All brands strive to have an excellent Image in their respective markets, where Image is comprised of such components as reputation and trustworthiness. For this purpose, companies often conduct surveys among their customers to inquire about their satisfaction, complaints, and whether expectations are being met. An interesting question that arises is that, given such survey results, whether we can predict the brand’s Image.
Package plspm in R contains a dataset called mobile, which contains variables that pertain to the above issue. Specifically it contains 24 variables that encapsulate the following latent (underyling) concepts: Image, Expectations, Quality, Value, Satisfaction, Complaints, and Loyalty. The variable scale is from 0-100. For example, the Image latent concept, has five corresponding variables in the dataset and the Expectations latent concept has three corresponding variables in the dataset. There are a total of 250 observations in the dataset.
A methodology often used for data with latent concepts is that of Principal Components Analysis (PCA), which is based on the computation of eigenvectors and eigenvalues of the data covariance matrix. In this post, we will employ Principal Components Regression(PCR), Partial Least Regression(PLSR), and Ridge Regression (all related to PCA) to build a model and create a prediction for the average Image ratings of the products in the dataset. So the response variable will be the average of the 5 variables related to Image, and predictors will be the variables related to the other concepts (Value, Satisfaction, etc). Although, all aforementioned regressions are based on the Principal Components idea, they differ in how they treat the low/high variance directions. PCR just keeps a certain number of high variance directions and throws away the rest. PLSR inflates some of the high variance directions, while shrinking the low variance directions [Has13]. On the other hand, Ridge Regression shrinks all directions, exhibiting a preference for the high-variance directions (i.e., it shrinks low-variance more). Finally, for comparison purposes, we also compute the linear regression of the predictors. As is shown in the code below, PCR and PLSR do the best in predicting the average Image rating of each product. This could indicate that keeping/inflating the high variance directions produces better predictions for the dataset, than shrinking high-variance directions less than low-variance directions as is done in Ridge Regression.
[Has13] Hastie, T., Tibshirani, R. and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Springer, 2013.
Below is the link for the full R code:
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