A guide to SEM analysis procedures

By Riya Jain and Priya Chetty on January 5, 2022

Structural equation modelling (SEM) is a complicated analysis used to build structural links between measured variables and latent constructs. This type of analysis requires following specific procedures. The previous article stated the initial steps in conducting SEM analysis. It involved establishing validity and reliability. This article provides a detailed description of the SEM analysis procedures.

SEM analysis pre-process

A structural equation model (SEM) is a set of linear equations that describes the relationship of numerous variables. SEM generally consists of two parts i.e. a structural model and measurement model (Fan et al., 2016).

Types of SEM
Figure 1: Types of SEM

Herein, the structural model connects the constructs. It, therefore, expresses the endogenous or dependent constructs as linear functions of the exogenous or independent constructs. The measurement model connects the constructs to observed measurements. This measurement form is similar to the confirmatory factor analysis (CFA) model (Novikova, 2013).

SEM can be visualized using path diagrams. The model as a collection of multivariate techniques is used to test whether models fit data in a confirmatory rather than exploratory manner (Kumar, 2012). Most of the multivariate techniques accidentally overlook measurement error, whereas SEM estimates the measurement error variance parameters for both independent and dependent variables. Thus, to analyze basic models, SEM as an advanced statistical tool requires sample sizes of at least 200. More complicated models would necessitate even bigger samples. (Kline, 2011)

While testing the model, missing data is addressed using full-information maximum likelihood (FIML) as the estimation approach. FIML does not provide missing data imputation. Rather, it estimates missing data coverage at the covariance matrix level. FIML employs all potential data points during data analysis as an extension of maximum likelihood (Novikova, 2013). Further, the pre-processing of the dataset requires the examination of validity and reliability of the dataset to state the efficiency of constructs in building an adequate model. These validities and reliability could be assessed using convergent validity, discriminant validity, or construct reliability (Taherdoost, 2018). With this as the model is derived to be effective, the final model is built to fulfil the study purpose.

SEM analysis procedures

SEM analysis procedures
Figure 2: SEM analysis procedures

Step 1: Specify the model

In the model specification, the researcher specifies the model by determining every relationship between variables relevant to the researcher’s interest. For this reason, the researcher should undertake a thorough literature study (Malkanthie, 2019).

For example; the productivity of an individual though is dependent on various factors, but a study focuses on examining the influence of psychological stress on productivity. The specification of the linkage states psychological stress as a predictor while productivity is the outcome variable.

SEM model specification
Figure 3: SEM model specification

Step 2: Identify the model

The identified model has a unique solution for all of the model’s parameters. The major concern in the identified model is whether or not the researcher can obtain a unique value for each parameter from the observed data. It is determined by various aspects such as specification fixation, free parameter, and restraints in SEM (Shaheen et al., 2017). The parameter estimations can be trusted if a model is identified. When a model is unidentified, its degrees of freedom are zero or negative. However, if more constraints are placed, i.e., the degrees of freedom equal or exceed one, such a model may be overidentified (Malkanthie, 2019).

For example; the model is identified by stating the linkage between time management, lack of satisfaction, and stress.

SEM model identification
Figure 4: SEM model identification

Step 3: Estimate the model

The specified model comprises parameters, the values of which must be estimated using sample statistics by the researcher. Maximum likelihood (ML), generalized least squares, weighted least squares, and partial least squares are among the estimation methods used in SEM. Maximum Likelihood (ML) estimation is the most well-known and often utilized method in this area. (Shaheen et al., 2017). Herein, by estimating the parameters of the model, the software is used for presenting the model concerning the respective variables.

For example; In the below figure, a model is estimated to state the effect of the teacher on students’ achievements in SBS and school.

SEM model (Kocakaya & Kocakaya, 2014)
Figure 5: SEM model (Kocakaya & Kocakaya, 2014)

Step 4: Test the model fit

Model fitness contributes towards examining the efficiency of the mode. This step is based on examining model fitness of the model by assessing model fit indices CMIN/Df, RMSEA, GFI, AGFI, SRMR, TLI, NFI, PNFI, IFI, PGFI, and PCFI (Malkanthie, 2015). The below tables shows the acceptance range of all the model indices. Based on the acceptance level, the model fitness for the variables is determined.

Model Fit IndicesAcceptable Level
CMIN/DFBetween 2 and 5
RMSEAValue Less than 0.10
GFIA value greater than 0.90
AGFIA value greater than 0.90 
SRMRLess than 0.05
TLIA value greater than 0.90
NFIA value greater than 0.90
IFIA value greater than 0.90
PNFIGreater than 0.05
PCFIGreater than 0.05
PGFIGreater than 0.05
Table 1: Criteria range of the model fit indices (Kocakaya & Kocakaya, 2014; Weston & Gore, 2006)

Step 5: Manipulate the model

If model fitness is not meeting expectations, try to enhance model fitness by eliminating some parameters, adding new parameters, or altering a model (Shaheen et al., 2017). Modification of the model is done by building in covariances i.e. examining the modification indices values and building in covariance between the error terms for improving the model effectiveness.

Thus, following the above-stated procedures, the SEM analysis can be incorporated and a linkage is established between the variables to determine the status of the relationship. The assessment of model fit gives a general idea of how well the theoretical model can recreate the observed data.

References

  • Ahmadpoor Samani Ph in Management, S. D. (2016). Steps in Research Process (Partial Least Square of Structural Equation Modeling (PLS-SEM)). International Journal of Social Science and Business, 1(2), 55.
  • Fan, Y., Chen, J., Shirkey, G., John, R., Wu, S. R., Park, H., & Shao, C. (2016). Applications of structural equation modeling (SEM) in ecological studies: an updated review. Ecological Processes, 5(1). https://doi.org/10.1186/s13717-016-0063-3
  • Kline, R. B. (2011). Principles and Practice of Structural Equation Modeling.
  • Kocakaya, S., & Kocakaya, F. (2014). A Structural Equation Modeling on Factors of How Experienced Teachers Affect the Students’ Science and Mathematics Achievements. Education Research International, 1–8. https://doi.org/10.1155/2014/490371
  • Kumar, K. (2012). A Beginner’s Guide to Structural Equation Modeling, 3rd edn. In Journal of the Royal Statistical Society: Series A (Statistics in Society) (Vol. 175, Issue 3). https://doi.org/10.1111/j.1467-985x.2012.01045_12.x
  • Malkanthie, A. (2015). Structural Equation Modeling with AMOS.
  • Malkanthie, A. (2019). Chapter-1 The Basic Concepts of Structural Equation Modeling 1.1. Introduction. January. https://doi.org/10.13140/RG.2.1.1960.4647
  • Novikova, S. I. (2013). Structural Equation Modeling.
  • Shaheen, F., Ahmad, N., Waqas, M., Waheed, A., & Farooq, O. (2017). Structural Equation Modeling (SEM) in Social Sciences & Medical Research: A Guide for Improved Analysis. International Journal of Academic Research in Business and Social Sciences, 7(5). https://doi.org/10.6007/ijarbss/v7-i5/2882
  • Taherdoost, H. (2018). Validity and Reliability of the Research Instrument; How to Test the Validation of a Questionnaire/Survey in a Research. SSRN Electronic Journal, January 2016. https://doi.org/10.2139/ssrn.3205040
  • Weston, R., & Gore, P. A. (2006). A Brief Guide to Structural Equation Modeling. The Counseling Psychologist, 34(5), 719–751. https://doi.org/10.1177/0011000006286345
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