CHAPTER V ANALYSIS & INTERPRETATION

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1 CHAPTER V ANALYSIS & INTERPRETATION In this chapter the analysis of the data collected based on the frame of reference of this thesis is presented. First the empirical analysis of the proposed theoretical model using SEM is presented followed by demographic profile of the respondents. The chapter concludes by analyzing the demographic influences of consumers on their intention to use internet banking. 5.1 Introduction to Analysis and Interpretation To empirically validate the extended TAM model, Structural Equation Modeling (SEM) was used and hypotheses one to twenty were tested through the Structural Equation Modeling using AMOS 18. One way ANOVA was used for examining differences in consumer intention to use internet banking across select demographic variables, thereby testing hypothesis twenty one. Multiple regression was used to find out the influence of select demographic variables on consumer intention to use internet banking and tests hypothesis twenty two. The following section briefly describes an introduction to Structural Equation Modeling including the basic concepts of Structural Equation Modeling and moves on to present the psychometric checks done using the measurement model of SEM and the analysis results of the hypotheses testing done using the structural model. This is followed by the analysis of select demographic influence on internet banking usage intention. 140

2 5.2 Basic Concepts of SEM: An Introduction Structural Equation Modeling (SEM) is a multivariate technique, which estimates a series of inter-related dependence relationships simultaneously. The term Structural Equation Modeling conveys that the causal processes under study are represented by a series of structural (i.e. regression) equations, and that these can be modeled pictorially to enable a clearer conceptualization of the study. The hypothesized model can be tested statistically in a simultaneous analysis of the entire system of variables to determine the extent to which it is consistent with the data. If the goodness-of-fit is adequate, the model argues for the plausibility of postulated relations among the variables. Given below are some of the basic concepts of SEM and a few terms which are used in the analysis Latent and Observed Variables With regard to the measurement instrument, the variables are classifies as latent and observed variables. Latent variables are not observed directly. They are operationally defined in terms of behavior believed to represent it. The measured scores (measurements) are termed as observed or manifest variables, and they serve as indicators of the underlying construct which they presume to represent. Hence one latent variable has three or four statements (observed variables) to represent it Exogenous and Endogenous Latent Variables Exogenous latent variables are synonymous with independent variables; they cause fluctuations in the values of other latent variables in the model. Endogenous latent variables are synonymous with dependent variables and, as such, are influenced by the exogenous variables in the model, either directly or indirectly. 141

3 5.2.3 The Factor Analytic Model Factor analysis is one of the oldest and best known statistical procedures for investigating relationship between sets of observed and latent variables. In using factor analysis, the researcher examines the co-variation among a set of observed variables in order to gather information on their underlying latent constructs (i.e. factors). There are two basic types of factor analysis: Exploratory Factor Analysis (EFA) and Confirmatory Factor Analysis (CFA). The factor analytic model (EFA or CFA) focuses solely on how, and the extent to which, the observed variables are linked to their underlying latent factors. Specifically speaking, it is concerned with the extent to which observed variables are generated by the underlying latent constructs and thus strength of the regression paths from the factors to the observed variables (the factor loadings) are of primary interest. Exploratory Factor Analysis is designed for situations where links between the observed and latent variables are unknown or uncertain. Hence after the formulation of questionnaire items, an EFA will be conducted to determine the extent to which the item measurements are related to the latent constructs. In contrast, Confirmatory Factor Analysis (CFA) is used when the researcher postulates relations between the observed measures and the underlying factors a priori, based on knowledge of the theory, empirical research, or both, and then tests this hypothesized structure statistically. Because the CFA model focuses solely on the link between factors and their measured variables, within the framework of SEM, it represents what is called as a measurement model. In this study, the model was developed a priori, hence only the CFA was used. 142

4 5.2.4 The Process of Statistical Modeling The model in this study was based on the Technology Acceptance Model. First the model was specified and the researcher tested the plausibility of the model based on sample data that comprised of all observed variables in the model. The primary task in this model testing procedure was to determine the goodness-of-fit between the hypothesized model and the sample data. As such the structure of the hypothesized model was imposed on the sample data to test how well the observed data fits this restricted structure. Because it is highly unlikely that a perfect fit will exist between the observed data and the hypothesized model, there will be a differential between the two which is called as the residual. According to Joreskog (1993), the general strategic framework for testing Structural Equation Models could be strictly confirmatory (SC), alternative models (AM) and model generating (MG). This study adopts the strictly confirmatory scenario SEM Assumptions and Requirements The major assumptions of Structural Equation Modeling (SEM) are as follows: All the four levels of measurement (Nominal, ordinal, interval and ratio scales) can be used. Either a variance-covariance or correlation data matrix derived from a set of observed or measured variables can be used. But a covariance matrix is preferred. In other words, S =, then model fits the data, where S= Empirical/ observed/ sample variance/ covariance matrix 143

