Research often involves testing the relationship between variables in a hypothesis. While various quantitative techniques can be used for this purpose, it is structural equation modeling(SEM) approach that provides a visual & easy to interpret display of the causal relationship between the variables.
Structural equation modeling, a combination of factor and multiple regression analysis, is a multivariate statistical analysis technique that evaluates the structural relationships between latent constructs and measured variables. Structural equation modeling is of two types.
- Measurement model
This type of model represents the theory specifying how the measured variables group together to demonstrate the theory.
- Structure model
Here, the theory defining how the constructs are related to other constructs are represented.
In research, SEM technique depends on the popular statistical software known as Analysis of Moment Structures (AMOS). This is because AMOS produces tabular outputs and graphic models using user-friendly tool. However, prior to performing SEM, it is a must to consider few assumptions such as:
- Linearity – There should be a linear relationship between the endogenous and exogenous variables.
- Outlier – Since outlier impacts the model significance, the data should be free of outliers.
- Multivariate normal distribution – Maximum likelihood approach is used for multivariate distribution. Also, the small changes in the multivariate results in the larger difference in chi-square test.
- Sequence – There exists a cause and effect relationship between the exogenous and endogenous variables.
- Model identification – The models must be exactly or over-identified as the under-identified models aren’t considered.
- Uncorrelated error terms – The error terms are uncorrelated with other variable error terms.
- Non-spurious relationship – This implies that the observed variance should be true.
If all the above-mentioned assumptions hold good for SEM, AMOS then continues with the structuring equation modeling process by assuming that the data has been modeled. Some of the methods used by AMOS to perform SEM include:
- Generalized least squares – This method estimates the coefficients in the linear regression model if there exists correlation amongst the residuals.
- Unweighted least squares – This approach estimates residual errors to access the conditional mean.
- Browne’s asymptotic distribution free – This type of method is largely recommended when samples containing the non-normal data and SEM involves analysis of covariance structure.
Model construction in AMOS
On determining the type of model, the next step is to run AMOS by clicking ‘start’ menu and choosing the ‘AMOS graphic’ option. When the AMOS starts running, a window known as ‘AMOS graphic’ appears, in which the user can manually draw the SEM model.
- Data input – Choose the file name from the data file option and attach the data in AMOS for further SEM analysis. The user can also select this option by clicking the ‘select data’ icon.
- Observed variable – Use rectangle icon and draw the observed variables.
- Unobserved variable – Deploy circle icon and draw the unobserved variables.
- Covariance – To denote the covariance between variables, select a double-headed arrow.
- Cause-effect relationship – To establish the relationship between the observed and unobserved variable, use single-headed arrow in AMOS.
- Naming the variable – It is important to determine the variables to work with them precisely. Click on the variable in the graphical window, select ‘object properties’ option and name the variables in the AMOS.
- Error term – The error term appears next to the unobserved variable and is often used to draw the latent variable.
After running the analysis, the outputs are displayed on the graphic window. However, the graphic window will display only the error term weights, standardized & unstandardized regressions. Some of the results produced by AMOS include:
- Variable summary
AMOS and the text output variable provides the option of viewing how many variables and which variables have been used for SEM analysis process. The user can also the number of observed and unobserved variables present in the model.
- Accessing the normality
In the SEM model, data must be normally distributed. AMOS provides skewness, text outputs, Mahalanobis d-squared test, Kurtosis and also gives information about the normality of the data.
The modification index describes the reliability of the path in the SEM model. If the modification index value is huge, then more paths can be added to the SEM model.
The estimate option in the AMOS text output will provide the output for regression weight, residual, standardised loading factor, covariance, indirect effect, direct effect, correlation, total effect, and many more.
- Error message
If there is any error in the SEM model drawing process, then AMOS will either give an error message or will not calculate the result.
- Model fit
The model fit will provide the result for goodness fit model statistics and present goodness fit indexes such as RMR, GFI, BCI, TLI, RMSER, and many more.
Additionally, AMOS enables the functioning of SEM analysis and makes it easy to arrive at the statistics (where direct measurements are not possible).