|Back to Three-Mode Data Sets |

Background to the Happiness Data

Data analysed in: Kroonenberg, P. M. (2008). Applied multiway data analysis. Hoboken NJ: Wiley.

The object of the analysis of the Happiness data (Davis, 1977; originally published in Clogg, 1982) is to gain insight into the relationship between happiness as reported by participants in a survey, and the number of their siblings and the number of years of schooling they had completed. The main interest lies in the three-way interaction between the two predictors and the dependent variable Happiness. Of the two-way interaction terms, that between the two predictors is of limited interest because it bears no relation to the prediction of the criterion because it is the design interaction. Its relevance very much depends on the sampling frame.


Data description

The three-way contingency table has as its variables: Happiness reported by participants in a survey (3 categories), Number of siblings (Siblings - 5 categories) and the Years of schooling completed (Schooling - 4 categories). It is thus a frequency table containing in the cells the number of people with a particular combination of categories.

Rows (1st mode): Schooling

No.Abbreviation Description
1.<12 Less than 12 years
2. 12 12 years (equivalent to primary + secondary school)
3.13-16 13-16 year (some) college
4.17+ 17+ (more than undergraduate)

Columns (2nd mode): NumSiblings

No.Abbreviation Description

Slices (3rd mode): Happiness

No.Abbreviation Description
1.Happy-Not too happy
2.Happy+Pretty happy
3.Happ++Very happy

Data arrangement

A three-way data array X = (x(i,j,k)) has the following form

                   |-----|    |i=2
              |-----|    |    |..
              |     |    |    |..
              |     |    |____|i=I=4    k=K=3
              |     |____|            k=2
              |_____|              k=1



The actual data file has the following form:

            |     |i=2
            |     |..     k=1
            |     |..
            |     |i=2
            |     |..     k=2
            |     |..
            |     |i=2
            |     |..     k=3
            |     |..


Thus the first mode (i) is nested in the third mode (k) and there are 4 (Schooling) times 3 (Happiness) rows and 5 (NumSiblings) columns.

Data handling


Categorical data in contingency tables are usually divested of the influence of the marginal proportions which represent the model of independence. Thus the original frequencies are transformed in chi-terms ( = observed - expected)/sqrt(expected). These chi-terms are the basis for the correspondence analysis. For details see Kroonenberg (2008). Applied multiway data analysis. Hoboken NJ: Wiley (Chapter 17).


These published data have been taken from Prof. Clifford Clogg's publication. Please quote the original papers mentioned above. In principle it is not necessary to mention this website when using these data in a publication, but it would be nice.

[Download the zipped Happiness Data]

| Centre for Child and Family Studies | Institute of Education and Child Studies | The Three-Mode Company | Three-Mode Data Sets | TOP |
P.M. Kroonenberg
Institute of Education and Child Studies, Leiden University
Wassenaarseweg 52, 2333 AK Leiden, The Netherlands
Tel. *-31-71-5273446/5273434 (secr.); fax *-31-71-5273945
E-mail: kroonenb at fsw.leidenuniv.nl

Created: 10-7-2009
Last Updated: 7-8-2015