5 = Model implied variance / covariance matrix SEM deals with data in the variance- covariance matrix as shown below in table 5.1. Table 5.1 Variance and Covariance Matrix of SEM x1 x2 y x1 Var ( x1 ) x2 Cov (x1, x2 ) Var (x2) y Cov (x1, y) Cov (x2, y) Var (y) If correlation matrix is used, the following correlation coefficients are calculated: o product moment correlation when both variables are interval o Phi-coefficient when both variables are nominal o Tetra choric coefficient When both variables are dichotomous o Polychoric coefficient- When both variables are ordinal o Point-biserial coefficient when one variable is interval and other is dichotomous o Poly-serial coefficient when one variable is ordinal and the other is interval variable Latent variables are smaller than the number of measured variables. Data are normally distributed. Here, the usual univariate normality checks are made by analyzing the skewness and kurtosis of each variable. In case of non-normality, one has to look for outliers and transformation of data. Tests such as Mardia-Statistic can be used for checking the multivariate normality of all the variables considered together (Bentler 144

6 and Hu, 1995). The Satorra Bentler statistic (Satorra and Bentler, 1988, 1994) or the use of item parcels (subscales in the scale) and transformation of non-normal variables (West, Finch and Curran, 1995) can also be adopted. SEM assumes a linear relationship among the indicators of measured variables. In case of non-linear relationships, Kenny Judd model (Kenny and Judd, 1984) can be used. Even though a consensus has not been reached on the issue of sample size, a large sample size is required. Different authors have suggested different sample sizes as discussed earlier. However it is recommended that any sample less than 150 may not produce reliable estimates. There is a stochastic relationship between exogenous and endogenous latent variables. That is, not all of the variation in the dependent variable is accounted for by the independent latent variable (Kunnan, 1998) Basic Composition of SEM As mentioned earlier, in SEM there are two models: the Measurement model and the structural model. The measurement model defines relations between the observed and unobserved variables. It provides the link between scores on a measuring instrument (i.e. the observed indicator variables) and the underlying constructs they are designed to measure. The measurement model represents therefore the Confirmatory Factor Analysis (CFA), in that it specifies the pattern by which each measure loads on a particular factor. It concentrates on validating the model and does not explain the relationships between constructs. It represents how the measured variables come together to represent constructs and is used for validation and reliability checks. In other 145

7 words CFA is a way of testing how well the measured variables represent a particular construct. The purpose of CFA is twofold: 1) It confirms a hypothesized factor structure 2) It is used as a validity procedure in the measurement model On the other hand, the structural model defines relations among the unobserved variables. Accordingly it specifies the manner by which particular latent variables directly or indirectly influence (i.e. cause ) changes in the values of certain other latent variables in the model. Therefore it is concerned with how constructs are associated with each other and is used for hypotheses testing. In this study data was analyzed using Anderson and Gerbing s (1988) two step approach whereby the estimation of the confirmatory measurement model precedes the estimation of the structural model. Before evaluating the model fit, it is necessary to present the analysis of the psychometric properties of the instrument using the measurement model. The next section does so by presenting the validation and reliability checks of the instrument. 146

8 5.3 Validation of the Measurement Model: Psychometric Checks A Confirmatory Factor Analysis (CFA) was conducted using AMOS 18. Measurement model validity depends on establishing acceptable levels of goodness-of fit for the measurement model and finding specific evidence of construct validity. Validity is defined as the extent to which data collection methods accurately measure what they were intended to measure (Saunders and Thornhill, 2003). To satisfy the validity procedure, the following are the validity and reliability checks that were carried out: Content validity Convergent validity Composite Reliability Discriminant validity Nomological validity The content validity and nomological validity of the research model have already been presented in chapter four under methodology. The other psychometric property checks of the instrument are presented here Convergent Validity Convergent validity is shown when each measurement item correlates strongly with its assumed theoretical construct. In other words the items that are the indicators of a construct should converge or share a high proportion of variance in common. The value ranges between zero and one (0 1).The ideal level of standardized loadings for reflective indicators is 0.70 but 0.60 is considered to be an acceptable level (Barclay et al., 1995). 147

9 Convergent validity was verified through the t-statistic for each factor loading. All factor loadings are greater than 0.70 and range from 0.77 to The standardized factor loadings (λ) of construct items of the measurement model are presented in table 5.2 Table 5.2 AMOS Output Extract: Standardized Factor Loadings of Construct Items No Construct statements Standardized factor loadings (λ) Perceived Usefulness 1 Internet banking enables people to conduct financial transactions more quickly. 2 Internet banking improves one s effectiveness in conducting banking transactions. 3 Internet banking makes it easier to conduct banking transactions. 4 Internet banking provides convenience since it is available 24 hours, 7 days of the week. 5 Internet banking saves time compared to traditional banking. Perceived Ease of Use 6 It would be easy for me to become skilful at using internet banking Learning to use internet banking is easy Overall I believe that Internet banking is easy to use. Attitude Using internet banking is definitely advantageous Using internet banking is a good idea

