Factor analysis description

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. 

Chapter 10 provides an exhaustive description of how these techniques can be applied to a large number of industrial alloys and other materials. This includes a discussion of solution and substance databases and step-by-step examples of multi-component calculations. Validation of calculated equilibria in multi-component alloys is given by a detailed comparison with experimental results for a variety of steels, titanium- and nickel-base alloys. Further selected examples include the formation of deleterious phases, complex precipitation sequences, sensitivity factor analysis, intermetallic alloys, alloy design, slag, slag-metal and other complex chemical equilibria and nuclear applications. 

Basic Concepts. The goal of factor and components analysis is to simplify the quantitative description of a system by determining the minimum number of new variables necessary to reproduce various attributes of the data. Principal components analysis attempts to maximally reproduce the variance in the system while factor analysis tries to maximally reproduce the matrix of correlations. These procedures reduce the original data matrix from one having m variables necessary to describe the n samples to a matrix with p components or factors (p[Pg.26]

Factor analysis was used to identify principal types of emission sources and to select elemental source tracers. As factor analysis has been described in detail in the literature (10-13), only a general description of the technique will be given... 

Like other assessment instillments, the QLS was developed using patient interviews and factor analysis to derive those dimensions and questions that are most relevant to the patient s experience (Heinrichs et al., 1984). The QLS scale contains 21 items and is intended to be administered as a semi-structured interview. Each item consists of three parts a brief statement is provided to help the interviewee understand and focus on the parameter to be assessed a number of suggested questions are provided that may help the interviewer begin his exploration with the subject and a seven-point scale is provided for each item, with a brief description at four points to help the interviewee make... 

Comparison and ranking of sites according to chemical composition or toxicity is done by multivariate nonparametric or parametric statistical methods however, only descriptive methods, such as multidimensional scaling (MDS), principal component analysis (PCA), and factor analysis (FA), show similarities and distances between different sites. Toxicity can be evaluated by testing the environmental sample (as an undefined complex mixture) against a reference sample and analyzing by inference statistics, for example, t-test or analysis of variance (ANOVA). 

A number of methods have been proposed for particle shape analysis, including shape coefficients, shape factors, verbal descriptions, curvature signatures, moment invariants, solid shape descriptors, and mathematical functions (Fourier series... 

A comparison of factors determined with 100 random points and with 30 and 26 experimental points can be made from the data shown in Table III. A short description of the data may be useful to those unfamiliar with factor analysis. The values shown are "factor loadings" for the species on the factors, e.g. the top line under the 100 random point heading states that... 

A full description and derivation of the many factor analysis methods reported in the analytical literature is beyond the scope of this book. We will limit ourselves here to the general and underlying features associated with the technique. A more detailed account is provided by, for example, Hopke and others. 

Mathematical description of Factor Analysis and Principal Components Analysis... 

Examples of PCA application can be found in Henry and Hidy (1979, 1981), Wolff and Korsog (1985), Cheng et al. (1988), Henry and Kim (1989), Koutrakis and Spengler (1987), and Zeng and Hopke (1989). PCA provides a rather qualitative description of source fingerprints, which can be used later as input to a CMB model or a similar source apportionment tool. For more information about other factor analysis approaches the reader is referred to Hopke (1985). 

Mathematically this is the pattern recognition process of cluster and factor analysis in statistics. A top-down, helicopter view overcomes the problem of being unable to see the forest because the trees are in the way. Occam s helicopter, rises above the trees to see the forest and even the pattern of light in its glades. Occam s helicopter will be very useful to us throughout this book because our aim is physical, chemical, mathematical and social analysis rather than description. 

The YSQ-Sl (Young 1998) is a 75-item self-report measure of the 18 EMS outlined in Chapter 12, which are hypothesized to underlie psychopathology. Each EMS is measured by five items (the highest loading items from a factor analysis of the 205-item version of the form by Schmidt et al. 1995). (See Chapter 12 for a more detailed description of each schema described by Young.)... 

Dimension reduction is, as the name implies, a technique for reducing the dimensionality of a dataset, which is most often applied to the columns (variables) but may also be applied to the rows (cases or compounds) and results in a reduction from p variables to q variables or dimensions where q is often 2 or 3 (for ease of display of the resulting data matrix). A common method of dimension reduction is principal component analysis (PCA). A less-frequently used but related method is factor analysis (FA). Insufficient space exists here for a complete description of these techniques, so the reader is directed to references 26 and 27 for PCA and 28 and 29 for FA. Briefly, each computes new variables... 

The improvement in computer technology associated with spectroscopy has led to the expansion of quantitative infrared spectroscopy. The application of statistical methods to the analysis of experimental data is known as chemometrics [5-9]. A detailed description of this subject is beyond the scope of this present text, although several multivariate data analytical methods which are used for the analysis of FTIR spectroscopic data will be outlined here, without detailing the mathematics associated with these methods. The most conunonly used analytical methods in infrared spectroscopy are classical least-squares (CLS), inverse least-squares (ILS), partial least-squares (PLS), and principal component regression (PCR). CLS (also known as K-matrix methods) and PLS (also known as P-matrix methods) are least-squares methods involving matrix operations. These methods can be limited when very complex mixtures are investigated and factor analysis methods, such as PLS and PCR, can be more useful. The factor analysis methods use functions to model the variance in a data set. 

When subjects provide responses of the perceived intensity for a stimulus on a repeated trial basis, it allows for analyses of individual subjects, attributes, and products. A descriptive test of 10 products, 12 subjects, 3 replicates, and 40 attributes will yield 14 400 values, enabling a wide range of computations including summary statistics, the AOV, correlation of attributes. Factor Analysis, and Principle Components Analysis. In addition, the scaled values can be converted to ranks and additional analyses calculated. All these types of analyses are intended to provide different views of the results to verify that the product differences are consistent, that where interactions occur they have been taken into consideration. When the scaled differences and the ranks are in agreement, this adds to one s confidence with the results. 

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. 

There are methods in education, but I believe it is fair to say that all of them are oriented towards prescribing instruction rather than constructing learning theories. The social sciences contain many descriptive methods, such as factor analysis and its associated theory of... 

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