Models for multivariate dependent and independent data

An axis of contrast can be defined through any two squares representing tests. 

There are many useful features of a data set that can be revealed in a spectral map such as this and we can see that it is consistent with the patterns shown in the activity spectra (Fig. 8.11) since these two pairs of compoimds are grouped together on the plot. The use of the thickness of symbol contoms to denote the third factor is perhaps not very successful but modem computer graphics would allow easy display of such a plot in three dimensions. In this particular example, the third factor is probably not very important since it only describes eight per cent of the variance of contrasts. SMA is clearly a useful method for the analysis of any chemical problem in which a set of compounds is subjected to a battery of tests which produce some quantitative measure of response. It offers the advantage of a simultaneous display of the relationships between both tests and compounds. 

Chapters 6 and 7 described the construction of regression models (MLR, PCR, PLS, and continuum regression) in which a single dependent variable was related to linear combinations of independent variables. Can these procedures be modified to include multiple dependent variables One fairly obvious way to take account of at least some of the information in a multivariate dependent set is to carry out PCA or FA on the data and use the resulting scores to constmct regression models. 

The values in brackets are the standard errors of the regression coeffidents and it should be noted that R is quoted not as is more usual for multiple regression equations. The second PC was less well described by a shape parameter based on molecular connectivity ( K) and an indicator variable. 

Equation (8.2) only describes 60 per cent of the variance in PC2 and the high standard error for the shape descriptor term casts some doubt on the predictive ability of the equation. However, it is hoped that these two equations demonstrate the way in which regression models for multivariate dependent data can be generated by means of PCA. 

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