10 No Construct statements Standardized factor loadings (λ) 11 Using internet banking is a wise idea I would like to use internet banking Perceived Security 13 Banks offering Internet banking implement security measures to protect their customers and have adequate safeguard mechanisms. 14 Internet banking ensures that transactional information is protected and cannot be altered. 15 Internet banking systems have adequate safeguard mechanisms to ensure that financial or personal data of customers is not divulged to other parties. 16 I feel safe about the security and privacy issues connected with internet banking. 17 Using internet banking is as safe as using other modes of banking. Intention I intend to use internet banking is the near future Assuming I have access to computer systems, I intend to use internet banking. 20 I intend to increase my use of internet banking in the near future. Self Efficacy 21 I would feel comfortable using Internet banking on my own I am skilled at using computers and internet I have sufficient knowledge, ability and experience in using computers and internet

11 No Construct statements Standardized factor loadings (λ) 24 Given the facilities, I will be able to use internet banking Awareness 25 I am aware of internet banking and the facilities it offers. 26 I am aware of what needs to be done, to become an internet banking user. 27 I am aware of the services that could be done using internet banking. 28 I am aware of the security and privacy issues of internet banking. Bank Integrity 29 Banks offering Internet banking, deal sincerely with customers. 30 Banks offering Internet banking are honest with their customers. 31 Banks offering Internet banking, will keep promises they make. Bank Benevolence 32 The intentions of banks offering Internet banking are benevolent and kind. 33 Banks offering Internet banking, act in the best interest of their customers. 34 Banks offering Internet banking are concerned about their customers. Bank Competence 35 Banks offering Internet banking have sufficient expertise and are competent to do banking business on the Internet

12 No Construct statements Standardized factor loadings (λ) 36 Banks offering Internet banking have sufficient resources to do banking business on the Internet. 37 Banks providing Internet banking have adequate knowledge to manage their business on the Internet. Disposition to Trust It is easy for me to trust technology My tendency to trust technology is high I tend to trust a technology, even though I have little knowledge of it. Structural Assurances 41 There are adequate laws to protect me when I use internet banking. 42 The existing regulations / legal framework are good enough to protect Internet banking users. 43 There are reputable third party certification bodies to assure the trustworthiness of internet banks (ex. VeriSign, VISA). Consumer Trust on Internet banking 44 Internet banking is reliable and can be used for my banking transactions. 45 Internet banking can be trusted. There are not many uncertainties. 46 In general I can trust internet banking for my banking activities Note: All Factor loadings are significant at p<

13 Convergent validity was evaluated for the thirteen constructs using three criteria recommended by Fornell and Larcker (1981): (1) All measurement factor loadings must be significant and exceed 0.70, (2) Construct reliabilities must exceed 0.80, and (3) Average Variance Extracted (AVE) by each construct must exceed the variance due to measurement error for that construct (that is, AVE should exceed 0.50). In Structural Equation Modeling, for the convergent validity the factor loadings and Average Variance Extracted (AVE) should be greater than 0.5 (Fornell and Larcker, 1981). The average variance extracted (AVE) for each of the factors is calculated manually for all the constructs using the formula suggested by Hair et al., (1995) as given below: λ λ Where λ is the standardized factor loadings and indicator measurement error. is the This can be put forth in simple terms as sum of squared standard loadings divided by sum of squared standard loadings plus sum of indicator measure errors. For example, the AVE for the first factor Awareness was calculated as: 152

14 That is AVE for awareness is 2.89 / ( ) Therefore AVE for Awareness = 0.92 The Average variance extracted and the construct factor loadings are presented in table 5.3. As seen from the table, all AVE values and factor loadings are greater than 0.5 with almost all values above For all the constructs, all items have high loadings, with majority above 0.80 therefore demonstrating convergent validity. This study satisfied this criteria hence convergent validity was established. Table 5.3 AVE and Factor Loadings of the Constructs Construct AVE Construct Factor loadings Awareness Self Efficacy Perceived Usefulness Perceived Ease of Use Perceived Security Consumer Trust on Internet banking Bank Benevolence Bank Integrity Bank Competence Structural Assurances Disposition to trust Attitude Intention

15 5.3.2 Composite Reliability A requirement for construct validity is score reliability. Reliability can be defined as the degree to which measurements are free from error and, therefore yield consistent results. Reliability, also called consistency and reproducibility, is defined in general as the extent to which a measure, procedure, or instrument yields the same result on repeated trials (Carmines & Zeller, 1979). It can be used to assess the degree of consistence among multiple measurements of variables (Hair, Anderson, Tathman, & Black, 1998). Operationally reliability is defined as the internal consistency of a scale, which assesses the degree to which the items are homogeneous. For reflective measures, all items are viewed as parallel measures capturing the same construct of interest. Thus, the standard approach for evaluation, where all path loadings from construct to measures are expected to be strong (i.e. >=0.70) is used. Composite reliability measures the overall reliability of a set of items loaded on a latent construct. Value ranges between zero and one. Values greater than 0.70 reflect good reliability. Between is also acceptable if other indicators of the construct s validity are good (Hair et al., 2006) The internal reliability of the measurement models was tested using Fornell s composite reliability (Fornell and Larcker, 1981). Reliability of the factors was estimated by checking composite reliability. Composite reliability should be greater than the benchmark of 0.7 to be considered adequate (Fornell and Larcker, 1981). The formula for calculating composite reliability is as follows: 154

