Using Horn’s Parallel Analysis Method in Exploratory Factor Analysis for Determining the Number of Factors

Abstract

Psychological characteristics are of an abstract or latent nature rather than a tangible, observable one and they are called constructs or factors (Kline, 2005; Nunnaly & Bernstein, 1994). Constructs are hypothetical concepts and the existence of certain constructs is never absolutely confirmed. Therefore, observations of individual behavior mostly provide conclusions about psychological constructs. These psychological constructs such as intelligence, creativity, extrovertedness and introvertedness are not directly observable (Croker & Algina, 1986). Cronbach and Meehl (1955) define psychological construct as postulated attribute of people (as cited in Baykul, 2000). All constructs have two main features: 1. Every construct is an abstract summary of natural order; 2. Constructs are associated with observable entities or phenomena (Murphy & Davidshofer, 2001).According to Lord and Novick (1968), constructs that are not directly observable can be defined in two different ways: operational definition, which is essential to measure those constructs; and the theoretical relationship between a given construct and others and the relationship between a given construct and criteria in the outer world in addition to the operational definitions (Crocker & Algina, 1986). Operational definitions of constructs could relate to construct validity studies that discuss the development of a suitable measuring instrument for a construct and to what extent the instrument measures the related construct.Construct validity is based on the analysis of the relationships between responses to test items. To some extent, the process of establishing construct validity for a given test is the development of a scientific theory (Tekin, 2000). Construct validity is associated with the validity of implications about non-observable variables through observable variables. Construct validity shows how accurately a measuring instrument measures abstract psychological characteristics. Measuring the related abstract construct is based on transformation of the construct into a tangible, observable entity through observable behaviors. The transformation process into an observable construct includes the following stages: determining behaviors related to the measured construct, revealing constructs that are relevant or irrelevant to the measured construct and showing behavioral patterns that express others related to the measured construct (Murphy & Davidshofer, 2001).Construct validity studies could be conducted with different methods according to the quality and the form of a given construct and those of the measuring instrument used to measure the related construct, whether there are theories and scientific research on the construct and some other features (Erkus, 2003). Factor analysis is the most widely used method among these. In the literature, there is scientific consensus on the fact that factor analysis is a common statistical method used to determine construct validity (Anastasi, 1986; Atilgan, Kan, & Dogan, 2006; Crocer & Algina, 1986; Cronbach, 1990; Dancey & Reidy, 2004; Erkus, 2003; Pedhazur & Pedhazur, Schmelkin, 1991; Urbina, 2004). Because of the advantage entailed by internal dependencies in constructs by nature, factor analysis reduces the complexity of data and thus provides nearly the same amount of information as extensive data obtained by a number of original observations, with only a few factors (Cokluk, Sekercioglu, & Buyukozturk, 2010).According to Floyd and Widaman (1995), factor analysis has two approaches in the evaluation of psychological constructs: exploration and variable reduction. The exploratory aim of factor analysis defines lower dimensions of measuring instruments that represent a given construct, on the basis of the theoretical structure from which the instruments have been developed. Accordingly, the analysis focuses on the exploration of latent variables that form the basis of a scale. …