MTSU Social Work Department

SW 3120: Data Analysis for Social Work Practice
Handout 12

## Multi-variate Analysis; The Elaboration Model

Multi-variate Analysis - the examination of relationships between three or more variables.

The elaboration model helps us to better understand and interpret the explanatory or causal implications of relationships between two variables though the introduction of control variables.

Control variables - variables other than the independent or dependent variable which are introduced into multivariate analysis in order to test for spuriousness.

Possible results of the elaboration process:

1. Replication - the original relationship stays the same.

2. Explanation - the original relationship is explained away as spurious.

3. Interpretation ("reinterpretation" in the text) - our understanding of the original relationship is strengthened.

4. Specification - the conditions under which the original relationship exists are clarified.

Three-way crosstabulation - a type of multi-variate analysis which permits the introduction of a control variable into a crosstabulation of an independent and dependent variable.

Three-way crosstabulations are best understood when interpreted in the context of the original two-way relationship which they are meant to test. For example, this is the result of the crosstab of actual weight loss by participation in a weight loss program:

 Participation High Low Weight High 60% 45% Loss Low 40% 55% (200) (200)

The results of a three-way crosstabulation may be presented in two tables, as:

Weight loss (dependent) by Participation (independent) by Motivation (control)
 High Motivation Low Motivation Participation Participation High Low High Low Weight High 100% 90% 20% 0% Loss Low 0% 10% 80% 100% (100) (100) (100) (100)

If either the independent or control variables is dichotomous, the same results can be presented in one table omitting the cell percents of one of the values of that variable since they are redundant.

Percentages of those with high weight loss by participation controlling for motivation:

 Participation High Low Motivation High 100% 90% Low 20% 0%