16 Where λ is the standardized factor loadings and indicator measurement error. is the This can be explained as square of sum of standardized factor loadings divided by square of sum of loadings plus sum of indicator measurement errors. For example the composite reliability for the dimension Awareness was calculated as follows: i.e. Therefore the composite reliability for the construct Awareness is found to be Similarly composite reliabilities for other constructs were estimated. The composite reliability and AVE S of all constructs are presented in Table 5.4. All composite reliabilities of constructs have a value higher than 0.70, indicating adequate internal consistency. 155

17 Table 5.4 Composite Reliability and AVE of Constructs Construct Composite AVE Reliability Awareness Self Efficacy Perceived Usefulness Perceived Ease of Use Perceived Security Consumer Trust on Internet banking Bank Benevolence Bank Integrity Bank Competence Structural Assurances Disposition to trust Attitude Intention

18 5.3.3 Discriminant Validity Discriminant validity is the extent to which a construct is truly distinct from other constructs. It means that a latent variable should explain better the variance of its own indicators than the variance of other latent variables. In other words the loading of an indicator on its assigned latent variable should be higher than its loadings on all other latent variables. Discriminant validity check is done by comparing the AVE s with the squared correlation for each of the constructs. The AVE of a latent variable should be higher than the squared correlations between the latent variable and all other latent variables. The rule of thumb for assessing discriminant validity requires that the square toot of AVE be larger than the squared correlations between constructs (Cooper & Zmud, 1990, Hair et al., 1998) Discriminant validity is shown when each measurement item correlates weakly with all other constructs except for the one to which it is theoretically associated. Discriminant validity is shown when two things happen: 1. The correlation of the latent variable score with measurement item need to show an appropriate pattern of loading, one in which the measurement item load highly on their theoretically assigned factor and not highly on other factors. 2. Establishing discriminant validity requires an appropriate AVE (Average Variance Extracted) analysis. The test is to see if the square root of every AVE for each construct is much larger than any correlation among any pair of latent construct. As a rule of thumb, the square root of each construct should be much larger than the correlation of 157

19 the specific construct with any of the other constructs in the model (Chin,1998) and should be at least 0.50 (Fornell and Larker,1981) To examine discriminant validity, the shared variances between factors were compared with the Average Variance Extracted (AVE) of the individual factors (Fornell & Larcker, 1981). The proof of discriminant validity is presented in table 5.5. The diagonal items in the table represent the square root of AVE s, which is a measure of variance between construct and its indicators, and the off diagonal items represent squared correlation between constructs. As seen from the factor correlation matrix in Table 5.5. The lowest AVE value was 0.93 (for CTIB, INT, ATT constructs), which exceeded the largest squared correlation between any pair of constructs ( between Structural Assurance and CTIB). This analysis showed that the shared variance between factors were lower than the AVE s of the individual factors, which confirmed discriminant validity. 158

20 Table 5.5 Factor Matrix Showing Discriminant Validity AWA SE PU PEU SEC ATT DIS STA BB BI BC CTIB INT AWA 0.96 SEF PU PEU SEC ATT DIS STA BB BI BC CTIB INT Diagonal are square root of AVE and others squared correlation 159

21 5.4 Confirming the Measurement Model Using CFA After validation of the measurement instrument was satisfied, the results of the Confirmatory Factor Analysis (CFA) using AMOS 18 was used to evaluate the model fit of the measurement model to confirm the hypothesized structure The Measurement Model The measurement model shown in figure 5.1 comprises of thirteen factors. Each factor is measured by a minimum of three to a maximum of five observed variables, the reliability of which is influenced by random measurement error, as indicated by the associated error term. Each of these observed variables is regressed into its respective factor. Finally all the thirteen factors are shown to be inter-correlated Type of Model The hypothesized model is recursive, i.e., uni-directional. Recursive models are the most straightforward and have two basic features: their disturbances are uncorrelated, and all causal effects are unidirectional Model Identification Structural models may be just-identified, over-identified, or under-identified. A just identified model is one in which there is a oneto-one correspondence between the data and the structural parameters. That is, the number of data variances and co variances equals the number of parameters to be estimated. An under-identified model is one which the number of parameters to be estimated exceeds the number of variances and co-variances. As such the model would contain insufficient information for attaining a solution. 160

