| Standard plots when analyzing latent structure models |

In the numerical computations there are computed four sets of vectors, wa, pa, va, and ta, at each step. These vectors are schematically illustrated in Fig. 2. In the following it is described how one can look at these vectors and how they can be used in different types of plots.
· wa, the weight vector. It reflects the emphasis of the analysis. Different weights give different regression analysis. In the plots of the vectors we look for if one or more variables get small weights for all weight vectors. If one or more of them get generally small weights, it is investigated if they should be removed from analysis.
· ta, the score vector. It is computed as ta =Xa-1wa or ta = Xva. The score vectors define the latent structure. They show what has been used of X and how Y can be described. Pair wise plots of the score vectors show the variation in the part of data that is being used.
· pa, the loading vector. It is computed as pa =Sa-1wa. If S=XTX, then pa =XTta. If the X matrix has been auto-scaled, and ta scaled to unit length, the loading vector pa can be viewed as the correlation coefficients between the original variables and the a-th score variable. In the general case where S is any positive definite matrix, a similar interpretation is used. Pair wise plots of the loading vectors show the correlation structure in data.
· va, the loading weight vector. It is given by pa =Sva. They show how pa is derived from the correlations of the original X-variables. Since S0=S, if follows that v1=w1. The loading weight vectors are studied in order to know how the original variables generate the latent structure.
Fig. 2 shows that the vectors wa, pa, and va are of the same size. It also emphasizes that the score vectors ta are used for describing both X and Y, although the primary purpose with the analysis is to describe Y. In the applied work much time is spent on analyzing how the score vectors describe X.