Multi-Variate Statistical Analysis and Comparative Cross-National Surveys Data

A growing concern and professional practice in the social sciences is the comparison of social and political behaviours between social groups. The focus can be on economic, political, cultural, socio-psychological attitudes and behaviours, it can be at an individual or collective level and the groups of interest can be defined by gender, ethnicity, age, generation.  One particular type of groups will be at the centre of this course: nations or countries. Indeed, the trend in cross-national, and also cross-cultural, research has gained greater popularity in the last decades, especially since the developments of comparative cross-national data bases such as Eurobarometers, EVS, ISSP or ESS.

Thanks to methodological developments in comparative survey designs such as the one achieved by a survey like ESS or equivalent surveys, a significant step forward has been crossed over. A new big challenge for comparative survey analysis is thus to analysis these comparative data sets with statistical techniques and methods that make it possible to test for country effects. Unfortunately, many users still just juxtapose country by country their results and finally few are really dealing with the logic of statistical control for country effects. When they introduce country effects in their explanatory models, most of the time it is just on the form of dummy effects coding in regression analysis, which only account for the heterogeneity of the dependent variable in the different countries. But how to test for heterogeneity/homogeneity of beta parameters, the one estimating the effects of the explanatory variables on the dependent one ? How can we know that beta parameters estimated by a logistic regression analysis are statistically different across nations? How can we know that factorial structures diverge between countries or are similar ? This is the kind of big issues that this course will cover by looking at different methods, among the most used in statistical comparative analysis.  The course will focus every day on a specific method, with as strong emphasis on two blocks of methods : modelling techniques (regression, both linear and logistic, loglinear and latent class models) and data reduction techniques (factor analysis, multiple correspondence analysis). The complementarities between these types of methods will be emphasized.  Modelling techniques are the one proposing to the user to apply a model on their data structures : the model is an algebric expression such as the classical linear regression model. This family of methods attach great importance to hypotheses testing, in particular about significance of the models and their parameters. But, how to cope with the countries effects in that case? Tests may be sensitive to sample sizes for instance if a researcher compare two countries with fairly different N. How to know that when beta parameters have higher values in one country than another it really means a country difference? On the other hand, data reduction techniques are of great help for reducing the space of variables and/or individuals or cases: with big data bases like Eurobarometers or ESS, EVS, with so many indicators, reducing the data space to few dimensions is a very interesting objective. But what constitute a “factorial invariance” across countries? How could we say that the factorial space is homogeneous or not across nations? Factor analysis and correspondence analysis propose certain solutions to these problems. The course will concentrate mainly on exploratory factor analysis, the confirmatory factor analysis being also interesting for comparative analysis will be explained anyway but on a shorter basis.

A big point of this course is to offer a (non-exhaustive) panorama of some very important methods, helping comparatists to deal with country effects. The scope is not exhaustive but permits in only two weeks to save a huge amount of time : if working with a textbook only, a student could spend months to discover so many different techniques.  Attendants to the course should be aware that this is precisely the objective: to offer a panorama of some methods and practical solutions, in a non exhaustive framework but concentrated on most used methods. The objective is that after the summer school, participants know what methods are best adapted to their research perspectives and types of data.  The summer school offers other courses specialized on one method (such as confirmatory factor analysis, is structural equation models), which is a different choice. The course will show, both by theoretical presentations and empirical illustrations, the advantages and the limits of each method, knowing that no method is the perfect one.

The course is an introductory level one even if methods taught are multivariate ones. It is designed to help social sciences students that have difficulties into entering in the multivariate techniques world and to make them crossing over these first difficulties during the summer school.  Because the course is introductory, it does not require any other previous skills than basic descriptive statistics and hypotheses testing. If students need basic recall on these points, they can ask the instructor documents or advices before the course; in any case, if needed the instructor and/or the TA can propose a remedial on this in the very beginning of the summer school.