22 Figure 5.1 The Measurement Model 161

23 An over-identified model is one which the number of estimable parameters is less than the number of data points (i.e. variances and co variances of the observed variables). This results in positive degrees of freedom that allow for rejection of the model thereby rendering it of scientific use. The aim in SEM therefore is to specify a model which is over-identified. There are two basic requirements for the identification of any kind of Structural Equation Model: (1) there must be at least as many observations as free model parameters (df 0), and (2) every unobserved (latent) variable must be assigned a scale (metric). The proposed model in this study is an over-identified model with positive degrees of freedom (911) as shown in table 5.6 drawn from the AMOS output. In this model there are 1081 distinct sample moments (i.e., pieces of information) from which to compute the estimates of the default model, and 170 distinct parameters to be estimated, leaving 911 degrees of freedom, which is positive (greater than zero). Hence the model is an over identified one. Table 5.6 AMOS Output: Computation of degrees of freedom Number of distinct sample moments 1081 Number of distinct parameters to be estimated 170 Degrees of freedom (df) ( ) 911 Looking at the amount of information available with respect to the data, these constitute the variances and co variances of the observed variables. With p variables, there are [p(p+1)/2] such elements. Given that there are 46 observed measures in the model, it is known that there are 1081 [i.e. (46 [46+1]/2)] pieces of information 162

24 from which to derive the parameters of the model. Counting up the unknown parameters in the model, it can be seen that there are 170 parameters to be estimated (33 regression weights, 78 co variances and 59 variances) The degrees of freedom is positive (911), thus it is an over-identified model Model Estimation Method The most widely used estimation method is Maximum Likelihood (ML) estimation. The term maximum likelihood describes the statistical principle that underlies the derivation of parameter estimates: the estimates are the ones that maximize the likelihood (the continuous generalization) that the data (the observed co variances) were drawn from this population. That is, ML estimators are those that maximize the likelihood of a sample that is actually observed (Winer, Brown, & Michels,1991). It is a normal theory method because ML estimation assumes that the population distribution for the endogenous variables is multivariate normal. Other methods are based on different parameter estimation theories, but they are not currently used as often. In fact, the use of an estimation method other than ML requires explicit justification (Hoyle, 1995). Most forms of ML estimation in SEM are simultaneous, which means that estimates of model parameters are calculated all at once. For this reason, ML estimation is described in the statistical literature as a full information method. The method of ML estimation is very complicated and is often iterative, which means that the computer derives an initial solution and then attempts to improve these estimates through subsequent cycles of calculations. Improvement means that the overall fit of the model to the data generally becomes better from step to step. For most just-identified structural equation models, the fit will eventually be perfect. For over identified models, the fit of the model to the data may 163

25 be imperfect, but iterative estimation will continue until the increments of the improvement in model fit fall below a predefined minimum value. Iterative estimation may converge to a solution quicker if the procedure is given reasonably accurate start values, which are initial estimates of a model s parameters. If these initial estimates are grossly inaccurate for instance, the start value for a path coefficient is positive when the actual direct effect is negative then iterative estimation may fail to converge, which means that a stable solution has not been reached. Iterative estimation can also fail if the relative variances among the observed variables are very different; that is, the covariance matrix is ill scaled. In this study the minimum iteration was achieved, thereby providing an assurance that the estimation process yielded an admissible solution, eliminating any concern about multicollinearity effects Model Evaluation Criteria: Goodness of Fit Of primary interest in Structural Equation Modeling is the extent to which a hypothesized data fits, or in other words, adequately describes the sample data. Ideally evaluation of a model fit should derive from a variety of perspectives and be based on several criteria that assess model fit from a diversity of perspectives. The model fitting process involves determining the goodness-of fit between the hypothesized model and the sample data. Goodness of fit (GOF) indicates how well the specified model reproduces the observed covariance matrix among the indicator items (i.e. the similarity of the observed and estimated covariance matrices). Ever since the first GOF measure was developed, researchers have been striving to refine and develop new measures that reflect various facets of the model s ability to represent the data. As such, a number of 164

26 alternative GOF measures are available to the researcher. Each GOF measure is unique, but the measures are classified into three general groups: absolute measures, incremental measures, and parsimony fit measures. For all goodness of fit measures, statistics are presented in a continuum, with the independence model (a model in which all correlations among variables are zero) as the most restricted model and the saturated model (just identified model) as the least restricted one. The hypothesized model lies in between. In other words once the specified model is estimated, model fit compares the theory to reality by assessing the similarity of the estimated covariance matrix (theory) to reality (the observed covariance matrix). If the theory is perfect, the observed and estimated covariance matrices would be the same. The values of any GOF measure result from a mathematical comparison of these two matrices. The closer the values of these two matrices are to each other, the better the model is said to fit. Given below is a description of the goodness-of fit indicators used to evaluate model fitness in Structural Equation Modeling (SEM) Chi Square ( ) Goodness of Fit The Chi square goodness of fit metric is used to assess the correspondence between theoretical specification and empirical data in a CFA. By default, the null hypothesis of SEM is that the observed sample and SEM estimated covariance matrices are equal, meaning perfect fit. The chi-square value increases as differences (residuals) are found when comparing the two matrices. With the chi-square test, the statistical probability that the observed sample and SEM estimated covariance matrices are equal is assessed. The probability is the traditional p- value associated with parametric statistical tests. 165

