3 AMOS Model fitness and its evaluation index

Structural equation model is essentially a confirmatory model analysis , Test the fit or consistency between the data and the hypothetical model ,

In other words, the data is used to fit the hypothetical model . Fitness index is also called fitness index , It is to evaluate whether the data is consistent with the hypothetical model

Mutual matching , Instead of explaining the quality of the path analysis model diagram , It is not necessary for a model graph whose fitness completely meets the evaluation criteria Assurance is a useful model , It can only be said that the model diagram assumed by the researchers is more consistent with the actual data .

When testing the fitness index of the whole model , scholar Hair

wait forsomeone (1998) proposal , We should first check whether the model parameters have illegal estimation , We can start from the following three aspects ：(1) Is there a negative error variance ;(2) Is the standardized parameter coefficient correct ≥1;(3) Is there too much standard error . If there is no violation in the model test results , Then the fitness of the whole model can be tested .

generally speaking , Whether the overall model fitness meets the standard can be examined from the following four indicators ：

(1) Absolute fit statistics , Including chi square value , Chi square degree of freedom ratio （X2/df）, Mean square root of asymptotic residuals （RMSEA）,

GFI etc. ;

(2) Value added fitness statistics , as NFI,CFI etc. ;

(3) Reduced fitness statistics , as PNFI, Critical sample value CN, Provincial goodness of fit index （PGFI） etc. ;

(4) Residual analysis index , Such as standardized residual value and non standardized residual value . In this paper, we often use the following several fitting indicators to evaluate ：

(1) Chi square value , The smaller the index value is , The higher the fitting degree between the causal path diagram of the overall model and the actual data . But this index is easily affected by the sample size , The larger the number of samples , The easier it is to achieve significant results , Almost all models that fit well are rejected . therefore , Chi square degree of freedom ratio is commonly used as an alternative test index .X2/df

The smaller , The better the fit of the model . generally speaking ,X2/df<3 It indicates that the overall fitting degree of the model is good ;3<X2/df<5 Indicates that the model as a whole is acceptable , But it needs to be improved ;X2/df>10

It shows that the overall model is very poor .

(2) Asymptotic root mean square error （RMSEA）, This index is less affected by the number of samples , It is a good absolute fitting index . The smaller the index value is , The better the model fit . people say that ,RMSEA>0.1

It indicates that the fitting degree of the model is poor ;0.08-

0.1 The representation model is acceptable , With common adaptation ;0.05-0.08 It indicates that the model fits well ;RMSEA<0.05 It indicates that the fitting degree of the model is very good .

(3) Fitting index , The goodness of fit index was used （GFI）, Conventional fitting index （NFI） And compare the fitting index （CFI）, Adjust the goodness of fit index （AGFI）. The data values of these four fitting indexes are limited to

0-1 between , The closer they are 1 The better the fitting degree of the model , It is generally believed that their values are 0.8 It can be considered that the fitting degree of data and theoretical model is acceptable .

There are two main reasons for the poor fit of the model , One is the wrong model structure assumption , It may be due to the wrong external definition , Some observed variables or latent variables are omitted , It may also be due to the wrong internal definition , Causes the path in the model to be changed

False assumption or omission ; The other is that the assumption of model distribution is not satisfied with normal distribution .

When there is an internal definition error , The model can be continuously modified to achieve improvement , Other errors cannot be improved by model correction , And we need to take corresponding measures to improve the model . There are two ways to modify the model , One is minimalism , That is to eliminate or limit some paths ; The other is exhibition revision , That is to relax some path restrictions ,

In order to improve the degree of model fitting .

It should be noted that , The function of fitting index is to investigate the degree of fit between theoretical model and data , It can not be used as the only basis to judge whether the model is established or not . The model with high goodness of fit can only be used as a reference , We also need to discuss the rationality of the model according to the background knowledge of the problem . Even if the fitting index is not optimal , But a model that can be explained by relevant theories is more meaningful .

notes ： Need a full set of information or do plus QQ1564658423.

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