What is Johnson's relative weights analysis? In this article, Michael Lieberman explains Johnson’s relative weights analysis, a technique used to evaluate how the response (dependent) variable relates to a set of predictors when those are correlated to each other.
PrintEditor's note: Michael Lieberman is the founder and president of Multivariate Solutions, a New York-based research consulting firm. He can be reached at michael@mvsolution.com.
I like to say that there is nothing new under the sun statistically speaking. Almost all the math in common multivariate analyses were proven more than a century ago. Most new products are a mélange of existing techniques with a simple twist.
Every so often, however, a new technique emerges that leverages prevalent methodologies with growing bandwidth of personal and cloud computing. In this piece I will introduce importance weighting, a useful technique in marketing that allows marketers to assign varying levels of importance or priority to different factors or elements within their marketing strategies. I will outline one that is gaining popularity in the marketing research world – Johnson’s relative weights analysis.
In 2000, Jeff Johnson wrote a technical paper introducing relative importance weights. Prior to that, researchers relied on traditional statistics (e.g., correlations, standardized regression weights) that are known to yield affected information concerning variable importance – especially when predictor variables are highly correlated with one another. In the context of market research, relative weights refer to the importance or influence of different attributes or factors on consumer preferences or purchasing decisions. Common uses for relative weights are:
In Johnson’s relative weights analysis, the focus is on determining the relative impact of each variable on the dependent variable, taking into account the influence of other variables in the model. The relative weights of the variables are calculated based on their unique contribution to the outcome variable while considering the presence of other variables in the model.
The Johnson method utilizes not only standardized outcomes from regression analysis, but also correlations between the dependent and predictor variables, as well as eigenvector analysis (a linear algebra matrix method) into a more nuanced nine-step technique.
Johnson’s relative weighting can get granular with a large number of variables. By contrast, linear regression cannot easily handle, say, 20 variables. Differences between highly correlated variables would blur the outcome.
This is not the case with relative importance weights. Moreover, given the ease of programming, one can run the analysis across many dependent variables simply by changing one or two lines in R stat code. Using R or Python and calculating the relative importance weights has turned a multistep process into a few lines of code. The three lines of R stat code (below) reads in data and performs a relative weight analysis on a dependent variable and, in this case, nine predictor variables.
# Load the 'AvWeight' dataset
# Fit a linear regression model
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