Factorial factor analysis

Factor Analysis, 78 Factor spaces, 78 Factorial design, 29 Factors, 94... 

Factorial methods - factor analysis (FA) - principal components analysis ( PCA) - partial least squares modeling (PLS) - canonical correlation analysis Finding factors (causal complexes)... 

Much has been published concerning toxicity of metals to aquatic life although only during the past decade have there been interpretations of the toxicity data in terms of ]jie rela ive toxicity of particular speciation forms, e.g., Cu, CuOH, CuCO The specific objective of this paper is to illustrate the use of Factor Analysis in discriminating between toxic and nontoxic species. The procedure to be followed is determination of equilibrium aqueous speciation, calculation of appropriate factory correlation of toxicity with these factors, and interpretation of the correlation analysis in terms of particular species activities. 

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. 

Exploratory factor analysis (EFA) would discern the thematic patterns of mFSMAS on the basis of the sample data. However, as the sample size is limited to N =29, which means the sample to variable ratio is less than 3 1 (please see Brown and Onsman 2013) for arguments on sampling adequacy for factor analysis), the data is not sufficient to run EFA. Therefore, the factorial structure of an earlier study of mFSMAS on Turkish students in the context of chemistry education is used as a reference for the analysis (Kahveci, 2009). Table 1 shows the item-based factorial categories as drawn from Kahveci (2009) and Cronbach alpha values and the standardized descriptive statistics for the current sample N = 29) in the context of PChem II. There were six factors applied to this research as follows (1) confidence in learning physical chemistry, (2) satisfaction, (3) relevance, (4) personal ability, (5) gender difference, and (6) interest. 

Such arrays raise the question of more generalizations of the table-oriented techniques presented in Chapters 3.9 to 3.11. The most prominent representatives of factorial methods are the so-called Tucker3 [21] and PARAFAC (parallel factor analysis) [22] models. For three-way arrays, the Tucker3 model is expressed as... 

Duarte and colleagues used a factorial design to optimize a flow injection analysis method for determining penicillin potentiometricallyd Three factors were studied—reactor length, carrier flow rate, and sample volume, with the high and low values summarized in the following table. 

ANOVA in these chapters also, back when it was still called Statistics in Spectroscopy [16-19] although, to be sure, our discussions were at a fairly elementary level. The experiment that Philip Brown did is eminently suitable for that type of computation. The experiment was formally a three-factor multilevel full-factorial design. Any nonlinearity in the data will show up in the analysis as what Statisticians call an interaction term, which can even be tested for statistical significance. He then used the wavelengths of maximum linearity to perform calibrations for the various sugars. We will discuss the results below, since they are at the heart of what makes this paper important. 

We used a factorial analysis of variance with between and within subjects factors. In all statistical tests, a p value of <— 0.05 was considered significant. 

Table 14.4 shows a typical regression analysis output for the 2 factorial design in Table 14.3. Most of the output is self-explanatory. For the moment, however, note the regression analysis estimates for the parameters of the model given by Equation 14.5 and compare them to the estimates obtained in Equations 14.8-14.15 above. The mean is the same in both cases, but the other non-zero parameters (the factor effects and interactions) in the regression analysis are just half the values of the classical factor effects and interaction effects How can the same data set provide two different sets of values for these effects ...

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