27 Chi-square GOF test is the only statistical test of the difference between matrices in SEM and is represented mathematically by the following equation where N is the overall sample size. Or This statistic ( ) is also known as the likelihood ratio chisquare or generalized likelihood ratio. The estimation process in SEM will focus on yielding parameter values so that the discrepancy between sample covariance matrix (S) and the SEM estimated covariance matrix ( ) is minimal. The value of for a just-identified model generally equals zero and has no degrees of freedom. If = 0, the model perfectly fits the data (i.e., the predicted correlations and covariance s equal their observed counterparts). As the value of chi square increases, the fit of an over identified model becomes increasingly worse. Thus, chi square is actually a badness-of-fit index because the higher its value, the worse the model s correspondence to the data Degrees of Freedom (df) Degrees of freedom represent the amount of mathematical information available to estimate model parameters. The number of degrees of freedom for a SEM is calculated by the formula: 166

28 Where p is the total number of observed variables and k is the number of estimated (free) parameters. Subtracting the number of estimated parameters from the total amount of available mathematical information is similar to other multivariate methods. But the fundamental difference in SEM is in the method of calculation -, which represents the number of covariance terms below the diagonal plus the variances on the diagonal. It is not derived from sample size as in other multivariate techniques. The degrees of freedom in SEM are based on the size of the covariance matrix, which comes from the number of indicators in the model The Goodness-of-fit Index (GFI & AGFI) The goodness-of-fit index (GFI) was the very first standardized fit index (Joreskog & Sorbom, 1981). It is analogous to a squared multiple correlation ( ) except that the GFI is a kind of matrix proportion of explained variance. Thus, GFI = 1.0 indicates perfect model fit, GFI >.90 may indicate good fit, and values close to zero indicate very poor fit. However, values of the GFI can fall outside the range Values greater than 1.0 can be found with just identified models or with over identified models with almost perfect fit; negative values are most likely to happen when the sample size is small or when model fit is extremely poor. Another index originally associated with AMOS is the adjusted goodness-of-fit index (AGFI; Joreskog & Sorbom, 1981). It corrects downward the value of the GFI based on model complexity; that is, 167

29 there is a greater reduction for more complex models. The AGFI differs from the GFI only in the fact that it adjusts for the number of degrees of freedom in the specified model. The GFI and AGFI can be classified as absolute indices. The parsimony goodness-of-fit index (PGFI; Mulaik et al., 1989) corrects the value of the GFI by a factor that reflects model complexity, but it is sensitive to model size Normed Fit Index (NFI) The NFI is one of the original incremental fit indices introduced by Bentler and Bonnet (1980). It is a ratio of the difference in the value for the fitted model and the null model divided by the value for the null model. It ranges between zero to one. A Normed fit index of one indicates perfect fit Relative Fit Index (RFI) The relative Fit Index (RFI; Bollen, 1986) represents a derivative of the NFI; as with both the NFI and CFI, the RFI coefficient values range from zero to one with values close to one indicating superior fit (Hu and Bentler, 1999) Comparative Fit Index (CFI) The CFI is an incremental fit index that is an improved version of the NFI (Bentler, 1990; Bentler and Bonnet, 1980; Hu and Bentler, 1999). The CFI is Normed so that values range between zero to one, with higher values indicating better fit. Because the CFI has many desirable properties, including its relative, but not complete, insensitivity to model complexity, it is among the widely used indices. CFI values above 0.90 are usually associated with a model that fits well. But a revised cut off value close to 0.95 was suggested by Hu and Bentler (1999). 168

30 Tucker Lewis Index (TLI) The Tucker Lewis Index (Tucker and Lewis, 1973) is conceptually similar to the NFI, but varies in that it is actually a comparison of the Normed chi-square values for the null and specified model, which to some degree takes into account model complexity. Models with good fit have values that approach one (Hu and Bentler, 1999), and a model with a higher value suggests a better fit than a model with a lower value Root Mean Square Error of Approximation (RMSEA) Root Mean Square Error Approximation (RMSEA) was first proposed by Steiger and Lind (1980). It is one of the most widely used measures that attempts to correct for the tendency of the GOF test statistic to reject models with a large sample or a large number of observed variables. Thus it better represents how well a model fits a population, not just the sample used for estimation. Lower RMSEA values indicate better fit. Earlier research suggest values of <0.05. (Browne and Cudeck, 1993), Hu and Bentler (1999) have suggested value of <0.06 to be indicative of good fit Root Mean Square Residual (RMR) The Root Mean Square Residual represents the average residual value derived from the filling of the variance- covariance matrix for the hypothesized model to the variance covariance matrix of the sample data (S). Therefore, the RMR is the square root of the mean of the standardized residuals. Lower RMR values represent better fit and higher values represent worse fit. Recommended value of RMR is <

