The object of the analysis of the Irritable Babies data (Van den Boom, 1988; Van den Boom & Hoeksma, 1994) was to assess how mothers and babies react to each other during the first six months of the baby's life. This type of information is contained in the two-way and three-way interactions between the three variables. Note that it is the changes of the two-way interaction between baby and mother which is the focus of the analysis.
The three-way contingency table has as its variables: Child behaviour (7 categories), Mother behaviour (6 categories) and the first six months of the baby's life (6 categories). It is thus a frequency table containing in the cells the number of times particular combinations of mother and baby behaviour occurred together for each of six months.
|1.||Other; Non-baby related|
A three-way data array X = (x(i,j,k)) has the following form
|-----|i=1 |-----| |i=2 |-----| | |.. | | | |.. | | |____|i=I=7 k=K=6 | |____| k=2 |_____| k=1 j=1,.,J=6
The actual data file has the following form:
j=1,.,J=6 |-----|i=1 | |i=2 | |.. k=1 | |.. |_____|i=I=7 |-----|i=1 | |i=2 | |.. k=2 | |.. |_____|i=I=7 ....... |-----|i=1 | |i=2 | |.. k=6 | |.. |_____|i=I=7
Thus the first mode (i) is nested in the third mode (k) and there are 7 (Child behaviour) times 6 (Months) rows and 6 (Mother behaviour) columns.
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 Carlier and Kroonenberg (1996) and Kroonenberg (2008). Applied multiway data analysis. Hoboken NJ: Wiley (Chapter 17).
[Download the zipped Irritable Babies Data]