Structural Equation Modelling (SEM) is a statistical method used to test complex relationships among variables. It is widely used in various fields, such as psychology, sociology, education, and business. SEM allows researchers to develop and test theoretical models, which can help to explain and predict phenomena of interest. However, it is important to ensure that the model fits the data well before making any conclusions. In this article, we will discuss some guidelines for determining model fit in SEM.
There are several common errors that people tend to make when it comes to determining model fit in SEM. One of the most common errors is relying solely on the chi-square test to assess model fit. While the chi-square test is a popular method, it has some limitations, and should not be used as the only criterion for model fit. Other common errors include:
- Using inappropriate fit indices for the model
- Ignoring the importance of model complexity
- Not considering the sample size
- Not checking the assumptions of the model
Guidelines for Determining Model Fit
Use Multiple Fit Indices
As mentioned earlier, relying solely on the chi-square test is not recommended. It is important to use multiple fit indices to assess model fit. Some commonly used fit indices include:
- Root Mean Square Error of Approximation (RMSEA)
- Comparative Fit Index (CFI)
- Tucker-Lewis Index (TLI)
- Standardized Root Mean Square Residual (SRMR)
Each fit index has its own strengths and weaknesses, and using multiple indices can provide a more comprehensive assessment of model fit.
Consider Model Complexity
Model complexity is an important factor to consider when assessing model fit. A model that is too complex may fit the data well, but may not be generalizable to other samples. On the other hand, a model that is too simple may not fit the data well, and may not adequately explain the relationships among variables. It is important to strike a balance between model complexity and simplicity.
Like any statistical method, SEM has certain assumptions that must be met in order to ensure accurate results. These assumptions include:
- Normality of the data
- Linearity of the relationships among variables
- Homoscedasticity (equal variances) of the residuals
It is important to check these assumptions before conducting SEM, and to make any necessary adjustments to the model.
Let’s consider two examples to illustrate the guidelines for determining model fit in SEM:
A researcher wants to test a theoretical model that proposes a relationship between self-esteem and life satisfaction. The model includes four latent variables: self-esteem, positive affect, negative affect, and life satisfaction. The researcher collects data from a sample of 500 adults, and conducts SEM using the maximum likelihood estimation method.
After fitting the model, the researcher obtains a chi-square value of 350.03 (df=5, p<.001), which suggests a poor fit. However, when the researcher checks other fit indices (RMSEA=.05, CFI=.95, TLI=.94, SRMR=.04), the results suggest a good fit. The researcher also checks the assumptions of the model and finds no violations. Based on these results, the researcher concludes that the model fits the data well and provides support for the theoretical model.
A researcher wants to test a theoretical model that proposes a relationship between job satisfaction, job performance, and organizational commitment. The model includes six observed variables and one latent variable. The researcher collects data from a sample of 50 employees, and conducts SEM using the maximum likelihood estimation method.
After fitting the model, the researcher obtains a chi-square value of 80.12 (df=5, p<.001), which suggests a good fit. However, when the researcher checks other fit indices (RMSEA=.20, CFI=.60, TLI=.50, SRMR=.09), the results suggest a poor fit. The researcher also checks the assumptions of the model and finds violations (non-normality of the data and heteroscedasticity of the residuals). Based on these results, the researcher concludes that the model does not fit the data well and needs to be revised.