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Latent Variable
A latent variable is a variable that cannot be observed. The presence of latent variables, however, can be detected by their effects on variables that are observable. Most constructs in research are latent variables. Consider the psychological construct of anxiety, for example. Any single observable measure of anxiety, whether it is a self- report measure or an observational scale, cannot provide a pure measure of anxiety. Observable variables are affected by measurement error. Measurement error refers to the fact that scores often will not be identical if the same measure is given on two occasions or if equivalent forms of the measure are given on a single occasion. In addition, most observable variables are affected by method variance, with the results obtained using a method such as self-report often differing from the results obtained using a different method such as an observational rating scale. Latent variable methodologies provide a means of extracting a relatively pure measure of a construct from observed variables, one that is uncontaminated by measurement error and method variance. The basic idea is to capture the common or shared variance among multiple observable variables or indicators of a construct. Because measurement error is by definition unique variance, it is not captured in the latent variable. Technically, this is true only when the observed indicators are (a) obtained in different measurement occasions, (b) have different content, and (c) have different raters if subjective scoring is involved. Otherwise, they will share a source of measurement error that can be captured by a latent variable. When the observed indicators represent multiple methods, the latent variables also can be measured relatively free of method variance. This entry discusses two types of methods for obtaining latent variables: exploratory and confirmatory. In addition, this entry explores the use of latent variables in future research.
Exploratory Methods
Latent variables are linear composites of observed variables. They can be obtained by exploratory or confirmatory methods. Two common exploratory methods for obtaining latent variables are factor analysis and principal components analysis. Both approaches are exploratory in that no hypotheses typically are proposed in advance about the number of latent variables or which indicators will be associated with which latent variables. In fact, the full solutions of factor analyses and principal components analyses have as many latent variables as there are observed indicators and allow all indicators to be associated with all latent variables. What makes exploratory methods useful is when most of the shared variance among observed indicators can be accounted for by a relatively small number of latent variables.
The measure of the degree to which an indicator is associated with a latent variable is the indicator’s loading on the latent variable. An inspection of the pattern of loadings and other statistics is used to identify latent variables and the observed variables that are associated with them. Principal components are latent variables that are obtained from an analysis of a typical correlation matrix with 1s on the diagonal. Because the variance on the diagonal of a correlation matrix is a composite of common variance and unique variance including measurement error, principal components differ from factors in that they capture unique as well as shared variance among the indicators. Because all variance is included in the analysis and exact scores are available, principal components analysis primarily is useful for “boiling down” a large number of observed variables into a manageable number of principal components.
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