## Linear Stretching

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+++Englischer Blogbeitrag

Last month’s blog post explored the relationship between reality and the numerical scores we have in our datasets. This month, we apply those basic ideas to better understand the limitations of a popular harmonization technique: linear stretching. You might now the approach under another name, but chances are you have already come across it. The approach tries to solve one of the most obvious challenges in harmonization: What to do if two instruments differ in the number of response categories. One survey might offer four response options, another five, and yet another seven to capture the same construct. In this post, we will look into how linear stretching works, but also why it falls short of fully establishing comparability.

Linear stretching comes in many forms. To understand the basic idea, we look at a widespread variant: stretching shorter scales to the range of a longer scale. Consider two instruments with the same question wording, but one instrument offers seven response options (i.e., a seven-point scale) and the other only five (i.e., a five-point scale).

There is an obvious need to transform the data measured with one (or both) instrument(s) before combining them for our analyses. Linear stretching does this by transforming the scores measured with the shorter scale (five-point) into a format similar to the longer scale (seven-point). The algorithm is the following:

Set the lowest values of the scales as equal (here 1 = 1) and set the highest values of the scales equal (here 5 = 7). Then distribute the values in between with equal distances between the two endpoints 1. A five-point scale (1, 2, 3, 4, 5), translated into a seven-point scale, thus becomes a scale with the values 1, 2.5, 4, 5.5, 7. The small animation below illustrates why this is called linear “stretching.”

Vollständige Quelle: GESIS 