Regression analysis

(noun)

In statistics, regression analysis includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analysis helps one understand how the typical value of the dependent variable changes when any one of the independent variables is varied, while the other independent variables are held fixed.

Related Terms

Examples of Regression analysis in the following topics:

  • Analyzing Data and Drawing Conclusions

    • Quantitative data can be analyzed in a variety of ways, regression analysis being among the most popular .
    • More specifically, regression analysis helps one understand how the typical value of the dependent variable changes when any one of the independent variables is varied, while the other independent variables are held fixed.
    • A large body of techniques for carrying out regression analysis has been developed.
    • In practice, the performance of regression analysis methods depends on the form of the data generating process and how it relates to the regression approach being used.
    • Since the true form of the data-generating process is generally not known, regression analysis often depends to some extent on making assumptions about this process.

  • Network regression

    • The standard tool for this question is linear regression, and the approach may be extended to using more than one independent variable.
    • We can now perform a standard multiple regression analysis by regressing each element in the information network on its corresponding elements in the monetary network and the government institution network.
    • To estimate standard errors for R-squared and for the regression coefficients, we can use quadratic assignment.
    • Version 6.81 of UCINET offers four alternative methods for Tools>Testing Hypotheses>Dyadic (QAP)>QAP Regression.
    • QAP regression of information ties on money ties and governmental status by full partialling method

  • Introduction to comparing two relations for the same set of actors

    • The basic question of bivariate analysis of network data is whether the pattern of ties for one relation among a set of actors aligns with the pattern of ties for another relation among the same actors.
    • Three of the most common tools for bivariate analysis of attributes can also be applied to the bivariate analysis of relations:
    • This kind of question is analogous to the test for the difference between means in paired or repeated-measures attribute analysis.
    • This kind of question is analogous to the correlation between the scores on two variables in attribute analysis.
    • This kind of question is analogous to the regression of one variable on another in attribute analysis.

  • Regressing position on attributes

    • Tools>Testing Hypotheses>Node-level>Regression will compute basic linear multiple regression statistics by OLS, and estimate standard errors and significance using the random permutations method for constructing sampling distributions of R-squared and slope coefficients.
    • All of the basic regression statistics can be saved as output, for use in graphics or further analysis.
    • Figure 18.15 shows the result of the multiple regression estimation.
    • Multiple regression of eigenvector centrality with permutation based significance tests
    • Dialog for Tools>Testing Hypotheses>Node-level>Regression for California donor's eigenvector centrality

  • The Scientific Method

    • 4) Experiment (test and / or discussion of all of the above; in the social sciences, true experiments are often replaced with a different form of data analysis that will be discussed in more detail below)
    • Scientific measurements are usually tabulated, graphed, or mapped, and statistical manipulations, such as correlation and regression, performed on them.
    • In both cases, scientific progress relies upon ongoing intermingling between measurement and categorical approaches to data analysis.
    • An independent variable is a variable whose value or quality is manipulated by the experimenter (or, in the case of non-experimental analysis, changes in the society and is measured or observed systematically).
    • In lieu of holding variables constant in laboratory settings, quantitative sociologists employ statistical techniques (e.g., regression) that allow them to control the variables in the analysis rather than in the data collection.

  • A note on statistics and social network data

    • Social network analysis is more a branch of "mathematical" sociology than of "statistical or quantitative analysis," though social network analysts most certainly practice both approaches.
    • Statistical algorithms are very heavily used in assessing the degree of similarity among actors, and if finding patterns in network data (e.g. factor analysis, cluster analysis, multi-dimensional scaling).
    • Even the tools of predictive modeling are commonly applied to network data (e.g. correlation and regression).
    • Inferential statistics can be, and are, applied to the analysis of network data.
    • Since this text focuses on more basic and commonplace uses of network analysis, we won't have very much more to say about statistics beyond this point.

  • The probability of a dyadic tie: Leinhardt's P1

    • The approaches that we've been examining in this section look at the relationship between actor's attributes and their location in a network.Before closing our discussion of how statistical analysis has been applied to network data, we need to look at one approach that examines how ties between pairs of actors relate to particularly important relational attributes of the actors, and to a more global feature of the graph.
    • Network>P1 is a regression-like approach that seeks to predict the probability of each of these kinds of relationships for each pair of actors.

  • Preface

    • This book began as a set of reading notes as Hanneman sought to teach himself the basics of social network analysis.
    • It then became a set of lecture notes for students in his undergraduate course in social network analysis.
    • Through a couple extensions and revisions, it has evolved to cover more of the basic approaches to the analysis of social network data.
    • The book may also be suitable as course-support for undergraduate or introductory graduate training in social network analysis.
    • The concepts and techniques of social network analysis are informed by, and inform the evolution of these broader fields.

  • Two-mode correspondence analysis

    • For binary data, the use of factor analysis and SVD is not recommended.
    • As an alternative for binary actor-by-event scaling, the method of correspondence analysis (Tools>2-Mode Scaling>Correspondence) can be used.
    • Correspondence analysis (rather like Latent Class Analysis) operates on multi-variate binary cross-tabulations, and its distributional assumptions are better suited to binary data.
    • Figure 17.13 shows the location of events (initiatives) along three dimensions of the joint actor-event space identified by the correspondence analysis method.
    • Figure 17.15 show the plot of the actors and events in the first two dimensions of the joint correspondence analysis space.

  • Intorduction to qualitative analysis

    • This is because the various dimensional methods operate on similarity/distance matrices, and measures like correlations (as used in two-mode factor analysis) can be misleading with binary data.
    • Even correspondence analysis, which is more friendly to binary data, can be troublesome when data are sparse.
    • This approach doesn't involve any of the distributional assumptions that are made in scaling analysis.