Chapter 8: Summated scales in regression analysis
As noted in chapter 1, linear regression analysis presupposes that the variables are metric. But a large proportion of the variables in the ESS data sets are ordinal, and, in addition, most of them are measures of attitudes. Individual measures of attitudes tend to be inaccurate because they only extract particular aspects of the general attitudes we wish to measure, or because people’s answers to single-attitude questions are plagued by random inaccuracies. But both these problems can be alleviated somewhat by combining the values of several indicator variables into scales. This is done by taking their aggregate or average value.
Such summated scales can cover a wider range of manifestations of the relevant attitudes than single-attitude measures do, and positive random measurement errors can be offset by negative ones and vice versa. Furthermore, they have more values than their individual components and their values often have a distribution that is better adapted to linear regression analysis than single-attitude measurements are. If, for instance, we add two variables with two identical values each, we get a new variable with three values. The more indicator variables we combine, the more values the summated scale will have and the more symmetrically dispersed and similar to that of a metric variable its value distribution tends to be.
Indicator variables with identical value codes provide equal contributions to the combined variable. Thus, if we have no particular reason to assign more weight to some indicators than to others, we would prefer indicators with identical value ranges. (Or we might rescale them in order to make their value ranges equal.) The indicator variables to be used as components in a summated scale should be selected with care. SPSS provides tests that can be used to check candidate variables’ appropriateness. Factor analysis is used to select candidates for a scale by singling out variables that can be conceived as indicators of a common underlying attitude or phenomenon. Reliability analysis is used to check whether the associations between selected candidates are strong enough to make their sum a sufficiently accurate measure of the underlying phenomenon. Limitations of space prevent us from going into more detail about these methods other than to state that the reliability analysis option can be found under ‘Scale’ in the Analyze menu, and that, as a minimal test procedure, we could put the candidate indicators on the items list, click ’OK’ and accept all candidates if the resulting Cronbach’s alpha value exceeds 0.7, or try another candidate variable set if it does not. Make sure that the indicators are positively correlated (associated) with each other before you run the analysis. Limit the number of indicators in your candidate sets (3 - 6 ought to be enough). The cases we present here have alpha values greater than 0.7.