Regression Analysis for the Social Sciences

Rachel A. Gordon

• Publisher: Routledge
• Year: 2015
• ISBN:
  9781317607106
• Edition: 2
• Topic: Social Sciences
• Subtopic: Sociology
• Index: Social Sciences

Provides graduate students in the social sciences with the basic skills they need to estimate, interpret, present, and publish basic regression models using contemporary standards.

Key features of the book include:

•interweaving the teaching of statistical concepts with examples developed for the course from publicly-available social science data or drawn from the literature.

•thorough integration of teaching statistical theory with teaching data processing and analysis.

•teaching of Stata and use of chapter exercises in which students practice programming and interpretation on the same data set. A separate set of exercises allows students to select a data set to apply the concepts learned in each chapter to a research question of interest to them, all updated for this edition.

Part 1

GETTING STARTED

Chapter 1

EXAMPLES OF SOCIAL SCIENCE RESEARCH USING REGRESSION ANALYSIS

1.1 What is Regression Analysis?

1.2 Literature Excerpt 1.1

1.3 Literature Excerpt 1.2

1.4 Literature Excerpt 1.3

1.5 Literature Excerpt 1.4

1.6 Summary

CHAPTER 1: EXAMPLES OF SOCIAL SCIENCE RESEARCH USING REGRESSION ANALYSIS

“Statistics present us with a series of techniques that transform raw data into a form that is easier to understand and to communicate or, to put it differently, that make it easy for the data to tell their story.”

Jan de Leeuw and Richard Berk (2004)

Introduction to the Series

Advanced Quantitative Techniques in the Social Sciences

Regression analysis,* a subfield of statistics, is a means to an end for most social scientists. Social scientists use regression analysis to explore research questions and to test hypotheses. This statement may seem obvious, but it is easy to get sidetracked in the details of the theory and practice of the method, and lose sight of this bigger picture (especially in introductory statistics courses). To help keep the big picture in sight, this chapter provides excerpts from the social science literature.

These excerpts also help to focus attention on how regression analyses are used in journal articles, consistent with two of the major reasons graduate students learn about regression analysis: (a) to be able to read the literature, and (b) to be able to contribute to the literature. You have surely already read at least some articles and books that report the results of regression analyses (if not, you likely will be doing so in the coming weeks in your substantive courses). Examining such literature excerpts in the context of a course on regression analysis provides a new perspective, with an eye toward how the technique facilitates exploring the question or testing the hypotheses at hand, what choices the researchers make in order to implement the model, and how the results are interpreted. At this point, you do not have the skills to understand fully the regression results presented in the excerpts (otherwise this book would not be needed!), so the purpose of this chapter is to present these features in such a way that they overview what later chapters will cover, and why. We will revisit these excerpts in the final chapter of the book, to help to reinforce what we have covered (and what advanced topics you might still want to pursue).

We have purposefully chosen excerpts in this chapter that were written by young scholars from a broad array of subfields and using different types of data sources.

1.1: WHAT IS REGRESSION ANALYSIS?

Later chapters will develop the statistical details of regression analysis. But, in order to provide some guideposts to the features we will examine in the literature excerpts, it is helpful first to briefly consider what regression analysis is conceptually, as well as some of its key elements.

Why is it called regression, and why is it so widely used in the social sciences? The term regression is attributed to Francis Galton (Stigler 1986). Galton was interested in heredity and gathered data sets to understand how traits are passed down across generations. The data he gathered ranged from measures of parents’ and children’s heights to assessments of sweet peas grown from seeds of varying size. His calculations showed that the height or size of the second generation was closer to the sample average than the height or size of the first generation (i.e., it reverted, or regressed, to the mean). His later insights identified how a certain constant factor (such as exposure to sunlight) might affect average size, with dispersion around that group average, even as the entire sample followed a normal distribution around the overall mean. Later scientists formalized these concepts mathematically and showed their wide applicability. Ultimately, regression analysis provided the breakthrough that social scientists needed in order to study social phenomena when randomized experiments were not possible. As Stephen Stigler puts it in his History of Statistics “beginning in the 1880s … a series of remarkable men constructed an empirical and conceptual methodology that provided a surrogate for experimental control and in effect dissipated the fog that had impeded progress for a century” (Stigler 1986, 265).

Regression analysis allows scientists to quantify how the average of one variable systematically varies according to the levels of another variable. The former variable is often called a dependent variable or outcome variable and the latter an independent variable, predictor variable, or explanatory variable. For example, a social scientist might use regression analysis to estimate the size of the gender wage gap (how different are the mean wages between women and men?), where wage is the dependent variable and gender the independent variable. Or, a scientist might test for an expected amount of returns to education in adults’ incomes, looking for a regular increment in average income (outcome) with each additional year of schooling (predictor). When little prior research has addressed a topic, the regression analyses may be exploratory, but these variables are ideally identified through theories and concepts applied to particular phenomena. Indeed, throughout the text, we encourage forward thinking and conceptual grounding of your regression models. Not only is this most consistent with the statistical basis of hypothesis testing, but thinking ahead (especially based on theory) can facilitate timely completion of a project, easier interpretation of the output, and stronger contributions to the literature.

An important advantage of regression analysis over other techniques (such as bivariate t-tests or correlations) is that additional variables can be introduced into the model to help to determine if a relationship is genuine or spurious. If the relationship is spurious, then a third variable (a confounder, common cause, or extraneous variable) causes both the predictor and outcome; and, adjusting for the third variable in a regression model should reduce the association between the original predictor of focal interest and outcome to near zero. In some cases, the association may not be erased completely, and the focal predictor may still have an association with the outcome, but part of the initial association may be due to the third variable. For example, in initial models, teenage mothers may appear to attain fewer years of schooling than women who do not have a child until adulthood. If family socioeconomic status leads to both teenage motherhood and academic achievement, then adjusting for the family of origin’s education, occupation, and income should substantially reduce the average difference in school attainment between teenage and adult mothers. In Chapters 6 and 10, we will discuss how these adjustments are accomplished, and their limitations.

Such statistical adjustments for confounding variables are needed in the social sciences when randomized experiments cannot be conducted due to ethical and cost concerns. For example, if we randomly assigned some teenagers to have a child and others not to, then we could be assured that the two groups were statistically equivalent except for their status as teenage mothers. But, of course, doing so is not ethical. Although used less often than in the physical sciences to test basic research questions, experiments are more frequently used in certain social science subfields (e.g., social psychology) and applications (e.g., evaluations of social programs). When experiments are not possible, social scientists rely on statistical adjustments to observational data (data in which people were not assigned experimentally to treatment and control groups, such as population surveys or program records). Each literature excerpt we show in this chapter provides examples of using control variables in observational studies in an attempt to adjust for such confounding variables.

Regression models also allow scientists to examine the mechanisms that their theories and ideas suggest explain the association between a particular predictor variable and an outcome (often referred to as mediation). For example, how much of the wage gap between men and women is due to discriminatory practices on the part of employers and how much is due to differences in family responsibilities of men and women (such as child-rearing responsibilities)? If the mediators—discriminatory practices and family responsibilities—are measured, regression models can be used to examine the extent to which they help to explain the association between the focal pre...