Confirmatory Factor Analysis (CFA)

Tate (1998:311) defined confirmatory factor analysis as “a statistical analysis which is conducted to estimate and test the hypothesised measurement model for all latent variables having more than one observed indicator. Model revisions are made, if necessary, to arrive at a model adequately fitting the data”. Constructs are unobservable variables that cannot be measured directly but can be represented or measured by one or more variables called indicators. Unobserved variables are sometimes called latent variables.

CFA is usually used in data analysis to test the relationships between variables (Hurley et al., 1997). In other words, in instances whereby the researcher is interested in examining different concepts and relationships to portray the strengths of a pre-determined factor model that is in line with an observed set of data, then the CFA is applied. In CFA, researchers try to statistically test the significance of the proposed model. In addition, the researchers have a priori-specified theoretical model (which is the case of this study). Thus, CFA will be performed in this research to examine the relationships between variables (organisational, individual and TAM factors) and to confirm or reject the proposed model.

The CFA is made up of a design that is closely fitted with data, a statistical method used to measure the approximated model for all latent variables that carry with it multiple indicators (Tate, 1998). CFA assists in eliminating errors that are associated with the path

148 model by taking advantage of several observed variables per unobserved variable (Garson, 2009).

The examination done on the CFA is comprised of the estimation of the covariance matrix followed by sequenced assessment and practice to show the degree of fit of the covariance matrix. Alterations of the measurement model will be made after the standardised residuals as well as the modification indices were analysed, as recommended by several researchers (Byrne, 1998; MacCallum, 1986; Segars, 1997). The model modifications should be conducted gradually (one at a time) because any slight alteration on the model may influence other parts of the resolution (Holmes-Smith et al., 2006). According to Garson (2009), in order to enhance the goodness-of-fit for the proposed models, variables with undesirable estimates – such as large standard errors, negative variances and standardised coefficients >1.0 – should be deleted.

As the utmost objective of this research study is to develop a model of factors affecting the adoption of ERP systems by HEIs, the model should be authentic and considerable and should be well-fitting the data statistically. To achieve this, the general guidelines for identification criteria suggested by Bollen (1998) were taken into consideration. He advised that:

 Each unobserved variable should have at least two observed variables

 Factors should be correlated

 Each observed variable was determined by only one unobserved variable

 Any measurement errors should be uncorrected

CFA is used to test any model by comparing the two matrices. Models that produce an estimated covariance matrix that is within the sampling variation of the observed covariance matrix are generally thought of as good models and would be said to fit well. That is to say, the difference between two matrices plays a key role in determining the fit of the CFA model, where a small value of difference is acceptable for use. Unlike SEM,

149 CFA does not need to distinguish between dependent (endogenous) variables and independent (exogenous) variables. Latent variables could be independent or dependent variables. Using CFA, only the loadings theoretically linking a measured item (observed variable) to its corresponding latent factor (unobserved variable) are calculated.

In this research, both SEM and CFA will be applied to examine the validity of the hypothesised measurement model (Tabachnick and Fidell, 2007). Two comparison steps between the CFA model and the SEM model will be performed to assess the validity of the structural model prior to the path analysis. Loading estimates will be performed on the structural model as the first step and the constructs’ variations will be reported. The purpose of using loading estimates was to support the structural model’s validity and ensure the consistencies of factor-loading estimates are unchangeable for both models. The next step will be to examine the goodness-of-fit for the structure model, as well as to perform a comparison between the model fit measures that stemmed from the CFA model and the structural model.

5.2.1.2.1 CFA Notations

Figure 5.2 illustrates the notation used in CFA. The two-way arrows represent covariance or correlations between factors. A one-way arrow from a factor to an observed variable represents regression coefficients or factor loadings, indicating the degree to which an underlying factor is measured by the variables. A one-way arrow from an error term to a variable represents the error associated with that variable.

