Confirmatory factor analysis
Encyclopedia
In statistics
, confirmatory factor analysis (CFA) is a special form of factor analysis
. It is used to test whether measures of a construct are consistent with a researcher's understanding of the nature of that construct (or factor). In contrast to exploratory factor analysis
, where all loadings are free to vary, CFA allows for the explicit constraint of certain loadings to be zero. CFA has built upon and replaced older methods of analyzing construct vailidity such as the MTMM Matrix
as described in Campbell & Fiske (1959).
A typical example of a CFA on a 50 item personality test
that claimed to be measuring the "Big Five" Personality Traits
, might assess the fit of the proposed model. A model could be developed that assumed structure, where each item loads on only one factor. The correlations between latent factors could be free to vary or they could be constrained to be zero. Model fit measures could then be obtained to assess how well the proposed model captured the covariance between all the items on the test. If the fit is poor, it may be due to some items measuring multiple factors. It might also be that some items within a factor are more related to each other than others.
For some applications the requirement of zero loadings for indicators not supposed to load on a certain factor has been regarded as too strict. A newly developed analysis method, "exploratory structural equation modeling", specifies hypothesis about the relation between observed indicators and their supposed primary latent factors while allowing for estimation of loadings with other latent factors as well (Asparouhov & Muthén, 2009).
CFA is commonly used in social research
(Kline, 2010). CFA is frequently used when developing a test, such as a personality test
, intelligence test, or survey
.
Structural equation modeling
software is typically used for performing the analysis. LISREL
, EQS, AMOS and Mplus are popular software programs. CFA is also frequently used as a first step to assess the proposed measurement model in a structural equation model. Many of the rules of interpretation regarding assessment of model fit and model modification in structural equation modeling
apply equally to CFA. CFA is distinguished from structural equation modeling by the fact that in CFA, there are no directed arrows between latent factors. In other words, while in CFA factors are not presumed to directly cause one another, SEM often does specify particular factors and variables to cause one another. In the context of SEM ,the CFA often is called 'the measurement model', while the relations between the latent variable
s (with directed arrows) are called 'the structural model'
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, confirmatory factor analysis (CFA) is a special form of factor analysis
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, uncorrelated variables called factors. In other words, it is possible, for example, that variations in three or four observed variables...
. It is used to test whether measures of a construct are consistent with a researcher's understanding of the nature of that construct (or factor). In contrast to exploratory factor analysis
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, uncorrelated variables called factors. In other words, it is possible, for example, that variations in three or four observed variables...
, where all loadings are free to vary, CFA allows for the explicit constraint of certain loadings to be zero. CFA has built upon and replaced older methods of analyzing construct vailidity such as the MTMM Matrix
Multitrait-multimethod matrix
The multitrait-multimethod matrix is an approach to examining Construct Validity developed by Campbell and Fiske. There are six major considerations when examining a construct's validity through the MTMM matrix, which are as follows:...
as described in Campbell & Fiske (1959).
A typical example of a CFA on a 50 item personality test
Personality test
-Overview:There are many different types of personality tests. The most common type, the self-report inventory, involves the administration of many questions, or "items", to test-takers who respond by rating the degree to which each item reflects their behavior...
that claimed to be measuring the "Big Five" Personality Traits
Big Five personality traits
In contemporary psychology, the "Big Five" factors of personality are five broad domains or dimensions of personality which are used to describe human personality....
, might assess the fit of the proposed model. A model could be developed that assumed structure, where each item loads on only one factor. The correlations between latent factors could be free to vary or they could be constrained to be zero. Model fit measures could then be obtained to assess how well the proposed model captured the covariance between all the items on the test. If the fit is poor, it may be due to some items measuring multiple factors. It might also be that some items within a factor are more related to each other than others.
For some applications the requirement of zero loadings for indicators not supposed to load on a certain factor has been regarded as too strict. A newly developed analysis method, "exploratory structural equation modeling", specifies hypothesis about the relation between observed indicators and their supposed primary latent factors while allowing for estimation of loadings with other latent factors as well (Asparouhov & Muthén, 2009).
CFA is commonly used in social research
Social research
Social research refers to research conducted by social scientists. Social research methods may be divided into two broad categories:* Quantitative designs approach social phenomena through quantifiable evidence, and often rely on statistical analysis of many cases to create valid and reliable...
(Kline, 2010). CFA is frequently used when developing a test, such as a personality test
Personality test
-Overview:There are many different types of personality tests. The most common type, the self-report inventory, involves the administration of many questions, or "items", to test-takers who respond by rating the degree to which each item reflects their behavior...
, intelligence test, or survey
Statistical survey
Survey methodology is the field that studies surveys, that is, the sample of individuals from a population with a view towards making statistical inferences about the population using the sample. Polls about public opinion, such as political beliefs, are reported in the news media in democracies....
.
Structural equation modeling
Structural equation modeling
Structural equation modeling is a statistical technique for testing and estimating causal relations using a combination of statistical data and qualitative causal assumptions...
software is typically used for performing the analysis. LISREL
LISREL
LISREL, an acronym for linear structural relations, is a statistical software package used in structural equation modeling. LISREL was developed in 1970s by Karl Jöreskog, then a scientist at Educational Testing Service in Princeton, NJ, and Dag Sörbom, later both professors of Uppsala University,...
, EQS, AMOS and Mplus are popular software programs. CFA is also frequently used as a first step to assess the proposed measurement model in a structural equation model. Many of the rules of interpretation regarding assessment of model fit and model modification in structural equation modeling
Structural equation modeling
Structural equation modeling is a statistical technique for testing and estimating causal relations using a combination of statistical data and qualitative causal assumptions...
apply equally to CFA. CFA is distinguished from structural equation modeling by the fact that in CFA, there are no directed arrows between latent factors. In other words, while in CFA factors are not presumed to directly cause one another, SEM often does specify particular factors and variables to cause one another. In the context of SEM ,the CFA often is called 'the measurement model', while the relations between the latent variable
Latent variable
In statistics, latent variables , are variables that are not directly observed but are rather inferred from other variables that are observed . Mathematical models that aim to explain observed variables in terms of latent variables are called latent variable models...
s (with directed arrows) are called 'the structural model'