Page 204 - Encyclopedia of Nursing Research

FACTOr ANALySIS n 171

than .10. Eighth, regression techniques can be drawn from the items and point to a latent
used to identify influential cases by examin- construct.
ing large Mahalanobis distances when all Mathematically speaking, factor analysis F
variables are included in the analysis. Ninth, generates factors that are linear combinations
there should be adequate factorability within of variables. The first step in factor analysis is
the correlation matrix, which is indicated by factor extraction, which involves the removal
several sizable correlations between pairs of of as much variance as possible through the
variables that exceed .30. Thus, the correla- successive creation of linear combinations
tion of variables within a factor should be that are either orthogonal (unrelated) or
higher with each other than with variables oblique (related) to previously created combi-
outside of the factor. nations. Other methods of factor extraction,
When planning for factor analysis, which analyze common factor variance (i.e.,
the first step is to identify a theoretical variance that is shared with other variables),
model that will guide the statistical model include the principal factors method, the
(Ferketich & Muller, 1990). The next step is to alpha method, and the maximum likelihood
select the psychometric measurement model, method (Nunnally & Bernstein, 1994).
either classic or neoclassic, that will reflect Various criteria have been used to deter-
the nature of measurement error. The classic mine how many factors account for a sub-
model assumes that all measurement errors stantial amount of variance in the data set.
are random and that all variances are unique The most important is that factors should be
to individual variables and not shared with made up of items with primary factor load-
other variables or factors. The neoclassic ings higher than .40 and without any sec-
model recognizes both random and system- ondary factor loadings higher than .30. Items
atic measurement error, which may reflect should be removed if this is violated. Another
common variance that is attributable to useful tool is examining the residual correla-
unmeasured or latent factors. The selection tion matrix. The residual correlation matrix
of the classic or neoclassic model influences is the difference between the correlation
whether the researcher chooses principal matrix of the sample and the implied correla-
components analysis (classic) or common fac- tion matrix created by the statistical program
tor analysis (neoclassic; Ferketich & Muller). to fit the data. Good fitting factor solutions
Conceptually, common factor analysis should have an average difference in residual
is based on a reflector model, in which the correlations of more than .05. It is also impor-
latent construct drives the answers given to tant to review the factor correlation matrix
the items (observed variables) that make the when using oblique rotation, correlations
model. For example, one’s level of depression between two factors by more than .60 are so
(the latent construct) drives the responses highly correlated that they could represent
to items that reflect depression. In a graphic a single factor. Another approach is to use a
model, arrows representing factor loadings screen test to identify the number of factors
would be drawn going from the latent con- above the elbow.
struct point to the items. In comparison, The first step in running any factor anal-
principal component analysis is based on ysis is to determine the number of factors to
a producer model, in which the subjects’ be tested on the basis of logic, theory, or prior
responses to the items drive the latent con- empirical evidence, and set the number of
struct. For example, responses to items on factors to be estimated. The next step is to test
the chronic illness checklist drive the total factor models with solutions of plus or minus
score of the number of chronic illnesses (the two factors above or below the number of
latent construct). In a graphic model, arrows factors originally identified. For example, if
representing the factor loadings would be four factors were originally hypothesized,