Structural Equation Modeling Analysis Process
1. Case background
A researcher wants to study the impact of major sporting events on the branding of a tourist destination. Sports events are generally held in places with rich tourism resources, complete facilities and equipment, and a good city image. The holding of large-scale sports events will drive the development of local tourism, and the relationship between the two is complementary. In order to study the impact of large-scale sports events on the brand of tourist destinations, the researchers collected a total of 200 questionnaires, some of which are as follows:
2. Model construction
To construct structural equations, researchers generally need to determine the initial research theoretical model based on previous research results, including the measurement relationship of the model, the influence relationship, and the determination of the name of the latent variable of the model, etc. After reviewing relevant literature and existing research results, the data theoretical model of this case is determined as follows:
From the theoretical model of this case, there are 11 measurement items, A1~A4, B1~B2, C1~C3, D1~D2; the 4 latent variables are image fit, image extension, brand identity, and tourism purpose ground image.
The structural equation model includes two parts of the structure, namely the measurement relationship and the influence relationship.
From the perspective of measurement relationship, latent variable image fit is measured by A1~A4; image extension is measured by B1~B2; brand identity is measured by C1~C3; tourist destination image is measured by D1~D2.
From the perspective of influence relationship, image fit and image extension have an impact on brand identity; brand identity has an impact on tourist destination image.
The construction of structural equation model using SPSSAU is as follows:
The MI indicator in the upper right corner of the analysis page is not output by default, and you can choose to output it in subsequent model adjustments, and then perform model correction based on the MI indicator. And the second-order structure of the middle part of the scale is used when several latent variables are combined and the model has one more level. This analysis does not involve it and does not set it.
To build a model in the SPSSAU system, SPSSAU uses the maximum likelihood method to estimate the parameters of the model by default. After obtaining the model parameters, it is necessary to evaluate the quality of the model, including the model fitting, model influence relationship, and model measurement relationship. Make an evaluation.
3. Model evaluation
(1) Model fitting index
The most commonly used model fitting indicators for structural equations and their standards are as follows:
SPSSAU will output more than a dozen fitting indicators, only the most commonly used indicators in this analysis result are shown here, see the table below:
It can be seen from the model fitting index that the chi-square degree of freedom ratio is 1.371<3, GFI=0.955>0.9, RMSEA=0.043<0.1, RMR=0.033<0.05, CFI, NFI and NNFI are all greater than 0.9, and the indicators are all within the standard In the range, it shows that the model is better and the model results are reliable.
(2) Influence relationship
The model regression coefficient summary table is as follows:
The above table shows the influence relationship between latent variables and the measurement relationship. First, analyze the influence relationship. From the above table, we can see that image fit will have a significant impact on brand recognition (p=0.004<0.05), and the standardized regression coefficient is 0.411, indicating that image fit will have a positive impact on brand recognition. The same analysis shows that the degree of image extension will have a significant positive impact on brand identity; brand identity will have a significant positive impact on the image of a tourist destination.
(3) Measurement relationship
From the measurement relationship in the above table, A1, B1, C1, and D1 are reference items, and no index value is output. Generally speaking, if the measurement relationship is good, the standardized regression coefficient should be greater than 0.6, but in the above table, the standardized regression coefficients of measurement items A1, A3, A4, and C2 are all less than 0.6, indicating that the model measurement relationship is not good.
If exploratory factor analysis and confirmatory factor analysis have been carried out before the construction of the structural equation model, it may have been found that the measurement relationship of the relevant measurement items is not good, and adjustments have been made.
When building a structural equation model, if you find that the measurement relationship is not good, you can choose to delete the relevant measurement items and try the analysis again. However, there are many variables involved in this analysis, and if all of them are deleted, the actual research significance may be lost, so other means are needed to adjust the model.
4. Model adjustment
The construction of a structural equation model is usually not successful once, and generally requires multiple adjustments. The adjustment of the structural equation model can be divided into two aspects, namely the model adjustment method and the MI index adjustment method. The model adjustment method is to directly adjust the model. Specifically, the model can be split, or the measurement relationship of the structural equation model can be abandoned and the path analysis method can be used instead. The MI index adjustment method refers to the model adjustment based on the MI index, including the establishment of new covariance relationship and influence relationship.
