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CHAPTER FOUR RESULTS
To verify the hypothesized motivational model and to test if it fits the data, statistical analysis was conducted and the result will be presented in this chapter, including the development of the model and the effects among the variables in the model.
The Development of the Model Examination of the Hypothesized Model
The data from 302 participants was used to develop the motivational model. The model was analyzed with AMOS 18 statistical program to test the goodness of fit of the model. The Maximum Likelihood Estimation (MLE) was employed to estimate the parameters and test the goodness of fit.
Concluding from literature reviewed, the hypothesized model of this study was constructed as Figure 13. The model includes 5 latent variables: Integrativeness, Instrumentality, Intrinsic Orientation, Extrinsic Orientation, and Motivational Behaviors. In this model, Integrativeness, Instrumentality, Intrinsic orientation, Extrinsic Orientation are exogenous variables. Motivational Behaviors is endogenous variables. The observed variables of Integrativeness are Integrative Orientation, Attitude toward English Speaking Countries, and Interest in Foreign Languages. The observed variables of Instrumentality are Instrumental Orientation. The observed variable of Intrinsic Orientation is Intrinsic Orientation. The observed variables of Extrinsic Orientation are Identified Regulation, Introjected Regulation, and External Regulation. The observed variables of Motivational Behaviors are Motivational Intensity, Attitude toward Learning English and Desire to Learn English.
Because the hypothesized model was constructed from literature, the data from
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302 participants was used to examine it. The results of the analysis showed that the chi-squared value of the model was 234.750; the degrees of freedom was 37;
RMSEA= .118(>.08); NFI=.902; CFI=.915; PNFI=.505; GFI=.901; AGFI=.824(<.90);
PGFI=.505. The findings indicated that the model needs modification.
Standardized estimates Default model χ²=234.750(P=.000); df=37
AGFI=.824; GFI=.901 RMSEA=.118; CN=85
Figure 13. Path Diagram of the Hypothesized Motivational Model
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Modifications of the Hypothesized Model
The hypothesized model was then undergone modifications based on the modification indices, the discrepancy with the past research findings, while keeping the intactness of the theory. After modification, the path between Intrinsic Orientation and Motivational Behaviors, and the path between Instrumentality and Motivational Behaviors, which were not significant, were removed. The modified model was shown in Figure 14, and the summary of the fit indices for the modified model was shown in Table 17.
In general, a lower chi-squared value indicates higher goodness of fit to the data.
A chi-squared value which is not statistically significant indicates smaller discrepancy between the model and the data, while a significant one indicates poor fit to the data.
A significant chi-squared value of this study might result from sample size. Since chi-squared value is sensitive to sample size, and large sample often results in
statistically significant chi-squared values (Marsh, Bella & McDonald, 1988), March and Hocevar (1985) suggests the assessment of chi-squared value is related to the degrees of freedom (df). The chi-squared / degrees of freedom(χ2/df) ratio can be employed to assess the goodness of fit of the model. A χ2/df ratio which is lower than 5 is considered acceptable. The χ2/df ratio of this model, 3.461, was acceptable. The CN value of the model was lower than the threshold level of 200, but it was still acceptable. The AIC value did not achieve the criterion but was very close to it. The RMSEA value was acceptable as well. It can thus be concluded that the goodness of fit of the modified model was acceptable.
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Standardized estimates Default model χ²=121.127(P=.000); df=35
AGFI=.901; GFI=.948 RMSEA=.080; CN=158
Figure 14. Path Diagram of the Modified Motivational Model
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The Summary of the Fit Indices for the Modified model
Fit Indices Model Fit Criterion Results Assessment of Fit Absolute Fit Indices
χ² p>.05 121.127(p=.000) Poor
RMR <.05 .017 Good
RMSEA
<.05(good fit);
<.08(acceptable fit) .080 Acceptable
GFI >.90 .948 Good
AGFI >.90 .901 Good
Relative Fit Indices
NFI >.90 .948 Good
RFI >.90 .919 Good
IFI >.90 .963 Good
TLI >.90 .941 Good
CFI >.90 .962 Good
Parsimonious Fit Indices
PGFI >.50 .503 Good
PNFI >.50 .603 Good
PCFI >.50 .612 Good
CN
>200(good fit);
<75(poor fit) 158 Acceptable
χ²/df
<3(good fit);
<5(acceptable fit) 3.461 Acceptable
AIC
183.217>132.000 Poor
CAIC
336.516<458.570 Good
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The Goodness of Fit of the Model Overall Goodness of Fit of the Model
Three categories of fit measures proposed by Hair and his colleagues (1998) were used to assess the goodness of fit of the model.