31 5.4.6 Assessing Overall Measurement Model Fitness The results shown in table 5.7 provide a quick overview of the model fit, which includes the value ( ), together with its degrees of freedom (911) and probability value (0.000). In the table NPAR stands for Number of parameters, and CMIN ( ) is the minimum discrepancy and represents the discrepancy between the unrestricted sample covariance matrix S and the restricted covariance matrix. Df stands for degrees of freedom and P is the probability value. Table 5.7 AMOS Output Showing Model Fit Model NPAR df P /df Default model Saturated model Independence model In SEM a relatively small chi-square value supports the proposed theoretical model being tested. In this model the value is and is small compared to the value of the independence model (25250). Hence the value is good. Although the seems good, it is also appropriate to check the value of divided by df (Wheaton, Muthen, Alwin and Summers, 1977) as the statistic is particularly sensitive to sample sizes (that is, the probability of model rejection increases with increasing sample size, even if the model is minimally false), and hence chi-square ( ) divided by degrees of freedom is suggested as a better fit metric (Bentler and Bonnett, 1980). It is recommended that this metric not 170

32 exceed five for models with good fit (Bentler, 1989). For the current CFA model, as shown in table 5.7, was ( = ; df = 911), suggesting acceptable model fit. The other different common model-fit measures used to assess the models overall goodness of fit as explained earlier is shown in table 5.8. Table 5.8 Fit statistics of the Measurement model Fit statistic Recommended Obtained df significance p < = < GFI > AGFI > NFI > RFI > CFI > TLI > RMSEA < RMR < Goodness of Fit index (GFI) obtained is 0.92 as against the recommended value of above 0.90, The Adjusted Goodness of Fit Index (AGFI)is 0.91 as against the recommended value of above 0.90 as well. The Normed fit Index (NFI), Relative Fit index (RFI), Comparative Fit 171

33 index (CFI), Tucker Lewis Index (TLI) are 0.95, 0.94, 0.98, 0.98 respectively as against the recommended level of above RMSEA is 0.02 and is well below the recommended limit of 0.05, and Root Mean Square Residual (RMR) is also well below the recommended limit of 0.02 at This can be interpreted as meaning that the model explains the correlation to within an average error of (Hu and Bentler, 1990). Hence the model shows an overall acceptable fit. The model is an over identified model. The confirmatory factor analysis showed an acceptable overall model fit and hence, the theorized model fit well with the observed data. It can be concluded that the hypothesized thirteen factor CFA model fits the sample data very well. 5.5 The Structural Model Path Diagram The structural model shown in Figure 5.2 shows the hypotheses formulated. Before moving on to the structural model analysis it is necessary to understands the structural model path diagram. SEM is actually the graphical equivalent of its mathematical representation whereby a set of equations relates dependent variables to their explanatory variables. In reviewing the model presented in figure 5.2 it can be seen that there are 13 unobserved latent factors and 46 observed variables. These 46 observed variables function as indicators of their respective underlying latent factors. Associated with each observed variable is an error term (e1 e46). And with the factor being predicted, for example Perceived 172

34 Usefulness (PU), a residual term (r1) is associated. Errors associated with observed variables represent measurement error, which reflects on their adequacy in measuring the related underlying factors. Residual terms represent error in the prediction of endogenous factors from exogenous factors. For example the residual r1 in figure 5.1 represents error in prediction of PU (the endogenous factor) from SE (the exogenous factor). Certain symbols are used in path diagrams to denote hypothesized processes involving the entire system of variables. In particular, one-way arrows represent structural regression coefficients and thus indicate the impact of one variable on another. In figure 5.2, for example, the unidirectional arrow pointing toward the endogenous factor PU (Perceived Usefulness), implies that the exogenous factor SE (Self Efficacy) Causes PU. Likewise the four unidirectional arrows leading from SE to each of the four observed variables (SE1, SE2, SE3, SE4); suggest that these score values are each influenced by their respective underlying factors. As such these path coefficients represent the magnitude of expected change in the observed variables for every change in the related latent variable (or factor). The one-way arrows pointing from the enclosed error terms (e1 e46) indicate the impact of measurement error on the observed variables, and from the residual (r1), the impact of error in the prediction of PU. 173

35 Figure 5.2 The Structural Model 174

36 5.6 Structural Model Hypotheses Testing Next the SEM was conducted on the structural model using Amos18 to test the hypotheses formulated as shown in figure 5.2. Here the full structural equation model is considered and the hypotheses to be tested relates to the pattern of causal structure linking several variables that bear on the construct of usage intention. In reviewing the SEM path model it can be seen that Usage Intention is influenced by the Perceived Usefulness, Attitude and Consumer Trust on Internet Banking. Perceived Usefulness, Perceived Ease of Use and Perceived Security are influenced both by Awareness and Self-Efficacy. Perceived Ease of Use is hypothesized to influence Perceived Usefulness and the antecedents of Consumer Trust on Internet Banking are hypothesized as Perceived Security, Bank Competence, Bank Integrity, Bank Benevolence, Structural Assurances and Disposition to Trust. All these paths reflect finding in the literature and the model shown in figure 5.2 represents only the structural portion of the Structural Equation Modeling (SEM). In this section of analysis the hypotheses testing and results are presented before which, the inter- construct correlation matrix is presented in table

