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Partial least squares regression:

I will do some consulting around structural equation modeling (SEM) techniques to solve unique business problems. We try to identify customers’ preferences for various products, and traditional regression is not enough because of the high components of the data set and the multicollinearity of the variables. PLS is a powerful and efficient way to deal with these problematic data sets.

Principal component regression is one option we will explore, but when doing background research, I found that PLS might be the better choice. We will look at PLS regression and PLS path analysis. I don’t believe a return to tradition is valuable at this point because we don’t have a good sense or theory to make assumptions about the underlying structure. In addition, due to the large number of variables in the data set, we are extending SEM technology to its limits. An interesting discussion of this limitation can be found in Haenlein, M&Kaplan, A., 2004, “Preliminary Guideline Partial least squares Analysis”, Understanding Statistics, 3 (4), 283-297.

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The data consisted of 16 variables and 30 observations.

One of the interesting things about PLS regression is that you can have multiple response variables and PLsDepot can accommodate this type of analysis. In this case, I want to analyze only one Y variable, and that is price.

The package places the response variable column at the end of the data frame.

Pls1 $x.lads X-loadings $y.lads X-loadings (U-components) $y.lads Y-loadings $ Cor.xyt score correlation $raw.wGS Original weight $mod.WGS Modified weight $STd.coEFS Standard coefficient $reg.CoEFS Conventional coefficient $R2 R squared $R2Xy explain the variance of Xy T $y.piny - Predict $resid Residual $T2 T2 economic coefficientCopy the code

Word-wrap: break-word! Important; “> Notice what is highly correlated with price

#plot Predictions and actual observations for each observation

We will have to continue to look at different numbers of components to determine the best model and see if the underlying variables make sense from a practical point of view.

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