ABSTRACT
In. both. of. these. situations. the. number. of. simple. correlations. among. the. variables. is. very. large,. and. it. is. quite.difficult. to. summarize. by. inspection.precisely.what. the. pattern.of.correlations.represents..For.example,.with.30.variables,.there.are.435.simple. correlations..Some.means.is.needed.for.determining.if.there.is.a.small.number.of.underlying.constructs.that.might.account.for.the.main.sources.of.variation.in.such.a.complex. set.of.correlations. Furthermore,. if. there.are.30.variables. (whether.predictors.or. items),.we.are.undoubt-
edly.not.measuring.30.different.constructs;.hence,. it.makes.sense.to.find.some.variable. reduction.scheme.that.will. indicate.how.the.variables.cluster.or.hang. together..Now,. if. sample.size.is.not.large.enough.(how.large.N.needs.to.be.is.discussed.in.Section.11.7),.then. we.need. to. resort. to.a. logical. clustering. (grouping).based.on. theoretical.or. substantive. grounds..On.the.other.hand,.with.adequate.sample.size.an.empirical.approach.is.preferable..Two.basic.empirical.approaches.are.(a).principal.components.analysis.and.(b).factor. analysis..In.both.approaches.linear.combinations.of.the.original.variables.(the.factors).are. derived,.and.often.a.small.number.of.these.account.for.most.of.the.variation.or.the.pattern. of.correlations..In.factor.analysis.a.mathematical.model.is.set.up,.and.the.factors.can.only. be.estimated,.whereas. in.components.analysis.we.are.simply.transforming.the.original. variables.into.the.new.set.of.linear.combinations.(the.principal.components). Both.methods.often.yield.similar.results..We.prefer.to.discuss.principal.components.for.
several.reasons:
