Yes. The important thing is to choose the correct estimator for your SEM analysis.

When working with ordinal data the recommended estimator is Diagonal Weighted Least Squares. If you are working with the software Mplus or the "lavaan" package in R, two estimators in this category are WLSMV and ULSMV.

Greetings,

Roberto

In addition to Roberto Melipillan's post, you may refer to:

• C.-H. Li, " Confirmatory factor analysis with ordinal data: Comparing robust maximum likelihood and diagonally weighted least squares ", 2016 - https://link.springer.com/content/pdf/10.3758%2Fs13428-015-0619-7.pdf
• Rhemtulla et al., " When Can Categorical Variables Be Treated as Continuous? A Comparison of Robust Continuous and Categorical SEM Estimation Methods Under Suboptimal Condition ", 2012 - http://psychmodels.ucdavis.edu/uploads/8/6/3/9/86398102/rhemtullabrosseauliardsavalei_pm.pdf
• D. Mindrila, " Maximum Likelihood (ML) and Diagonally Weighted Least Squares (DWLS) Estimation Procedures: A Comparison of Estimation Bias with Ordinal and Multivariate Non-Normal Data ", 2010 - https://pdfs.semanticscholar.org/ddbf/f72ab683f207e1dd7ec835b99100a08657a7.pdf

When facing with small sample size, refer to:

• [Consistent PLS] Schuberth et al., " Partial least squares path modeling using ordinal categorical indicators ", 2016 - https://opus.bibliothek.uni-wuerzburg.de/opus4-wuerzburg/frontdoor/deliver/index/docId/14401/file/Schuberth_Partial_least_squares_path_modeling.pdf
• [Factor Score Regression compatible with categorical data]

Thank you Roberto Melipillan . Can this be performed using SPSS?

Thank you Stéphane Breton for these references.

Hi Shubhajit,

SPSS does not include the estimators that you need for this type of analysis (i.e., WLSMV or ULSMV).

If you think you will be working on a regular basis with models like EFA/CFA/SEM, I would encourage you to learn how to program these analyses using either Mplus or the "lavaan" package in R. Greetings,

Roberto

KNNs/UV-Diagrams may also be linked to SEM in analyzing Likert-type ordinal scale data by referring to the connex issue on RG: https://www.researchgate.net/post/Can_we_use_Machine_Learning_Method_K-Nearest_Neighbor_Algorithm_Approach_to_analyse_Likert_scale_based_data

Switching from SEM to KNNs/UV-Diagrams is better understood based on the following references:

• Jordan et al., " An Introduction to Variational Methods for Graphical Models ", 1999 - https://people.eecs.berkeley.edu/~jordan/papers/variational-intro.pdf
• Kulis et al., " Revisiting k-means: New Algorithms via Bayesian Nonparametrics ", 2012 - https://people.eecs.berkeley.edu/~jordan/papers/kulis-jordan-icml12.pdf

Dear Shubhajit Sadhukhan

The short answer is yes.

Structural Equation Modelling (SEM) does not require specific type of data with compared to traditional analysis.

· SEM allows for the assessment of the relationships specified in the hypotheses and the SEM is used to validate the theoretically driven model and it is ideal when testing theories that include latent variables.

· The SEM consists of the measurement model and the structural model. Specifically, the path coefficients are examined with attention to the strength, direction, and significance of the relationships.

· The CFA was a construct based on theoretical understanding that determined the variation and covariation between the observed variables, which were indicators and latent variables, unobserved variables, and measurement errors. It identified whether the number of factors and loadings of the measured variables on them conformed to what was expected on the basis of pre-established theory. Hence, CFA attempted to explain the variation and covariation in a set of observed variables in terms of a set of theoretical and unobserved factors.

· CFA should meet three assumptions: 1) latent and observable variables are measured as deviations from their means; 2) the figure of observable variables in the indicators was bigger than the number of unobservable variables; and 3) and the common and also unique factors were not correlated.

· When you have sample, the sample size justification could be based on several perspectives to calculate the ideal sample size for an SEM model.

· For instance Rule of Thumb which requires the multiplication of the number of unknown parameters by 5-20, or Less Optimal and Minimum Sample Size Approach assumes that the sample size for SEM should be in the range of 100-200, as 100 is the less optimal sample size, while some other propose 200 is satisfactory number for the minimum sample size for the SEM. This number might be increased according to complexity of the model.

Please check the following dissertation and manuscript that I co-authored to see an applied SEM technique:

https://www.researchgate.net/publication/312876363_The_Impact_of_Mobbing_and_Job-Related_Stress_on_Burnout_and_Health-Related_Quality_of_Life_The_Case_of_Turkish_Territorial_State_Representatives

https://www.tandfonline.com/doi/abs/10.1080/01900692.2016.1204553?journalCode=lpad20

Dissertation: https://www.researchgate.net/publication/329829038_THE_IMPACT_OF_MOBBING_AND_JOB-RELATED_STRESS_ON_BURNOUT_AND_HEALTH-RELATED_QUALITY_OF_LIFE

https://stars.library.ucf.edu/etd/5021/

Hope helps