(Redirected from Factor Analysis)

A Latent Factor Analysis Task is an dimensionality compression task that requires the identification of latent variables.

## References

### 2013

• http://en.wikipedia.org/wiki/Factor_analysis#Type_of_factor_analysis
• Exploratory factor analysis (EFA) is used to identify complex interrelationships among items and group items that are part of unified concepts.[1] The researcher makes no "a priori" assumptions about relationships among factors.
• Confirmatory factor analysis (CFA) is a more complex approach that tests the hypothesis that the items are associated with specific factors. CFA uses structural equation modeling to test a measurement model whereby loading on the factors allows for evaluation of relationships between observed variables and unobserved variables. Structural equation modeling approaches can accommodate measurement error, and are less restrictive than least-squares estimation. Hypothesized models are tested against actual data, and the analysis would demonstrate loadings of observed variables on the latent variables (factors), as well as the correlation between the latent variables.
1. Polit DF Beck CT (2012). Nursing Research: Generating and Assessing Evidence for Nursing Practice, 9th ed.. Philadelphia, USA: Wolters Klower Health, Lippincott Williams & Wilkins.
• http://en.wikipedia.org/wiki/Factor_analysis#Applications_in_psychology
• Factor analysis is used to identify "factors" that explain a variety of results on different tests. For example, intelligence research found that people who get a high score on a test of verbal ability are also good on other tests that require verbal abilities. Researchers explained this by using factor analysis to isolate one factor, often called crystallized intelligence or verbal intelligence, which represents the degree to which someone is able to solve problems involving verbal skills.

Factor analysis in psychology is most often associated with intelligence research. However, it also has been used to find factors in a broad range of domains such as personality, attitudes, beliefs, etc. It is linked to psychometrics, as it can assess the validity of an instrument by finding if the instrument indeed measures the postulated factors.

1. Fabrigar et al. (1999). "Evaluating the use of exploratory factor analysis in psychological research.". Psychological Methods.
2. Suhr, Diane (2009). "Principal component analysis vs. exploratory factor analysis". SUGI 30 Proceedings. Retrieved 5 April 2012.
3. SAS Statistics. "Principal Components Analysis". SAS Support Textbook.

### 2011

• (Fabrigar & Wegener, 2011) ⇒ Leandre R. Fabrigar, and Duane T. Wegener. (2011). “Exploratory Factor Analysis." Oxford University Press. ISBN:0199813515
• QUOTE: … Factor analysis refers to a set of statistical procedures designed to determine the number of distinct constructs needed to account for the pattern of correlations among a set of measures. Alternatively stated, factor analysis is used to determined the number of distinct constructs assessed by a set of measures. These unobservable constructs presumed to account for the structure of correlations among measures are referred to as factors or more precisely as common factors. The specific statistical procedures comprising factor analysis provide information about the number of common factors underlying a set of measures. They also provide information to aid in interpreting the nature of these factors. The nature of common factors is clarified by providing estimates of the strength and direction of influence each of the common factors exerts on each of the measures being examined. Such estimates of influence are usually referred to as factor loadings. For cases in which the researcher has no clear expectations or relatively incomplete expectations about the underlying structure of correlations, procedures exist to conduct exploratory factor analysis (EFA) or unrestricted factor analysis. In this book we focus on these procedures and refer to them as ERA. When a researcher has a clear prediction about the number of common factors and the specific measures each common factor will influence, procedures are available to conduct confirmatory factor analysis (CFA) or restricted factor analysis (see Bollen, 1989).