivariate Analysis, including the end-of-module test, or have had previous equivalent training in statistics (verified by the Skill Check). You will need to be confident in the use of Stata; if you are not, then please take the SSRMC’s Introduction to Stata or 90-minute Stata courses.

Readings and resources

• Caliendo, M., & Kopeinig, S. (2008). Some practical guidance for the implementation of propensity score matching. Journal of Economic Surveys, 22(1), 31-72.
• Dehejia, R.H., & Wahba, S. (2002). Propensity score-matching methods for nonexperimental causal studies. The Review of Economics and Statistics, 84(1), 151-161.
• Guo, S., & Fraser, M.W. (2010). Propensity score analysis: Statistical methods and applications. SAGE Publications Ltd. USA.
• Morgan, S.L., & Winship, C. (2007). Counterfactuals and casual inference: Methods and principles for social research. Cambridge University Press.
• Rosenbaum, P.R., & Rubin, D.B. (1983). The central role of the propensity score in observational studies for casual effects. Biometrika, 70(1), 41-55.
• Rubin, D.B. (2001). Using propensity scores to help design observational studies: Application to the tobacco litigation. Health Services & Outcomes Research Methodology, 2, 169-188.

Assessment

There may be an online open-book test at the end of the module; for most students, the test is not compulsory.

Sessions

How to Book

Bookings can be made via the Modules List where you will also find the module dates. Click on the module you want and you will be taken to a booking screen. As soon as you book, you will receive an automated email confirming your place. Please note, some modules (though not all) have multiple iterations in the Michaelmas and Lent Term.

This intensive course on structural equation modelling will provide an introduction to SEM using the statistical software Stata. The aim of the course is to introduce structural equation modelling as an analytical framework and to familiarize participants with the applications of the technique in the social sciences.

The application of the structural equation modelling framework to a variety of social science research questions will be illustrated through examples of published papers. The examples used are drawn from recent papers as well as from publications from the early days of the technique; some use path analysis using cross-national data, others confirmatory factor analysis, and other still full structural models, to test particular hypotheses. Some example papers may be found below, though they should not be treated as the gold standard, rather as an illustration of the variety of approaches and reporting techniques within SEM.

• Duff, A., Boyle, E., Dunleavy, K., & Ferguson, J. (2004). The relationship between personality, approach to learning and academic performance. Personality and individual differences, 36(8), 1907-1920.
• Garnier, M., & Hout, M. (1976). Inequality of educational opportunity in France and the United States. Social Science Research, 5(3), 225-246.
• Helm, F., Müller-Kalthoff, H., Mukowski, R., & Möller, J. (2018). Teacher judgment accuracy regarding students' self-concepts: Affected by social and dimensional comparisons?. Learning and Instruction, 55, 1-12.
• Parker, P. D., Jerrim, J., Schoon, I., & Marsh, H. W. (2016). A multination study of socioeconomic inequality in expectations for progression to higher education: The role of between-school tracking and ability stratification. American Educational Research Journal, 53(1), 6-32.

Students will engage in a critique of such examples, with the aim of gaining a better understanding of the SEM framework, as well as its application to real-life data. To further facilitate this application focus, the theoretical introduction will be accompanied by practical examples based on real, publicly-available data.

This course is intended for students who in their research may want to engage with the testing of multiple hypotheses, or with complex relationships between variables.

Prerequisites

• No prior knowledge of SEM is assumed, and only a basic familiarity with Stata (or any other command-based statistical software) is needed.
• Students should have an understanding of the principles of multivariate regression
• Background reading (see below)

Topics 

• Introduction to the general principles of SEM;
• Latent variables, measurement models, and confirmatory factor analysis;
• Path analysis and mediation analysis, with practical application in Stata;
• Confirmatory factor analysis and latent variable models.

Reading

• Schumacker, R.E. & Lomax, R.G. (fourth edition, 2016, but other editions will also be fine) A beginner's guide to structural equation modelling
  • Chapter: 1 (Introduction);
  • Chapter 5 (Path Models);
  • Chapter 6 (Factor Analysis).

The text is a particularly accessible introduction to SEM. It contains examples in a variety of software packages, although not in Stata©.

Students should focus on understanding the concepts of the technique rather than software issues in preparation for the course. Chapters 1, 5, and 6 provide the core concepts of structural equation modeling, and are required reading for everyone enrolling on the course.

Students who are less confident about their background in quantitative data analysis may want to also read Chapters 2 (Data Entry and Edit Issues), 3 (Correlation) and 4 (Regression Models).

Assessment

There may be an online open-book test at the end of the module; for most students, the test is not compulsory.

Sessions

How to Book

Bookings can be made via the Modules List where you will also find the module dates. Click on the module you want and you will be taken to a booking screen. As soon as you book, you will receive an automated email confirming your place. Please note, some modules (though not all) have multiple iterations in the Michaelmas and Lent Term.

Description

Panel data consists of repeated observations measured at multiple time points, collected from multiple individuals, entities, or subjects over a period of time. For instance, child A’s numeracy test score in Year 1, Year 2, Year 3 and Year 4. Country B’s GDP per capita in year 2020, 2021, 2022 and 2023. Panel data analysis, as a subset of longitudinal data analysis, is particularly useful for addressing research questions that try to understand how variables change over time and how individual units differ in their responses to changes. An example research question could be: how do children's numeracy scores vary across different socioeconomic backgrounds, and how have these disparities changed over the years? Panel data analysis holds several advantages, such as (1) increased statistical efficiency, (2) more effective at controlling for unobserved individual or entity-specific effects, and (3) more capable to study the dynamics of relationships over time.

Over the course of this module, participants will learn how to work with panel data. Through hands-on exercises and practical examples, participants will gain proficiency in data manipulation, visualisation, and advanced statistical techniques tailored specifically for panel data.

Target audience

The module is suitable for postgraduate students and researchers at any stages of their study and research. However, foundational Stata skills are required.

Prerequisites

If you are not already an experienced user of Stata software then we recommend you take the Introduction to Stata module.

Learning objectives

1. Understand panel data: Define and differentiate between cross-sectional, time series and panel data. Explain the advantages and limitations of using panel data in different research contexts

2. Prepare panel data and exploratory data analysis: Collect, clean and prepare panel datasets for analyses. Conduct descriptive analyses, including summary statistics and data visualisation. Identify patterns and trends within longitudinal data

3. Fixed effects, random effects and mixed models: Understand the differences between fixed effects, random effects and mixed models in panel data analysis. Apply these models to account for individual-specific and/or time-specific effects

4. Diagnostics tests Use diagnostics tests to examine which model should be used for the panel data, and address issues of heteroskedasticity and endogeneity.

5. Interpretation and reporting. Communicate the results of panel data analyses.

Teaching Format

The module consists of 8-hours spread over two half days.

Sessions

How to Book

Bookings can be made via the Modules List where you will also find the module dates. Click on the module you want and you will be taken to a booking screen. As soon as you book, you will receive an automated email confirming your place. Please note, some modules (though not all) have multiple iterations in the Michaelmas and Lent Term.