Output for Latent Factors

Figure 1. Weights
Weights

The predictor weights represent the association between the predictors and the Y scores, by latent factor. Likewise, the weights for the dependent variable lnsales represents the association between lnsales and the X scores. As expected from the VIP table, the weight for price is largest on the first latent factor and relatively small in the others, while the weight for engine_s is relatively small on the first factor. What becomes clear from this table is to which factors engine_s contributes most; it has the largest weight of any predictor on the third factor and the second largest on the fourth. Its relatively small weight on the fifth factor explains the slight dip in cumulative importance from the four-factor model to the five-factor model.

Figure 2. latentFactors dataset
latentFactors dataset

The weights and loadings, which are similar to the weights and will not be discussed here, are saved to the latentFactors dataset and can be used in further analysis of the data. The factor weights charts, for example, are created using this dataset.

Figure 3. Factor weights 2 vs. 1
Factor weights 2 vs. 1

The factor weights charts provide a visualization of the pairwise comparison of factor weights for the first three factors. In the two-dimensional space defined by the first two factor weights, you can see that price, horsepow, and [type=Automobile] appear are negatively correlated with lnsales, since they point in opposite directions. length, wheelbase, and mpg are somewhat positively correlated with lnsales, and the others are at best weakly correlated with lnsales because they point perpendicularly to lnsales.

Figure 4. Factor weights 3 vs. 1
Factor weights 3 vs. 1

In the space defined by factor weights 3 and 1, fuel_cap, which was positively correlated with engine_s in the 2 vs. 1 plot, is negatively correlated on factor 3.

Figure 5. Factor weights 3 vs. 2
Factor weights 3 vs. 2

In the space defined by factor weights 3 and 2, lnsales appears more strongly correlated with mpg, engine_s, and fuel_cap than in previous plots, illustrating the importance of multiple points of view.

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