Factor Analysis(Lecture11: Statistics and Informatics for Disaster Managers)Mohammad Samsul AlamAssistant Professor of Applied StatisticsInstitute of Statistical Research and Training (ISRT)University of DhakaEmail:[email protected]Lecture101
Introduction to Factor Analysis IFactor analysis is one of the most widely used multivariatestatistical procedures in applied research endeavors across amultitude of domains (e.g., psychology, education, sociology,management, public health).The fundamental intent of factor analysis is to determine thenumber and nature oflatent variables or factorsthat account forthe variation and covariation among a set ofobserved measures,commonly referred to asindicators.Specifically, a factor is an unobservable variable that influencesmore than one observed measure and that accounts for thecorrelations among these observed measures.Email:[email protected]Lecture102
Introduction to Factor Analysis IIIn other words, the observed measures are intercorrelated be-cause they share a common cause (i.e., they are influenced bythe same underlying construct); if the latent construct was par-tialed out, the intercorrelations among the observed measureswould be zero.Thus, factor analysis attempts a more parsimonious under-standing of the covariation among a set of indicators becausethe number of factors is less than the number of measuredvariables.Email:[email protected]Lecture103
Application of Factor Analysis IIn applied research, factor analysis is most commonly used inpsychometric evaluations of multiple-item testing instruments.For example, a researcher may have generated20questionnaireitems that he or she believes are indicators of the unidimensionalconstruct of self-esteem.In the early stages of scale development, the researcher mightuse factor analysis to examine the plausibility of this assumption(i.e., the ability of a single factor to account for the intercor-relations among the20indicators) and to determine if all20items are reasonable indicators of the underlying constructof self-esteem (i.e., how strongly is each item related to thefactor?).Email:[email protected]Lecture104
Application of Factor Analysis IIIn addition to psychometric evaluation, other common uses forfactor analysis include construct validation (e.g., obtaining evi-dence of convergent and discriminant validity by demonstratingthat indicators of selected constructs load onto separate factorsin the expected manner).Another use of factor analysis is data reduction (e.g., reducinga larger set of intercorrelated indicators to a smaller set ofcomposite variables, and using these composites—i.e., factorscores—as the units of analysis in subsequent statistical tests).Email:[email protected]Lecture105
Multivariate DataMultivariate Dataarises by measuring a set of random variablesX1, X2, . . . , Xpfrom a number of individuals where the variablesare assumed to be correlated with each other.