The article argues against the popular belief that linear regression should not be used when the dependent variable is a dichotomy. The relevance of the statistical arguments against linear analyses, that the tests of significance are inappropriate and that one risk getting meaningless results, are disputed. Violating the homoscedasticity assumption seems to be of little practical importance, as an empirical comparison of results shows nearly identical outcomes for the two kinds of significance tests. When linear analysis of dichotomous dependent variables is seen as acceptable, there in many situations exist compelling arguments of a substantive nature for preferring this approach to logistic regression. Of special importance is the intuitive meaningfulness of the linear measures as differences in probabilities, and their applicability in causal (path) analysis, in contrast to the logistic measures.

Linear versus logistic regression when the dependent variable is a dichotomy

An important open question in sociology with obvious policy implications is how to assess the magnitude of the effect of educational attainment on intergenerational social mobility. To examine this, we propose a general method of path analysis, which can be used to estimate direct and indirect effects even in systems where some of the variables are categorical. It provides an additive decomposition of total effects which is exact when the effects are expressed as mean differences, and approximate but typically quite accurate for other measures of association such as log-odds-ratios. Estimates of the effects and their standard errors can be calculated by using standard output for fitted models. The method is illustrated by an analysis of British survey data on social mobility.

/pdf/path-analysis-for-discrete-variables-the-role-of-education-2de54f4zzk.pdf

Path analysis for discrete variables: The role of education in social mobility

In the literature on the relationship between class of origin and educational attainment, the typical conclusion is that class inequality was stable over the last century, and the attempts at egalitarian reform thus proven ineffective. The conclusion turns out to depend on the choice of statistical measure, in this case loglinear measures of association. Also linear measures of association give similar results. If instead, measures of inequality are used, the contrasting conclusion of a strong reduction in the class bias in recruitment to higher education emerges.

As the provision of higher education has increased over time, the trends in the results of these three measures differ. It is argued that it is measures of inequality that capture inequality in the allocation of higher education or bias in the allocation mechanisms. The argument in favor of using loglinear measures has been the special property of “margin insensitivity” attributed to them. It has also been suggested that they capture bias in the allocation mechanism, which may develop in a way different from the trend in the inequality of the allocation outcome. It is argued that neither claim is tenable.

Measuring Social Inequality In Educational Attainment

In Rosenberg's work can be found the basis for both a path analytical approach-where relationships between variables are explained—and an R Square measurement—where a variable is explained—for nominal variables. The first approach has been expanded enormously by different authors. In this article we dig into the R Square alike problem.

Extending Rosenberg's idea about conjoint effects

Regression standardization has characteristically been used to examine mean differences, while approaches such as log-linear analysis have been more often employed when variables are dichotomous or do not satisfy interval-level assumptions. The typological regression standardization (TRS) procedure presented in this paper combines the analytical power of ordinary multiple regression with the typological advantages of contingency table analysis. It permits researchers to deal with multicollinearity among a limited number of predictors and can be used with both continuous and discrete dependent variables, if appropriate precautions are taken in the discrete case. TRS offers greater versatility in handling both predictor and dependent variables than do logit and probit specifications, and it has the further advantage of permitting more straight forward interpretation of results. Its disadvantages include the well-known problems connected with regression model specification, especially when the dependent variable is dichotomous. TRS may be especially useful, however, to researchers who are primarily interested in examining the relationship of one independent variable to a dependent variable while taking into account several potentially confounding factors.

Simultaneous Control and Crosstabular Presentation with Polytomous Variables: The Case of Religion Predictors

In the classics of quantitative sociological analysis, such as The People's Choice (Lazarsfeld et al, 1948) or The American Soldier (Stouffer et al, 1949), percentage tables were the principal tools of statistical analysis Using this simple instrument, the researchers managed to shed empirical light on interesting theoretical ideas, such as cross-pressures or relative deprivation, presenting the results in a way that gave even the lay reader an opportunity to follow the steps in the statistical analysis Even today, most students are introduced to the logic and procedures of quantitative analysis by working with cross-tables, and many research reports still present their findings in the form of percentage tables The varying quality of these analyses indicates the critical importance of the imagination and skills of the researcher Over the last decade, however, more elaborate statistical techniques, going a long way towards routinising the analysis, have gradually taken over in articles in the leading journals as well as in advanced courses in statistics Such techniques provide systematic procedures for reaching precise answers to highly complex questions However, it may be asked whether the price paid for these advances in statistical sophistication i n terms of hard labour for students, a widening gap between the quantitatively oriented and the rest of the sociological community, and a virtual breakdown in communication with a broader public--has so far been offset by gains in the substantive interest of the results reached For a sociologist with an average training in statistics who tries to keep pace with the latest developments within this field, the highly technical presentation is frustrating, and the disagreements among the specialists concerning what seem to be factual questions are confusing This article does not engage in skirmishes along the frontier of advances in statistics; here, the

Decomposing proportions and differences in proportions: Approaches to contingency-table analysis

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Ottar Hellevik

Author Tools

Chat about Author

Papers

Decomposing proportions and differences in proportions: Approaches to contingency-table analysis