International Collaborative Aging Project

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Topics Addressed

  1. Public Health
  2. Correspondence Analysis
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The purpose of the International Collaborative Aging Project (ICS II) is to identify the biological, behavioral and sociostructural factors that place certain individuals at higher risk to oral disease and dysfunction, with focus on the elderly, since they are rapidly becoming an increasing segment of the population. Within the elderly, characteristics between different ethnic groups in the population may differ and thus were examined as well. An earlier study, ICS-I, concluded that beliefs of the population regarding oral health and commitment of a country and its dental profession to implementing prevention activity might be the best indicators of oral health status. This study attempts to pursue the conclusions of the earlier study by examining those behaviors and attitudes which oral health promotion might be able to influence in order to improve oral health status for the population as a whole.

The following Table gives a 7x7 contingency table of brushing habits versus flossing habits of 3,610 individuals from Baltimore, Maryland, San Antonio, Texas, and Sioux and Lakota (Navaho) communities.

We use the program ANACOR (see Chapter 8, Gifi (1990), Wiley) to perform Correspondence Analysis on this dataset. The singular values (see pages 266-268 in Gifi (1990)) are given in the following Table.

               Singular Values
               ===============
                 1   0.3755
                 2   0.0890
                 3   0.0440
                 4   0.0286
                 5   0.0071
                 6   0.0007
               ---------------
These results indicate that a one dimensional solution works well for this dataset. In this case we treat rows and columns symmetrically (note that the ANACOR program also allows the user to treat the row points as the center of gravity of the column points, or the column points as the center of gravity for the row points).

The category quantifications of the rows and columns are presented in Graph 1. Clearly the solution orders the categories of both Brush and Floss from low to high; although the row scores look like a convex function of the original categories, while the column scores a concave one. Also observe that the last category in the row scores is separated from the other categories. In Graph 2 we plot the row vs the column scores.

Graph 3is a re-edit of the original contingency table, with distances between categories corresponding to the optimal quantifications. In addition the two lines for linear regression are drawn.

As pointed out in Gifi (1990) (page 279) these results have mainly correlational significance: optimal scaling of brushing and flossing habits can not produce a correlation larger than .375 (the value of the largest singular value).

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George Michailides
gmichail@stat.ucla.edu