Factor Analysis

Factor analysis was employed to answer question 2, which seeks to identify the contemporary perceived factors that have considerable influence on the increase in e- banking fraud in Nigeria; Research question 3 and 4, which seeks to recognize the current mechanisms of prevention and detection of e-banking fraud in Nigeria; and to answer related research questions (see Section 1.3). The purpose of factor analysis is the method simplification of many interrelated measures or components into a small number of representative factors or constructs (Ho, 2006). A researcher may choose to perform

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factor analysis as either as R- mode or Q-mode. The R-mode deals with the columns, resulting in a minimization in the number of variables of observations, while Q-mode factor analysis deals with the rows, leading to a reduction in the number of observed variations. It is argued by scholars that R-mode factor analysis is more generally accepted, since many researchers are concerned with minimizing the number or total of variables in any given research situation (Miesch, 1975; Udofia, 2011).

Factor analysis assists a researcher minimizing a large volume of variables. In factor analysis, it is presumed that entire variables are correlated or interrelated to some level or degree. It is thus assumed that variables with comparable or parallel dimensions should be highly correlated while those with different dimensions would have low correlation. Therefore, in the correlation matrix, these low- and high-correlation coefficients become obvious as variables with related dimensions that are interrelated or correlated (Ho, 2006, p 203).

Three main steps are necessary in factor analysis (Raykov & Penev, 2001; Ho, 2006; Udofia, 2011). These are the computation of the correlation matrix, extraction of the initial factor loadings, and rotation of extracting factors. In the computation of the correlation matrix, intercorrelation coefficients of variables were computed, which was followed by the extraction of initial factors with the use of SPSS Version 23 software. There are two main techniques for extracting initial factors: common factor analysis and principal components analysis. The SPSS program further provides an additional six techniques under common factor analysis (Pallant,2001). The principal component analysis (PCA) method was suitable and appropriate for this study, since it is designed for data reduction to attain a small number of constructs or factors to represent the original data set (Holland, 2008). Therefore, in this study, to select the appropriate and suitable loaded factors with the use of PCA the following techniques

4.11.2.1 Correlation Matrix

Loaded factor to be satisfactorily interpreted, it is important to evaluate the appropriateness of the data for factor analysis. One method of performing this is to

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visually examine the magnitude of factor loadings on the correlation matrix, such as correlation coefficients between the factors and the variables they represent. Factors with correlation coefficients greater than 0.33 (i.e. Approximately 10% of the total variance in the variable is described by the factors) were accepted and considered noteworthy and significant; those with lesser values may not yield interpretable and acceptable factors (Pallant, 2007).

4.11.2.2 Bartlett’s Test of Sphericity

Another technique for evaluating the appropriateness and suitability of the data set for factor analysis is by computation of Bartlett’s test of sphericity (Willians, Onsma & Brown, 2010) and the Kaiser-Mayer-Olkin (KMO) measure of sample statistics (Pallant, 2005; Batlett,1950). Pallant (2010) opines that the KMO index (extending between 0 and 1) ought to be at least 0.6 for satisfactory and suitable factor analysis, while the Bartlett’s test ought to be significant at 0.05 (p < 0.05) which were also considered in this study.

4.11.2.3 Eigenvalue

Eigenvalue reflects the number of extracted factors, which is equal to the number of items that are accounted for in factor analysis. The number of the initial loading factors to be retained and rotated or extracted can be ascertained by three conventional approaches: eigenvalues, scree plot test criteria and parallel analysis. The eigenvalue is the ratio between the common variance and unique variance explained by exact factors extracted (Pallant, 2010). With the eigenvalue principle, only factors with an eigenvalue of 1 and above are considered significant while those less than 1 are disregarded. Therefore, eigenvalue was employed to select the loaded latent factors used in this study.

4.11.2.4 Scree Plot

Scree plot is a line graph of the eigenvalues of all the factors. This line graph is suitable for determining the number of factors to retain. The scree plot test is used to recognize the maximum number of factors that can be extracted before the total of unique variance starts to dominate the common variance structure (Hair et al., 2007). If the numbers of

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extracting factors on the x-axis are plotted in order against eigenvalues on the y-axis, then a scree plot test ensues. The scree plot is shown in a graphical form as a steep slope between the initial large factors and the gradual tailing off the rest of the factors. The minimum number of factors to be retained is specified at the point of inflection of the curve. In summary, the factors above the inflection are retained and considered useful while those below are not. Therefore, scree plot was used to support eigenvalues in the selection of the loaded factors in this study.

4.11.2.5 Parallel Analysis

Parallel analysis was equally adopted to determine the number of factors to retain out of the factors with an eigenvalue greater than 1(Ledesma & Valero-Mora, 2007). Systematically, the first eigenvalue obtained from principal component analysis (PCA) in SPSS was compared with the equivalent first result from the random values obtained from parallel analysis. The factor was retained if the eigenvalue from principal component analysis (PCA) in SPSS was greater than the criterion result from parallel analysis; if it was otherwise, the factor was rejected (Hayton, Allen & Scarpello, 2004; Willianms, Onsman & Brown, 2010). In this study, these criteria were adopted in determining the numbers of factors to be extracted.

4.11.2.6 Rotation Component Matrix

The initial factors are always difficult to interpret; thus, there is a need for rotation of the extracted factors (Pallant, 2005). The rotation component matrix does not essentially change anything but eases the interpretation of the analysis (Ulbrich et al., 2009). There are two approaches: oblique and orthogonal (Udofia, 2011; Ho, 2006). The orthogonal rotation approach maintains the reference axes of the factors at 90º if the factors are independent, while the oblique rotation approach maintains correlated factors at the level of independence amongst the rotated factors. In view of this, the existing study adopts orthogonal rotation. Scholars have debated three major approaches of orthogonal rotation: varimax, quartimax and equimax (Ho, 2006; Udofia, 2011; Pallant, 2007). The varimax

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rotation was used in this study as it is the method that most commonly used by scholars which seems to give the purest separation of factors (Pallant, 2005; Ho, 2006).

In addition, the factor loadings on the varimax rotated component matrix were observed for substantial cross-loading that fits the interpretation of output. Investigation of the factor loadings proved that most of the variables were highly loaded on the first factor (Pallant, 2005; Williams, Onsman & Brown, 2010; Olawale & Garwe, 2010). However, Kiolbassa et al., (2011) suggests possible ways to handle this by evaluating the wording of the cross-loaded variables and, grounded on their face validity, allocating them to the factors that are most logically or conceptually representative, and, thereafter, naming the factors. Finally, factor analysis was adopted to categorize the factors of e-banking fraud increase and e-banking fraud prevention and detection mechanisms, because of the sample size (200), which is large enough and there was appropriate significant correlation in the data matrix. This was further processed using structural equation modelling (SEM).