An examination of regionality in a configuration of smallest space analysis using Loevinger’s homogeneity coefficient

An examination of regionality in a configuration of smallest space analysis using Loevinger’s... When applying smallest space analysis to behavioural science data, we may observe a radex structure in the two-dimensional output. This study proposes a method to support the investigation of the radex. A radex structure includes both polar and modular facets as defined in facet theory, where the modular facet of the concentric circles represents the frequency of variables. The polar facet of the pie shape, intersected by lines emanating from the centre, represents the semantic theme, grouped by variable clusters. When a dataset of dichotomous variables is analysed in this type of structure, variables with a higher proportion of positive answers often fall near the centre, whereas variables with a lower proportion of positive answers tend to fall near the outer area. When a few variable points fall along the line emanating from the centre to the outer rim, that series of variables may form a Guttman scale. The proposed method first determines the centre of the concentric circles, based on variable frequencies, using the quasi-Newton method of optimisation. Next, weighted Loevinger’s homogeneity coefficients ( $$H_{w}$$ H w ) are used to measure the degree of Guttman scalability. The author examined possible borders among the regions of the polar facet by investigating the peaks and troughs of $$H_{w}$$ H w values, using different ways of weighting homogeneity coefficients. Applications of the method to artificial and survey data showed that the proposed method was adequately effective for detecting the centre of concentric circles and radial lines to suggest regionality for the polar facet in a radex. Quality & Quantity Springer Journals

An examination of regionality in a configuration of smallest space analysis using Loevinger’s homogeneity coefficient

Loading next page...
Springer Netherlands
Copyright © 2014 by Springer Science+Business Media Dordrecht
Social Sciences, general; Methodology of the Social Sciences; Social Sciences, general
Publisher site
See Article on Publisher Site


You’re reading a free preview. Subscribe to read the entire article.

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches


Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.



billed annually
Start Free Trial

14-day Free Trial