AMOS vs SmartPLS for SEM

What is the difference between CB-SEM and PLS-SEM?

Both methods estimate a measurement model (how items relate to constructs) and a structural model (how constructs relate to each other). But the way they do it is different, and so is the purpose.

In covariance-based SEM each construct is taken as a common factor. The factor is why its items move together, and the balance is error. The whole model is estimated in one go, and then the program compares the covariances your model implies with those in your data. From this comparison only you get global fit statistics. In Indian universities AMOS is the most known program for CB-SEM, mostly because it comes along with IBM SPSS licences. There are others also, like the free R package lavaan, and the SEM modules in JASP and jamovi, which run lavaan underneath.

PLS-SEM forms each construct as a weighted composite of its items. Then the paths between these composites are estimated through a series of regressions. The goal is to explain as much variance as possible in the outcome constructs. SmartPLS is the program most people use. You can also use the R packages seminr and cSEM, or ADANCO and WarpPLS.

Software and method are two separate things. SmartPLS 4 can now run CB-SEM also, and R can do both kinds. Writing just “we used SmartPLS” leaves the examiner guessing which method you ran. In the thesis, give the method name first and then the software.

Which should you choose for your thesis?

First look at your research aim. Only after that look at the model.

• Your aim is to test an established theory and you want to see if the full model fits the data. Then go for CB-SEM (AMOS).
• Your aim is to explain or predict a key outcome, or you are putting new constructs into a theory. For this PLS-SEM (SmartPLS) suits better.
• Your model has formative constructs, say an index built from separate components. PLS-SEM handles this more simply.
• Your model has a feedback loop (X affects Y and Y affects X back). Only CB-SEM can do this.
• Your model is very large with many constructs and paths. Mostly PLS-SEM estimates such a model with less trouble.
• Your field’s top journals mostly use one method for this type of model. You can count that as a fair reason, as long as it is not the only one.

Many times none of these points clearly applies. Suppose your model is a normal reflective one and you have a few hundred survey responses. In that case either method is fine, and usually both reach similar conclusions. Then you can go by what is common in your field, and by what your guide knows to run. You should be able to explain the choice, that is all.

A note on hypotheses

Some theses set up everything as confirmatory hypothesis testing of an established theory. Then the same thesis chooses PLS-SEM “for prediction”. At the viva-voce someone will surely ask about this mismatch. Your stated aim and your method have to agree.

Which justifications do examiners accept?

A big share of PLS-SEM papers give only two reasons for the method, small sample size and non-normal data. Methodologists have criticised both these reasons quite strongly. Rönkkö and Evermann (2013) argued that PLS gives no real advantage when the sample is small. Even Hair and colleagues, who are among the main supporters of PLS-SEM, have said these two should not be the main reasons for picking it.

Weak on their own

• “The sample is small.” Yes, PLS will run with small sample. Still the estimates can be unreliable. You still need enough power for the effects you are expecting. Our sample size guide explains the inverse square root method that is used for PLS.
• “The data is not normal.” Likert data is almost never normal. CB-SEM already has well-known fixes for this, like bootstrapping in AMOS and the MLR estimator with corrected standard errors in lavaan. Non-normal data by itself is no reason to shift to PLS.
• “It gave better results.” This has nothing to do with the method. Don’t use it for deciding, and don’t write it in the thesis either.

Stronger

• The study wants to predict or explain the variance in a key outcome, say intention to adopt a technology.
• There are formative constructs in the model.
• The model is complex and has many constructs, mediators and moderators.
• You are putting new constructs into an existing theory, which makes part of the study exploratory.
• For CB-SEM, the aim is to confirm a well-established theory, and overall model fit is needed to judge it.

When you write the justification, cite the method literature. Hair, Risher, Sarstedt and Ringle (2019) explain when PLS-SEM is a fit and what you should report. On the CB-SEM side, Kline’s textbook Principles and Practice of Structural Equation Modeling is a standard reference.

What do you report for each method?

Reviewers and examiners are expecting a standard set of results for each method. Miss one item and the chapter comes back. It is one of the most common reasons SEM chapters return for corrections.

CB-SEM in AMOS

• Measurement model (CFA). Give standardised loadings, composite reliability, AVE, discriminant validity and the fit indices (chi-square with degrees of freedom, CFI, TLI, RMSEA with its confidence interval, SRMR).
• Every modification you made, like correlated error terms, and a theoretical reason for each one.
• Structural model. Report fit indices again, plus standardised path coefficients with significance and R² for each outcome.
• Indirect effects, tested through bootstrapping and shown with confidence intervals.
• The way you dealt with missing data and non-normality.

PLS-SEM in SmartPLS

• Measurement model. Loadings, Cronbach’s alpha, composite reliability (rho_A and rho_C), AVE and HTMT for discriminant validity. If constructs are formative, give the weights, their significance and collinearity (VIF).
• Structural model. Collinearity (VIF), path coefficients with bootstrapped confidence intervals, R², f², and predictive power through PLSpredict (Shmueli and colleagues, 2019).
• Bootstrapping settings, meaning the number of subsamples (5,000 or more is what people commonly use and report) and which confidence interval method you used.
• SRMR, if you are reporting it. Add a line that using it as a fit measure in PLS is still debated.

In both methods, show the measurement model results before the structural model. If the measurement part has problems, nobody trusts the path results.

Practical points: licences, learning and common errors

Licences

IBM gives the licence for AMOS, and many Indian universities have it in their SPSS site licence. So ask your computer centre or department before buying. SmartPLS sells its licences separately. There is a trial period, and the terms are different for students and for institutions. Check the current terms on each vendor’s website. If money is a problem, R (lavaan for CB-SEM, seminr for PLS-SEM) and JASP are free, and journals are accepting them more these days.

Use a properly licensed copy of either program. Don’t install a cracked copy, that is against the licence terms. Also, journals are now asking more and more for the software and version used.

Learning curve

Both programs lets you draw the model on screen. Because of this it is easy to start, and equally easy to use wrongly. Drawing is the small part of the work. Keep proper time aside to understand what the output is saying, not only which button to click.

Errors we see often

• Giving only Fornell–Larcker and leaving out HTMT.
• In AMOS, adding correlated errors between items of different constructs till the fit looks acceptable.
• In SmartPLS, deleting items one at a time till every loading is above 0.70, and ending up with two-item constructs.
• Using the Baron and Kenny steps for mediation when bootstrapped indirect effects should be tested (see mediation and moderation analysis).
• Calling a cross-sectional PLS model “causal” in the discussion chapter.
• Copying pages of raw output into the thesis when formatted tables are wanted.

How do you write the justification in the methodology chapter?

One or two paragraphs are enough. Mention the method, your reasons linked to the aim and the model, and the software along with its version. You can follow a pattern like this one.

The study used partial least squares structural equation modelling (PLS-SEM), since its main aim was to explain and predict variance in adoption intention. Two formative constructs were also part of the model (Hair et al., 2019). SmartPLS [version] was the software used, and the significance tests came from bootstrapping with 10,000 subsamples.

or

Covariance-based SEM was used because the study tested an established theory, and judging how well the theorised model fitted the data was central to the research questions. The analysis was done in IBM SPSS AMOS [version] with maximum likelihood estimation. As several indicators were not normally distributed, standard errors were obtained through bootstrapping.

Fill in the bracketed parts. Then go back to your introduction once and see that the reason given here matches what it says the study is for.