(1) Model adjustment method
In this case, the measurement relationship of the model is not good, and the standardized regression coefficients of 4 measurement items are all less than 0.6, so you can choose to abandon the measurement relationship of the model and use the path analysis method instead. Path analysis method is a special case of structural equation model, which does not consider the measurement relationship at all, but only studies the influence relationship.
The operation can be divided into the following two steps: ① Change latent variables into explicit variables; ② Establish path analysis model
① Latent variables become explicit variables
Scale data, usually averaged. In this case, the latent variable of image fit is represented by four measurement items A1~A4, so take the average of these four as the explicit variable. In the same way, image extension, brand identity, and tourism destination image can be processed as variables. The operation of using the generate variable function in SPSSAU is as follows:
② Establish path analysis model
Select [Path Analysis] in the SPSSAU system to establish the path analysis model as follows:
First look at the path analysis model fitting indicators, see the table below:
It can be seen from the above table that the chi-square degree of freedom of this analysis model is 1.997<3, and other indicators are also within the standard range, indicating that the model fits well and the model has strong reliability.
Next, look at the influence relationship of the model, as shown in the table below:
It can be seen from the above table that the degree of image fit and image extension will have a significant positive impact on brand identity, and at the same time, brand identity has a significant positive impact on the image of a tourist destination, and the model influence relationship is well established. The final construction path analysis model is as follows:
The above is to use the path analysis method in the model adjustment method to adjust the model. In addition, the model adjustment method also includes the model splitting method and the linear regression method. For specific analysis, please refer to the SPSSAU help manual.
https://spssau.com/helps/research/semmodify.html
(2) MI index adjustment method
When the fitting indexes of the model are not up to standard, the MI index adjustment method can be used. The MI index adjustment method is to let SPSSAU output the suggested value of the MI correction index, and judge the co-variation between variables according to the MI value. When the MI value between the variables is large, it is necessary to add a path between the two, expand the model, and repeat the operation , until the optimal model is obtained.
Let the SPSSAU system output the MI index, you can choose the size of the MI index according to professional knowledge, generally choose MI>10 to output, the operation:
The output is as follows:
Generally, the MI value > 20 indicates that there is a strong relationship between the two, and a covariance relationship between the two can be considered.
As can be seen from the above table, the MI value between B2 and C1 is 10.226, which means that if a covariance relationship is established between B2 and C1, then the chi-square value can be reduced by 10.226, and a covariance relationship between the two can be considered. (Because the data in this case is better, here is only for demonstration). SPSSAU operates as follows:
After establishing the covariance relationship between B2 and C1, analyze again, and the model fitting indicators are as follows:
As can be seen from the above table, the chi-square degree of freedom ratio of the model has decreased from 1.997 to 1.124, and other indicators have also changed slightly. If the model fitting index is still not up to standard, you can continue to establish the covariance relationship or influence relationship based on the MI index. All the indicators of this analysis model have reached the standard, and the final analysis model is as follows:
For the complete MI indicator adjustment method, please refer to the help manual: https://spssau.com/helps/research/semmodify.html
V. Summary
This paper intends to use structural equation modeling to study the impact of large-scale sports events on tourist destination brands. After model testing, it is found that the measurement relationship of the model is not good, so the measurement relationship of the model is finally abandoned, and only the influence relationship of the model is retained, that is, simply using research path analysis. The study found that both image fit and image extension have a significant positive impact on brand identity; at the same time, brand identity has a significant positive impact on the image of a tourist destination.
Structural equation modeling considers both the measurement model and the impact model, so it is more and more widely used in recent research. When the model fit is not good, the MI index adjustment method can be used for model correction; when the model index is not up to standard anyway, the model adjustment method can be used instead of other methods for research, such as path analysis, regression analysis, etc.
Reference: Research on the Impact of Major Sports Events on Tourism Destination Brands-Wang Jing