1. Absolute Fit Indices
(1) Chi-squared test: A ch-squared value which is not statistically significant indicates path diagram of the model fits the data. Chi-squared is sensitive to sample size. A large the sample usually leads to a significant chi-squared value. The chi-squared value of the model was 121.127 (p=.000), which is significant, so other indices need to be considered.
(2) Root mean square residual (RMR): RMR indicates the distance between the covariance matrix of the data and that of the theoretical model. In general, the acceptable value has to be lower than .05. The sample yielded the RMR value of .17, indicating the model was good-fitting.
(3) Root mean square error of approximation (RMSEA): The smaller RMSEA value is, the better goodness of fit of the model is. RMSEA value that is lower than .05
indicates good fit, while a value lower than .08 indicates mediocre fit; lower than .10, acceptable fit. The RMSEA value of the model was .08, indicates a mediocre fit to the data.
(4) Goodness-of-fit index (GFI): GFI indicates the extent to which the model
covariance explains the data covariance. A GFI value that is very close to 1 indicates perfect fit. The GFI value of the model was .948, indicating the model can explain 94% of the data, which was a good fit.
(5) Adjusted goodness of fit index (AGFI): AGFI means an adjusted GFI. AGFI value is better to be as big as possible. The AGFI value of the model was .901, indicating a good fit.
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2. Relative Fit indices
(1) Normal fit index (NFI): NFI value means the extent to which the model hypothesized model improves from the independent model. The larger NFI means greater improvement. NFI value higher than .90 means good fit. The NFI value of the model, 0.948, means good fit.
(2) Relative fit index (RFI): RFI value is between 0 and 1, and a higher value means a better fit. RFI which is larger than .90 means the model is acceptable. The RFI value of .919 indicates an acceptable model.
(3) Incremental fit index (IFI): IFI value is a modification of RFI to lower the influence of sample size. IFI value is between 0 and 1, and a higher value means a better fit. IFI which is larger than .90 means the model is acceptable. The IFI value of .963 indicates a good-fitting model.
(4) Tacker-Lewis index-non-normal fit index (TLI): TLI is used to compare the goodness of fit of two models. TLI value is between 0 and 1, and a higher value means a better fit. TLI which is larger than .90 means the model is acceptable. The TLI value of .941 indicates an acceptable model.
(5) Comparative fit index (CFI): CFI means the discrepancy between the
hypothesized model and the independent model. CFI value is between 0 and 1, and a higher value means a better fit. CFI which is larger than .90 means the model is acceptable. The CFI value of .962 indicates a good-fitting model.
3. Parsimonious Fit Indices
(1) Parsimonious goodness-of fit (PGFI): PGFI value is between 0 and 1, and a higher value means a better fit. PGFI which is larger than .50 means the model is acceptable.
The PGFI value of .503 indicates an acceptable model.
(2) Parsimonious normed fit index (PNFI): PNFI is often used to compare models with different degrees of freedom, and a higher value means a better fit. PNFI which
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is larger than .50 means the model is acceptable. The PNFI value of .603 indicates an acceptable model.
(3) Parsimony-adjusted Comparative Fit Index (PCFI): PCFI value is between 0 and 1, and a higher value means a better fit. PCFI which is larger than .50 means the model is acceptable. The PCFI value of .612 indicates an acceptable model.
(4) Critical N (CN): CN is used to estimate how many samples are enough to estimate the model and to fit the data. CN value that is higher than 200 means good fit while lower than 75 means poor fit. The CN value of 158 indicates the model is acceptable.
(5) χ²/df: A smaller value of χ²/df indicates the hypothesized model is a better fit to the data. When it is lower than 3, it means the model is a good fit. Value that is lower than 5 is acceptable. The χ²/df value of 3.416 indicates the model is acceptable.
(6) Akaike information criteria (AIC): The AIC penalizes a model with more
estimated parameters. The AIC value of default model needs to be smaller than that of independence model and saturated model. The sample yielded an AIC value that is lower than independence model, but higher than the saturated model. Though it indicates an unacceptable model, the model is very close to a good-fitting one.
(7) Consistent Akaike information criterion (CAIC): CAIC value is to take the influence from sample size into the estimation formula. The CAIC value of default model needs to be smaller than that of independence model and saturated model. The sample yielded an AIC value that is lower than independence model and saturated model, indicating an acceptable model.
In conclusion, in the 17 fit indices, 12 of them meet the criteria, and it can be concluded that the model fits the data.
