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Perceptual maps and multidimensional scaling - Attribute vector fitting

Q: What are the steps of vector fitting?

Pre-process the data by standardizing the dimension coordinates such that each dimension in the MDS had a mean of 0 and a standard deviation of 1. Do this by transforming into z-scores . Run a series of multiple regression models , one for each attribute, with attributes as dependent variables and the coordinates of the brands in the perceptual map as the independent variables ( e.g. diet = b0 + b1zdimI + b2zdimII ). We then get values for b1 and b2, which are the x and y values of the head of the attribute vector.

Q: What are the 3 different choices of plotting vectors and how are they depicted?

Using normed b-weights - vector head Using raw b-weights - diamond shape Using betas - star shape

Q: What are the different reasons for choosing each vector type?

Normed b-values - putting all vectors on equal footing . All attributes will fall on a circle. Useful when you are only interested in direction . Raw b-weights - maintains directionality but the lengths reflect the variances of the attributes as well as the R^2 or how well the vector fits the space . Beta weights - maintains directionality and the R^2 or fits in space, but the lengths are corrected for the attribute variances .

4 important questions on Perceptual maps and multidimensional scaling - Attribute vector fitting

What method can be used as a more objective means of interpretation of perceptual maps?

Vector fitting

What are the steps of vector fitting?

Pre-process the data by standardizing the dimension coordinates such that each dimension in the MDS had a mean of 0 and a standard deviation of 1. Do this by transforming into z-scores.
Run a series of multiple regression models, one for each attribute, with attributes as dependent variables and the coordinates of the brands in the perceptual map as the independent variables (e.g. diet = b0 + b1zdimI + b2zdimII).
We then get values for b1 and b2, which are the x and y values of the head of the attribute vector.

What are the 3 different choices of plotting vectors and how are they depicted?

Using normed b-weights - vector head
Using raw b-weights - diamond shape
Using betas - star shape

What are the different reasons for choosing each vector type?

Normed b-values - putting all vectors on equal footing. All attributes will fall on a circle. Useful when you are only interested in direction.
Raw b-weights - maintains directionality but the lengths reflect the variances of the attributes as well as the R^2 or how well the vector fits the space.
Beta weights - maintains directionality and the R^2 or fits in space, but the lengths are corrected for the attribute variances.