Correspondence factor analysis CFA

In this respect, the weight coefficients are proportional to the column-sums. Distances of Chi-square form the basis of correspondence factor analysis (CFA) which is discussed in Chapter 32. 

Fig. 32.6. (a) Generalized score plot derived by correspondence factor analysis (CFA) from Table 32.4. The figure shows the distance of Triazolam from the origin, and the distance between Triazolam and Lorazepam. (b) Generalized loading plot derived by CFA from Table 32.4. The figure shows the distance of epilepsy from the origin, and the distance between epilepsy and anxiety. 

The log-linear model (LLM) is closely related to correspondence factor analysis (CFA). Both methods pursue the same objective, i.e. the analysis of the association (or correspondence) between the rows and columns of a contingency table. In CFA this can be obtained by means of double-closure of the data in LLM this is achieved by means of double-centring of the logarithmic data. 

Correspondence factor analysis (CFA) is most appropriate when the data represent counts of contingencies, or when there are numerous true zeroes in the table (i.e. when zero means complete absence of a contingency, rather than a small quantity which has been rounded to zero [47]). A detailed description of the method is found in Section 32.3.6. 

Ounnar and co-workers [31,32] widely apply in their QSRR studies the approach called correspondence factor analysis (CFA). CFA is mathematically related to PCA, differing in the preprocessing and scaling of the data. Those authors often succeeded in assigning definite physical sense to abstract factors, e.g., they identified the Hammett constants of substituents in meta and para positions of 72 substituted /V-benzylideneanilines (NBA) in determining the first factorial axis resulting from the CFA analysis of retention data of NBA in diverse normal-phase HPLC systems. 

Multivariate methods of data analysis were first applied in chromatography for retention prediction purposes [7. More recently, principal component analysis (PCA), correspondence factor analysis (CFA) and spectral mapping analysis (SMA) have been employed to objectively cla.ssify. stationary phase materials according to the retention... 

Large data tables may hide information which is not easily detected by simple inspection of the various columns. Principal component analysis and some closely related techniques such as factor analysis (FA), correspondence factor analysis (CFA) and non-linear mapping (NLM), reduce a data matrix to new supervariables retaining a maximum of information or variance from the original data matrix. These new variables are called latent variables or principal components, and are orthogonal vectors composed of linear combinations of the original variables. This concept is shown schematically in Fig. 22.15. 

Among the different linear multivariate methods that can be used to analyze Table 12.2, correspondence factor analysis (CFA) was selected because its yf metrics permits work on data prohles and the natural biplot representation of the variables and objects which greatly facilitates the interpretation of the graphical displays [26], In addition, CFA has been used successfully on similar data matrices for rationalizing (eco)toxicologi-cal information [27-30],... 

Boolean descriptors. These descriptors are easy to derive but their introduction in dummy regression analysis can yield statistical pitfalls when they are used for predictive purposes. To overcome this problem, it is possible to use the stochastic regression analysis. This method consists of performing, as a first step, a correspondence factor analysis (CFA) and then carrying out a regression analysis from the CFA factors. The stochastic regression analysis can also be used when the molecular descriptors are frequencies of occurrence. ... 

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