Goodness of Fit of the Internal Structure
To assess the goodness of fit of the model to the sample, the measurement and
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structural model were tested.
1. The quality of the measurement model
The quality of the measurement model can be assured by testing the reliability and validity. The factor loadings and significance of the observed variables can be used to examine the validity of the observed variables (Bollen, 1989). The factor loadings of observed variables were presented in Table 18 The absolute value of CR (t) of all the parameters except γ12 were higher than 1.96, indicating the observed
variables reflect the latent variables well.
Table 18
Values of Estimated Parameters and the Test of Significance
Parameters Description Esti-mate Standardized
Estimate S.E. C.R. P
γ11 Motivational
Behaviors <- Integrativeness 1.000 .853 γ12 Motivational
Behaviors <-- Extrinsic
Orientation -.020 -.019 .056 -.360 .719 λX23
IDR <-- Extrinsic
Orientation 1.000 .932 λX21
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Parameters Description Esti-mate Standardized
Estimate S.E. C.R. P
Orientation <->
Intrinsic
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As to the reliability of the measurement model, the factor loadings of the
observed variables, their reliability coefficients, the composite reliability and average variance extracted (AVE) was presented in Table 19. The individual item reliability coefficients which are significant are acceptable (Bollen, 1989), and the coefficients which are higher than .50 indicates good reliability. The results showed that all of the individual item reliability coefficients are higher than .50, indicating good reliability.
Table 19
Factor Loadings, Squared Multiple Correlations (SMC),Composite Reliability(CR), and Average Variance Extracted (AVE) of the Observed Variables
Latent Variables
Instrumentality ISO 1.000 1.000 Intrinsic
2. The quality of the structural model
The direction and weightings of the parameters were used to assess the structural model.
In the original hypothesized model, integrativeness, instrumentality, intrinsic orientation and extrinsic orientation all directly influences motivation Behaviors. In the modified model, there are only two direct influences: Integrativeness positively influences Motivational Behaviors while Extrinsic orientation negatively influences
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Motivational Behaviors. Moreover, the path between Extrinsic Orientation and Motivational Behaviors shows no significance. The other two paths were removed.
As to the correlations among the four components, all of the correlations reached significant level. The correlation coefficient between Extrinsic orientation and Integrativeness, .804 was the highest. Most of the other correlations are higher
than .50, except the correlation between Intrinsic orientation and Instrumentality only weights .371.
The predicting ability of the structural model to the latent variables can be examined by R-squared (R2). The R-squared value of Motivational Behaviors
was .703, indicating Integrativeness and Extrinsic orientation together predict 70.3%
of motivational Behaviors.
Because most of the structural variables, γ and Φ value, had reached significance level, it can thus be concluded that the quality of the structural model was acceptable.
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The Effect among the Variables
In addition to examining the goodness of fit and the quality of the model, the effects among the variables should be compared to understand the linear structure among the variables. The relationship among the variables is shown in Table 20. In the four paths in the hypothesized model, the direct influence from Integrativeness, Instrumentality, Intrinsic Orientation, and Extrinsic Orientation, to Motivational Behaviors, only two of them were supported by the data. The direct effect from integtrativeness to Motivational Behaviors was .853, and the direct effect from Extrinsic Orientation was -.019.
Table 20
The Effects among Variables (n=302) Hypothesized Paths Effects Independent
Variable
Dependent
Variables Direct Indirect Total
Integrativeness
The correlations among variables were presented in Table 21. Among correlations between the four components in the model, Integrativeness
Instrumentality, Extrinsic Orientation and Intrinsic Orientation Instrumentality, high correlations occurred between Integrativeness and Extrinsic Orientation, and
Integrativeness and Intrinsic Orientation. The correlation between Integrativeness and
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Extrinsic Orientation was .804, which was the highest, followed by the correlation between Integrativeness and Intrinsic Orientation (.678). The correlation between Integrativeness and Instrumentality came as the third (.652). On the other hand, the lowest correlation, the correlation between Intrinsic Orientation and Instrumentality was .371.
The correlation between Motivational Behaviors and Integrativeness, Instrumentality, Intrinsic Orientation, and Extrinsic Orientation were also higher than .50. The correlations from high to low are as follows. The correlation between Motivational Behaviors and Integrativeness was .838. The correlation between Motivational Behaviors and Extrinsic Orientation was .667. The correlation between Motivational Behaviors and Intrinsic Orientation was .567. The correlation between Motivational Behaviors and Instrumentality was .545.
Table 21
The Correlations among Variables (n=302)
Instrumentality Integrativeness
Intrinsic Instrumentality 1.000
Integrative-
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