Figure 5.2 contains seven observed (measured) variables (X1 to X7), two latent factors (F1 and F2), and seven error terms (e1 to e7). L1,1 to L4,1 and L5,2 to L7,2 represent the relationships between the latent variables and the respective measured items (factor loadings). Q1,2 represents the covariance matrix between two factors (F1 and F2). Mathematically, for example, the observed variable (X1) can be represented in the following equation:

150 The above equation is based on reflective measurement theory because CFA uses the concept of reflective rather than informative measurement theory. Reflective measurement theory is based on the idea that latent constructs cause the measured variables and that the error results in an inability to fully explain these measures. Because of that, the arrows are drawn from latent variables to measured variables. As an example, intention to use ERP systems is believed to cause specific measured indicators, such as: IU1, IU2, IU3 and IU4. Dropping the measured indicator, therefore, does not change the latent construct’s meaning. Variables with low factor loadings can be dropped from reflective models without serious consequences, as long as a construct retains a sufficient number of indicators.

Informative measurement theory is based on the assumption that the measured variables cause the construct and that the error is an inability to fully explain the construct. As an example, social class is often viewed as a composite of one’s educational level, occupational prestige and income. Dropping variables will decrease the total correlations. Typical social science constructs – such as attitudes, personality and behavioural intentions – fit the reflective measurement model well (Bollen and Long, 1993). Figures 5.3 and 5.4 illustrate the reflective measurement theory and informative measurement theory, respectively.

151

Figure 5.2: CFA Notations.

152

Figure 5.4: Informative Theory.

5.2.1.2.2 Assessing the Model’s Validity and Reliability

Stapleton (1997:9) stated that “factor analysis, long associated with construct validity, is a useful tool to evaluate score validity”. Assessing reliability and validity of the questionnaire is the next step after deriving the best-fitting measurement model. Convergent validity and discriminate validity tests will be used to examine the reliability and the validity of the measurement scales. Arnold (2006:197) stated that convergent validity “measures the degree to which the indicators of a latent construct measure the same construct”. In other words, convergent validity examines whether the measures for the same construct are correlated; whereas, discriminant validity “measures the degree to which two or more latent constructs measure different constructs” (Arnold, 2006:197).

Average variance extracted (AVE) and composite reliability (CR) will be used in this research to assess convergent reliability, as suggested by Fornell and Larcker (1981). According to Fornell and Larcker (1981), if the value of AVE is equal or above 0.5, this is an indication that the reliability of the questionnaire is good. To confirm convergent

153 validity, all factor loadings for the same construct should be higher than 0.7 (Gefen et al., 2000). Additionally, AVE and CR values for the measurement model should be above 0.5 and 0.7, respectively (Fornell and Larcker, 1981; Hair et al., 2010).

In order to assess the internal consistency among items in the questionnaire, Cronbach’s alpha – which is a commonly used statistical technique – will be used to judge the reliability of the questionnaire. Cronbach’s values range from 0 to 1 and measure the extent to which items in the questionnaire are correlated or associated with one another. According to Nunnally (1978), the questionnaire can be considered highly reliable when the Cronbach’s alpha value is higher than 0.7.

Discriminant validity is the extent to which a given construct is truly distinct from other constructs and is said to be present when the correlations between indicators measuring different factors are not excessively high and, therefore, factor correlations are only moderately strong (e.g., < 0.85) (Kline, 1998). Thus, high discriminant validity provides evidence that a construct is unique and captures some of those phenomena other measures do not. In addition, Hair et al. (1998) recommended that if the value of the square root for the average variance extracted (√AVE) is greater than the R2 _{coefficient of the construct,} this is an indication that discriminant validity is significant.

In addition to the convergent validity of discriminant validity tests, inter-item correlations for a measurement item were applied. According to Bollen and Lennox (1991), inter-item correlations enhance the validity of the research by providing researchers with information regarding whether the item has only one dimension or not. Jaber (2012:174) stated that “homogeneity of the scale items is assessed by inspecting the inter-item correlations”. According to Robinson et al. (1991), correlation coefficients that are greater than 0.3 are significant at the 0.01 level.