37 Table 5.9 Inter Construct Correlation Matrix. AWA SE PU PEU SEC ATT DIS STA BB BI BC CTIB INT AWA 1 SE ** 1 PU ** ** 1 PEU ** ** ** 1 SEC ** ** ** ** 1 ATT ** ** ** ** ** 1 DIS ** ** ** ** ** ** 1 STA ** ** ** ** ** ** ** 1 BB ** ** ** 0.063** ** ** ** ** 1 BI ** ** 0.104* * ** ** ** ** ** ** 1 BC ** ** ** ** ** ** ** ** ** ** 1 CTIB ** ** ** ** ** ** ** ** ** ** ** 1 INT ** ** ** ** ** ** ** ** ** ** ** ** 1 ** Correlation is significant at the 0.01 level 176

38 5.6.2 Assessing Structural Model Fitness The process of establishing the structural model s validity follows the general guidelines adopted for the measurement model. A new SEM estimated covariance matrix is computed and it is different from the measurement model, since the measurement model assumes that all constructs are correlated, but in structural model the relationships between some constructs are assumed to be zero. Therefore, for almost all conventional SEM models, the chi square GOF for the measurement model will be less than the GOF for the structural model. Table 5.10 presents select fit indices of the structural model. Table 5.10 Fit Indices of the Structural Model Fit statistics Values df 969 Goodness of fit index(gfi) 0.82 Adjusted Goodness of Fit Index ((AGFI) 0.80 Normed Fit Index (NFI) 0.89 Relative Fit Index (RFI) 0.88 Comparative Fit Index (CFI) 0.93 Incremental Fit Index (IFI) 0.93 Tucker Lewis Index (TLI) 0.92 Root mean Square Error of Approximation 0.05 ( RMSEA) Root Mean Square Residual (RMR)

39 The model fit indices also provide a reasonable model fit for the structural model. Goodness of Fit index (GFI) obtained is The Adjusted Goodness of Fit Index (AGFI) is The Normed fit Index (NFI), Relative Fit index (RFI), Comparative Fit index (CFI), Tucker Lewis Index (TLI) are 0.89, 0.88, 0.93, 0.92 respectively. RMSEA is 0.05, and Root Mean Square Residual (RMR) is also Hence it is concluded that the proposed research model fits the data reasonably Testing Structural Relationships The hypothesized research model exhibited good fit with observed data as mentioned above. Of greater interest for nomological validity is the path estimates in the structural model and variance explained ( value) in each dependent variable. All the 20 hypothesized paths are significant (p value <0.001), and hence supported. The standardized regression weights of the output and result of the hypotheses testing providing support for hypotheses HI through H20 is presented in table Table 5.11 AMOS Output Extract: Standardized Regression Estimates of the Hypotheses Tested No Hypotheses Path coefficients (β value) Supported / not supported H 1 Computer self efficacy(se) positively influences Perceived Usefulness (PU) H 2 Computer self efficacy(se) positively influences Perceived Ease of Use (PEOU) Supported Supported 178

40 H 3 Computer self efficacy(se) positively influences Perceived Security (PS) H 4 Awareness (AWA) positively influences Perceived Usefulness (PU) H 5 Awareness (AWA) positively influences Perceived Ease of Use (PEOU) H 6 Awareness (AWA) positively influences Perceived Security (PS) H 7 Perceived Usefulness (PU) positively influences attitude (ATT) H 8 Perceived Usefulness (PU) positively influences consumer intention (INT)to use internet banking H 9 Perceived Ease of use (PEOU) positively influences attitude (ATT) H 10 Perceived Ease of use (PEOU) positively influences Perceived Usefulness (PU) H 11 Perceived Security (PS) positively influences attitude (ATT) H 12 Perceived Security (PS) positively influences Consumer Trust in Internet banking (CTIB) Supported Supported Supported Supported Supported Supported Supported Supported Supported Supported 179

41 H13 Bank Competence (BC) positively influences Consumer Trust in Internet banking (CTIB) H 14 Bank Integrity (BI) positively influences Consumer Trust in Internet banking (CTIB) H 15 Bank Benevolence (BB) positively influences Consumer Trust in Internet banking (CTIB) H 16 Structural Assurances (STAS) positively influences Consumer Trust in Internet banking (CTIB) H 17 Personal Disposition to trust (DIS) positively influences Consumer Trust in Internet banking (CTIB) H 18 Consumer Trust in Internet banking (CTIB) positively influences attitude (ATT) H 19 Consumer Trust in Internet banking (CTIB) positively influences consumer intention (INT)to use internet banking H 20 Attitude (ATT) towards internet banking influences consumer intention (INT) to use internet banking Supported Supported Supported Supported Supported Supported Supported Supported *Significant at 0.01 level 180