F. Generalized Exploratory Factor Analysis (GEFA) aproach to reduce the dimension of data in calibration modeling

Abstract

Generalized Exploratory Factor Analysis (GEFA) is the development of factor analysis method, a statistical technique to reduce the dimension of data by declaring origin variables as a linear combination of a number of factors, so that could explain the diversity of origin variables data. GEFA can resolve the deficiencies in factor analysis, which is troubled by the number of observations less than the number of variables. This condition give the semi-positive definite properties to correlation matrix or covariance matrix. The objective of this research was to obtain the calibration model of medicinal plants, temulawak. The data used were the result of a high performance liquid cromatography (HPLC) analysis and fourier transform infrared (FTIR) in the temulawak powder. An active compound was obtained from HPLC analysis, furthermore it is called dependent variable (y). The result of FTIR produce 1866 transmittance percentage as a chemical functional group of identifier temulawak powder, called independent variable. The results of FTIR was the calibration data with the number of observations less than the number of variables, so as to be able to provide a good model, the data reduction is needed. The calibration model was obtained from the score factors, a result of the reduction of GEFA method, then it was regressed to dependent variable (y). To know the advantages of GEFA, conducted a comparisons with other reduction method, principal component analysis (PCA). Evaluation of a model to determine the goodness of the calibration model, measured from the closeness of dependent variable (y) (correlation coefficient) with the estimation of dependent variable (𝑦���𝑦���􀷜���), root mean square error (RMSE) value, prediction residuals (PRESS) and root mean square error of cross validation (RMSECV). GEFA method through the GEFALS algorithm (generalized least square exploratory factor analysis), give the results of the reduction with good graphics and similar patterns with preliminary data. loading factors estimator (L) and specific variance (Ψ) have been good on a lot of factors (k) = 4, since the value model goodness factors i.e. RMS overalls was 0.0027 or smaller than 0.05. However, to get a good score factor (F) for the calibration model, contained in a number of factors k = 14, with a value of RAdj was 0.9398. The results of PCA reduction method showed an inconsistent graph patterns, so it is not able to give a similar pattern with preliminary data. PCA method also give the best calibration model on k = 14, with a value of RAdj was 0.9392. Evaluation of the calibration model from the GEFA reduction and the PCA reduction give the simillar reduction. It can be seen from the correlation coeffiecient and RSME that give the same value, i.e. 0.992 and 0.0136, but the PRESS values and RMSECV of GEFA calibration model obtain a smaller value, and the graph pattern of the reduction of GEFA was similar with the preliminary data, it implies that the results of GEFA reduction is better than PCA reduction.