DATA ANALYSIS PROCEDURE AND METHODS

In order to investigate the objectives and test the hypotheses of this study, SPSS and AMOS software were used to help us analyze the collected data.

Furthermore, freeware ConstructMap was also employed to reduce the questionnaire items.

3.6.1 Rasch Model

Rasch model is a method for analyzing data from assessments to measure things such as abilities, attitudes, and personality traits. Rasch model is the most basic and the simplest model of item response theory (IRT), and is firstly proposed by Georg Rasch in 1960. Rasch model has only two ingredients, one ability parameter B_n for each person n and one difficulty parameter D_i for each item i.

These parameters are used to determine the probability of person n succeeding on

item i through log-odds. The equation below considered only dichotomous responses:

lnP 1B

(

)

P 0 B

(

)

where, P 1B

(

)

(

)

the probability of a “No” response. When B_n > D_i, the probability of a “Yes”

response is more than 50%. When B_n = D_i, the probability of a “Yes” response is 50%. When B_n < D_i, the probability of a “Yes” response is less than 50%.

In Rasch model, the estimation of the parameter B_n and D_i will not be affected by each other. And this mathematical property is called “test-free” and

“person-free” or “sample-free” measurement. It implies that the difficulty parameter of an item does not depend on the ability distribution of the sample, and the ability parameter of a person does not depend on the set of test items (Prieto, Alonso, and Lamarca, 2003).

In addition to dichotomous responses, Rasch model has been modified to be applicable to polytomous rating-scale instrument, such as Likert scales. The Polytomous Rasch model views one multinomial-choice problem as several binary choice problems and it can be divided into two different models, Rating Scale Model (RSM) and Partial Credit Model (PCM). The rating scale model is used for instruments in which the definition of the rating scale is the same for all items, while the partial credit model is used when the definition of the rating scale differs from one item to another (Chang and Wu, 2008).

In rating scale model, it modified the original difficulty parameter D_i to D_ix, and that represents the threshold of rating category x!1 to category x of item i.

Therefore, the log-odds of the probability that a person responds in category x for item i, compared with category x!1 can be represented:

ln P_nix

P_{ni x!1( )} = B_n! D_ix

The partial credit model is similar to the rating scale model except that each item i has its own threshold parameters F_ix, for each category. So the parameter D_ix is refined:

D_ix= D_i+ F_ix

and the partial credit model becomes

ln P_nix

P_{ni x!1( )} = B_n ! D_i! F_ix

Outfit (outlier-sensitive fit) and Infit (information-weighted fit) statistics are the most widely used diagnostics Rasch fit statistics. The comparison is with an estimated value that is near to or far from the expected value. They are reported as Mean-Squares (MNSQ), that is, the chi-square statistics divided by their degrees of freedom. If X is an observation, E is the expected value based on Rasch parameter estimates, and !² is the variance of expectation, then the squared standardized residual is:

z² = X ! E

( )

The Mean-Square Outfit statistics is obtained by the summed squared standardized residual with divided by total observation number N :

Mean-Square Outfit =

^! ( )

In addition to the Outfit statistics, the Infit statistics weights the squared residual by its variance !². It can be calculated as:

Mean-Square Infit =

^" ( )

!²

( )

"

Furthermore, the Outfit and Infit can be expressed as normalized residuals (Zstd) via a transformation into a t-statistic with an approximate unit normal distribution. The usually acceptable criteria of the fit statistics are 0.7 ! Mean-Square ! 1.3 and -2 ! Zstd ! 2.

3.6.2 Structural Equation Model

Structural equation model (SEM) is also called causal model, causal analysis, simultaneous equation model, analysis of covariance structures, path analysis, and confirmatory factor analysis. SEM is used to explain the relationships between a set of latent (unobserved) constructs, each measured by one or more observed variables (Reisinger and Turner, 1999). The observed variables can be directly measured, but the latent variables are not directly observed like attitudes, customer satisfaction, perception of value or quality.

SEM is a multivariate technique combining aspects of multiple and factor analysis. When using SEM, latent variables can be separated into “exogenous”

(independent) variables and “endogenous” (dependent) variables, and there existing several linear regression equations that describe how the endogenous variables depend on the exogenous variables. SEM encourages confirmatory rather than exploratory modeling, so it is critical that all construct of SEM must be directed by theory for model development and modification.

SEM is characterized by two components: the measurement model and the structural model. SEMs are most often represented graphically. Figure 3.2 show a graphical example of a SEM:

1. Measurement model represents the relationship between observed variables and latent variables including the relationship between latent endogenous construct and measured dependent variable, and the relationship between latent exogenous construct and measured independent variable. The equations are shown below:

y=!_y*" + # x=!x*"+#

Where x- measured independent variable y- measured dependent variable

! - latent exogenous construct explained by x-variables !- latent endogenous construct explained by y-variables !- error for x-variable

!- error for y-variable

!- correlation between measured variables and all latent constructs 2. Structural model includes the relationships among the latent constructs including exogenous construct and endogenous construct. The equation is shown below:

!="*!+#*$+%

Where !- latent endogenous construct

! - latent exogenous construct

! - correlations between endogenous latent constructs !

!- correlation between latent constructs ! (exogenous) and ! (endogenous)

! - structural error term

Figure 3.2 A Graphical Example of SEM Source: http://www.gsu.edu/~mkteer/sem2.html

Goodness-of-fit tests are used to determine whether the model should or should be rejected. A number of goodness-of-fit indexes are used to evaluate the overall fit, the comparative fit to a base model, and model parsimony. The recommended level of the goodness-of-fit indexes are shown in Table 3.2.

Table 3.2 Goodness-of-Fit Measures for Overall Model Fit Goodness-of Fit

<0.05 The average residuals between observed and estimated input matrices.

Root Mean Square Error of Approximation

(RMSEA)

'$%$( It is less affected by sample size than !² and it has been better than RMR.

Goodness of Fit (GFI)

>0.9 A descriptive goodness-of-fie measure ranged from 0 to 1.

Adjusted Goodness of Fit (AGFI)

>0.9 It adjusts the GFI for the number of degrees of freedom expended in estimating the model parameters.

Normal Fit Index

(NFI) >0.9 It assesses fit by comparing the tested model with a null model, and its range is from 0 to 1.

Nonnormed Fit Index (NNFI)

>0.9 It involves the degree of freedom, and it can exceed the 0 to 1 range.

Comparative Fit Index

(CFI) >0.9 It is used in small samples.