29 Facts About Factor analysis

Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors.

The observed variables are modelled as linear combinations of the potential factors plus "error" terms, hence factor analysis can be thought of as a special case of errors-in-variables models.

Factor analysis is commonly used in psychometrics, personality psychology, biology, marketing, product management, operations research, finance, and machine learning.

Observable data that go into factor analysis would be 10 scores of each of the 1000 students, a total of 10,000 numbers.

The purpose of factor analysis is to characterize the correlations between the variables of which the are a particular instance, or set of observations.

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The goal of factor analysis is to find a hyperplane which is a "best fit" to the data in some sense, so it doesn't matter how the factor vectors which define this hyperplane are chosen, as long as they are independent and lie in the hyperplane.

Goal of factor analysis is to choose the fitting hyperplane such that the reduced correlation matrix reproduces the correlation matrix as nearly as possible, except for the diagonal elements of the correlation matrix which are known to have unit value.

Exploratory factor analysis is used to identify complex interrelationships among items and group items that are part of unified concepts.

Confirmatory factor analysis is a more complex approach that tests the hypothesis that the items are associated with specific factors.

Principal component analysis is a widely used method for factor extraction, which is the first phase of EFA.

Factor analysis weights are computed to extract the maximum possible variance, with successive factoring continuing until there is no further meaningful variance left.

Canonical factor analysis seeks factors that have the highest canonical correlation with the observed variables.

Factor analysis regression model is a combinatorial model of factor model and regression model; or alternatively, it can be viewed as the hybrid factor model, whose factors are partially known.

Factor analysis discovered that school children's scores on a wide variety of seemingly unrelated subjects were positively correlated, which led him to postulate that a single general mental ability, or g, underlies and shapes human cognitive performance.

Thurstone introduced several important factor analysis concepts, including communality, uniqueness, and rotation.

Factor analysis advocated for "simple structure", and developed methods of rotation that could be used as a way to achieve such structure.

In Q methodology, Stephenson, a student of Spearman, distinguish between R factor analysis, oriented toward the study of inter-individual differences, and Q factor analysis oriented toward subjective intra-individual differences.

Factor analysis is used to identify "factors" that explain a variety of results on different tests.

Researchers explained this by using factor analysis to isolate one factor, often called verbal intelligence, which represents the degree to which someone is able to solve problems involving verbal skills.

Factor analysis is a frequently used technique in cross-cultural research.

Factor analysis is related to principal component analysis, but the two are not identical.

PCA can be considered as a more basic version of exploratory factor analysis that was developed in the early days prior to the advent of high-speed computers.

Factor analysis is clearly designed with the objective to identify certain unobservable factors from the observed variables, whereas PCA does not directly address this objective; at best, PCA provides an approximation to the required factors.

Factor analysis has been used successfully where adequate understanding of the system permits good initial model formulations.

Factor analysis takes into account the random error that is inherent in measurement, whereas PCA fails to do so.

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Factor analysis assumes that all the rating data on different attributes can be reduced down to a few important dimensions.

Factor analysis has been widely used in physical sciences such as geochemistry, hydrochemistry, astrophysics and cosmology, as well as biological sciences, such as ecology, molecular biology, neuroscience and biochemistry.

Factor analysis can be used for summarizing high-density oligonucleotide DNA microarrays data at probe level for Affymetrix GeneChips.

Factor analysis has been implemented in several statistical analysis programs since the 1980s:.