TEST OF VALIDITY AND RELIABILITY

The reliability of the tests was measured by the Chronbach’s Alpha test which is a proven test of the reliability and consistency of a set of scale or items such as Likert scale. Chronbach’s alpha is the average value of the reliability coefficients for all possible combinations of items when split into two half sets. In Chronbach’s alpha calculations, reliability is the proportion of the variance in the measurement scores that occurs due to differences in the true scores rather than due to random error.

The results table from the Chronbach Alpha test is in the appendix section.

The positive or negative relationship of the constructs with the behavioral intention is analyzed and calculated with the help of confirmatory factor analysis method (CFA) using structural equation modeling (SEM) path analysis method. The software used for the analysis is SPSS AMOS package. AMOS uses Bayesian analysis to improve estimates of model parameters. All the collected variables show high reliability. Chronbach’s alpha for the overall set of variables is also very high (0.9). Therefore, the data can be considered reliable.

Structural Equation Modeling (SEM): SEM is a method employed to study the causal relationship between two or more variables. It allows understanding of the direct or indirect, positive or negative relationships. These relationships could be between two or more independent variables, either continuous or discrete, with one or more dependent variables, continuous or discrete. The basis of SEM is formed by the measured variables. Measured variables are also termed as indicators. These are also called as manifest variables. A latent variable or factor or construct is the unobserved variable which manifests the indicators. In other words, the latent variable is inferred from manifest

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variables [132]. The relationships between the manifest variables are defined by the measurement model. The structural model defines the relationship between the latent variables. One of the advantages to SEM, is that latent variables are free of random error. This is because error has been estimated and removed, leaving only a common variance.

Generally, to define the model diagrammatically, measured variables are

indicated by rectangles or squares and latent variables are indicated by ellipses or circles. The goal in building a path diagram or other structural equation model is to find a model that fits the data well enough to serve as a useful representation of reality. In other words, the goal is to convey a meaningful representation of the collected data through SEM. The following table represents the descriptive statistics of the collected variables.

There are five steps involved in SEM construction:

1. Model Specification: The primary idea behind model definition and statistically assessing model validity and reliability is to define the relationship between the variables in the form of equations. The model consists of two types of variables namely, dependent and independent variables. The parameters to be estimated are:

a. regression coefficients and

b. Variances and covariances of the independent variables in the model. The general representation of the regression model with the help of Bentler-Weeks algebraic representation is as follows:

𝜂 = 𝛽𝜂 + 𝛾𝜉

where if q is the number of dependent variables and r is the number of independent variables, 𝜂 (eta) is a q × 1 vector of dependent variables, 𝛽 (beta) is a q × q matrix of regression coefficients between dependent variables, 𝛾 (gamma) is a q × r matrix of

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regression coefficients between dependent variables and independent variables, and 𝜉 (xi) is a r × 1 vector of independent variables. One of the major differences in regression and SEM is that in SEM even the dependent variables can be viewed as predictors.

2. Model Identification: For model identification, we need to count the number of data points and the number of parameters to be estimated. Variances and covariances in the sample covariance matrix from the data in SEM. If p is the number of measured variables, then the number of data points is 𝑝(𝑝+1)

2 . The number of parameters is found by adding together the number of regression coefficients, variances, and covariances that are to be estimated. In order for the model to be estimated, there need to be more data points than the parameters to be estimated. Hypothesized model with more data points than the number of parameters to be estimated is called over identified model. Hypothesized model with equal number of data points and parameters to be estimated is called just estimated model and the hypothesized model with less number of data points compared to the number of parameters to be estimated is called as an under identified model.

3. Model Estimation: The goal of estimation is to minimize the difference between the structured and unstructured estimated population covariance matrices.

4. Testing Model Fit : The goal of estimation is to minimize the difference between the structured and unstructured estimated population covariance matrices. To accomplish this goal a function, F, is minimized where, 𝐹 = (𝑠 − 𝜎(𝜙))𝑊(𝑠 − 𝜎(𝜙)), s is the vector of data (the observed sample covariance matrix stacked into a vector); s is the vector of the estimated population covariance matrix (again,

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stacked into a vector) and (Q) indicates that s is derived from the parameters (the regression coefficients, variances and covariances) of the model. W is the matrix that weights the squared differences between the sample and estimated population covariance matrix. In EFA, the observed and reproduced correlation matrices are compared. This idea is extended in SEM to include a statistical test of the differences between the estimated structured and unstructured population covariance matrices. If the weight matrix, W, is chosen correctly, at the minimum with the optimal, F multiplied by (N – 1) yields a chi-square test statistic. There are many different estimation techniques in SEM, these techniques vary by the choice of W.

5. Model Manipulation: Model manipulation is the mathematical adjustment process to eliminate the low weighted indicators. This is a valid process to eliminate the unwanted data elements which do not cause any difference to the model by their absence [18][19][141][142].

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