# Course modules

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## Module 1 - Using quantitative data in research

In Module 1 we look at quantitative research and how we collect data, in order to provide a firm foundation for the analyses covered in later modules. The aims of Module 1 are:

• To give a broad overview of how research questions might be answered through quantitative analysis. Such questions as the following are explored: How does quantitative analysis relate to other methods of inquiry? Why is it required and what sorts of evidence can it supply?
• To introduce the vocabulary of quantitative analysis and specify the common terminology to be used in later modules. Of particular importance is the operational definition of research concepts (how we get from real world characteristics to numbers in our data set) and how this leads to observable variables at different levels of measurement.
• To introduce sources of data and concepts relating to how it may be possible to generalise results from samples of various kinds to the populations they are drawn from.
• To discuss how variables are defined, what different types there are, and how this may influence how they are analysed.
• To give some emphasis to certain ideas such as the nature of variability or the recognition of hierarchical units of analysis that are central to multilevel modelling

## Module 3 - Multiple regression

Multiple regression is a technique used to study the relationship between an outcome variable and a set of explanatory or predictor variables. Module 3 covers the following topics:

• Regression with a single continuous explanatory variable
• Comparing groups: regression with a Single categorical explanatory variable (dummy variables)
• Regression with more than one explanatory variable (multiple regression), including:
• A discussion of the idea of statistical control
• The multiple regression model for continuous and categorical explanatory variables
• Modelling non-linear relationships
• Interaction effects (allowing the effect of one explanatory variable X1 to depend on the value of another X2)
• Allowing the slope of the relationship between Y and X1 to vary across groups defined by a categorical variable X2 by 1) fitting separate models for each value of X2, and 2) fitting an interaction between X1 and X2
• Testing for interaction effects
• Checking model assumptions in multiple regression
• Checking the normality assumption
• Checking the homoskedasticity (equal residual variance) assumption
• Outliers

The ideas are illustrated in analyses of hedonistic attitudes in Europe (using data from the European Social Surveys) and of trends in educational attainment (using data from the Scottish Youth Cohort Study).

## Module 4 - Multilevel structures and classifications

Multilevel modelling is designed to explore and analyse data that come from populations which have a complex structure. This module aims to introduce:

• a range of multilevel structures and classifications and how they correspond to real-world situations, research designs, and/or social-science research problems;
• the different types of data frames associated with each structure and how subscripts are used to represent structure;
• targets of inference;
• the distinction between levels and variables, and fixed and random classifications;
• the notion that multilevel structures are likely to generate dependent, correlated data that requires explicit modelling;
• the difference between long and wide forms of data structures;
• the advantages, both technical and substantive, of using a multilevel model, and the disadvantages of not doing so.

## Module 5 - Introduction to multilevel modelling

In the social, medical and biological sciences multilevel or hierarchical structures are the norm. Examples include individuals nested within geographical areas or institutions (e.g. schools or employers), and repeated observations over time on individuals. Other examples of hierarchical and non-hierarchical structures were given in Module 4. When individuals form groups or clusters, we might expect that two randomly selected individuals from the same group will tend to be more alike than two individuals selected from different groups. For example, children learn in classes and features of their class, such as teacher characteristics and the ability of other children in the class, are likely to influence a child's educational attainment. Because of these class effects, we would expect test scores for children in the same class to be more alike than scores for children from different classes. Multilevel models - also known as hierarchical linear models, mixed models, random effects models and variance components models - can be used to analyse data with a hierarchical structure. Throughout this module we refer to the lowest level of observation in the hierarchy (e.g. student) as level 1, and the group or cluster (e.g. class) as level 2.

The ideas are illustrated in analyses of hedonistic attitudes in 20 European countries (using data from the European Social Surveys) and of between-school variation in trends in students' educational attainment (using data from the Scottish Youth Cohort Study). The same datasets are analysed in Module 3 using multiple regression, ignoring country and school effects respectively. In this module, we emphasise the substantive insights that can be gained from a multilevel modelling approach.

## Module 6 - Regression models for binary responses

In Module 3 we considered multiple linear regression models for the relationship between a continuous response variable and a set of explanatory variables which may be continuous or categorical. Regression models need to be adapted to handle categorical response variables and, in this module, we consider methods for a particular type of categorical variable: binary or dichotomous responses, that is variables with only two categories.

The ideas are illustrated in analyses of voting intentions in the 2004 US general election (using data from the National Annenberg Election Study) and uptake of antenatal care in Bangladesh (using data from the 2004 Bangladesh Demographic and Health Survey).

## Module 7 - Multilevel models for binary responses

In Module 6 we saw how multiple linear regression models for continuous responses can be generalised to handle binary responses. In this module, we consider how these methods can be extended for the analysis of clustered binary data. We show that many of the extensions to the basic multilevel model introduced in Module 5 - for example random slopes and contextual effects - apply also to binary responses. However, there are some important new issues to consider in the interpretation and estimation of multilevel binary response models.

The ideas are illustrated in analyses of voting intentions in the 2004 US general election (using data from the National Annenberg Election Study) and uptake of antenatal care in Bangladesh (using data from the 2004 Bangladesh Demographic and Health Survey).

## Module 8 - Multilevel modelling in practice: Research questions, data preparation and analysis

In this module we consider the whole process of conducting a research project using multilevel modelling, taking as an example a study of ethnic differences in educational achievement and progress. The research process starts with the formulation of research questions as hypotheses that can be tested using multilevel models. The next step is to prepare the dataset for analysis, which includes decisions about issues such as coding variables, deriving new variables and handling missing data. The analysis then begins with a detailed exploration of the data before fitting multilevel models, building model complexity gradually. We show how the research process is iterative with the results from initial analyses leading to refinements in the original research questions.

This module builds on Module 5: Introduction to multilevel modelling.

## Module 13 - Multiple membership multilevel models

### Module Sections

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