Before we discuss multilevel modelling it is worthwhile doing a quick review of traditional single-level analysis, including multiple linear regression and logistic regression. 'Single-level' means that the analysis is carried out at one analytical level - typically the individual level, although sometimes the single level is an aggregate construct, such as the 'country'. For example, a single level analysis at an aggregate level might be carried out to assess the relationship between the unemployment rate and the crime rate for a set of countries. In this example there would be one pair of values of each country: the unemployment rate and the crime rate. A positive relationship between these two rates would indicate that countries with high unemployment rates would also have high crime rates. However this analysis would not allow any inferences to be made about individual level relationships, such as the individual level relationship between crime and unemployment.
You would use multiple linear regression analysis to relate a set of explanatory variables (sometimes also called 'independent variables' or 'x' variables) to an outcome of interest (sometimes also called a 'dependent variable', or a 'y' variable) that has an interval (continuous) scale. The explanatory variables can be either interval scale (such as age), categorical (such as ethnic group), and typically the explanatory variables will be a mixture of these two types. When the response variable is an interval scale and can be assumed to have a normal distribution, we can use multiple linear regression models to assess the nature and strength of the associations of the explanatory variables with the dependent variable. An example would be using multiple linear regression models to investigate the relationship between blood pressure -the outcome variable; an interval scale dependent variable with a normal distribution -with several explanatory variables: age in years (interval scale), gender, and occupation (categorical). Often in social science, the dependent variable is categorical, and often has two categories or can be re-coded to have two categories. This outcome is binary (and is sometimes also referred to as a dichotomous or 0/1 variable). Examples of binary outcomes are: whether or not someone considers themselves to have limiting long term illness, whether or not someone is unemployed, or whether or not someone turns out to vote. In these situations, logistic regression models are used instead of multiple linear regression models. For example, you could do a logistic regression analysis to model the chance of someone turning out to vote given information about their age, gender, highest educational qualification and employment status.