The SAM (Structural After Measurement) approach, formalized by Rosseel and Loh (2022) in Psychological Methods, is a relatively recent proposal for addressing a problem we have been carrying for decades in structural equation modeling: the conflation of the measurement model and the structural model. In standard SEM practice, both are estimated simultaneously, which can generate serious problems that many researchers do not even detect. The idea behind SAM is conceptually straightforward, although its statistical implementation has important nuances worth understanding.
In a traditional SEM, when you estimate a complete model with latent variables and structural relationships between them, the measurement model parameters (factor loadings, for example) can be affected by the specification of the structural model, and vice versa. This means that if your structural model is misspecified (if you are missing an important relationship or including one that should not be there), the factor loadings of your latent variables can become distorted. The result is that you could be measuring your constructs poorly precisely because your theoretical model about the relationships between them is incorrect. It is a circular problem that has been pointed out by several methodologists but is rarely discussed in applied articles.
SAM proposes a two-step solution. First, the measurement model is estimated independently, typically through a confirmatory factor analysis. Once the latent variables are well defined and the measurement model parameters are stable, the structural relationships between those latent variables are then estimated. In this way, the measurement component is protected from potential misspecifications in the structural component.
Advantages over traditional SEM
The most immediate advantage of SAM is robustness. By separating the two steps, you considerably reduce the risk that an error in the structural theory contaminates the estimation of your constructs. This is especially relevant in psychology, where theoretical models are often tentative and where the exploration of relationships between latent variables is part of the research process. With traditional SEM, a researcher who tests several alternative structural models is, unknowingly, slightly changing the definition of their own latent variables each time they modify the model. With SAM, the constructs remain stable regardless of which structural model is estimated.
Another practical advantage relates to convergence and computational stability. Complex SEM models, especially those with many latent variables or with moderate samples, sometimes present convergence problems, estimated negative variances (so-called Heywood cases), or non-positive definite covariance matrices. SAM tends to be more numerically stable because each step of the process is simpler than the complete model. This does not mean that SAM is free from technical problems, but in general it is less prone to the computational difficulties that complicate the lives of many researchers.
Limitations and practical considerations
SAM is not a magic solution, and it has its own limitations. The most obvious is that by estimating the model in two steps, the standard errors of the structural model do not incorporate the uncertainty from the first step (the estimation of the measurement model). This can lead to standard errors that are too small and, therefore, to confidence intervals that are too narrow and artificially low p-values. To address this problem, corrections have been proposed, such as the use of sandwich-type standard errors or bootstrap methods, but it is important to be aware of this issue when interpreting the results.
There are also situations where the separation between the measurement model and the structural model is not so clear-cut. For example, when there are relevant cross-loadings that depend on the theoretical context, or when the indicators of one latent variable are causally related to another latent variable in the model. In these cases, the simultaneous estimation of traditional SEM may be more appropriate, because the artificial separation of the two components does not reflect the reality of the phenomenon being studied.
Implementation and recommendations
In practice, SAM is available in software such as lavaan (the reference package for SEM in R), where the sam() function allows the two-step procedure to be performed relatively straightforwardly. lavaan also offers two variants: local SAM, which estimates each measurement block separately and is more robust with small samples, and global SAM, which fits a single joint measurement model. If you are working with a model that has many latent variables, or if you have experienced convergence problems with traditional SEM, SAM may be an alternative worth exploring. It is also a good option when your priority is to ensure that the measurement model is solid before venturing into the structural relationships.
My general recommendation is to compare the results of both approaches. If the structural estimates are similar with traditional SEM and with SAM, you can have greater confidence that your measurement model is robust and is not being distorted by the structural component. If the results differ substantially, that is a signal that something in your model needs attention, whether in the measurement component, the structural component, or both.
Step-by-step SAM in lavaan
For readers who want a concrete picture, a SAM analysis in lavaan proceeds in three logical phases, which the sam() function automates internally but which I describe here because seeing the moving parts makes interpretation easier. First, you fit the measurement model with cfa() and verify standard fit indices: CFI and TLI above .95, RMSEA below .06, SRMR below .08, and factor loadings ideally above .50 with no problematic cross-loadings. If the measurement model itself does not fit, no two-step procedure will save your structural conclusions. Second, lavaan computes either factor scores or the model-implied latent variance-covariance matrix from the measurement step. Local SAM uses local estimates (one block at a time), while global SAM uses the full measurement model. Third, the structural relationships are estimated on the latent quantities from step two, conditional on the measurement parameters being treated as known.
The syntax is essentially the same as for a standard sem() call: sam(model, data, sam.method = "local") or "global". The recommendation in the original Rosseel and Loh papers (2022, 2024) is to start with local SAM for smaller samples and switch to global SAM when the measurement model is large and well-identified. Output includes the structural coefficients, their standard errors (corrected for the two-step procedure), and fit indices comparable to those of a standard SEM. I recommend reading the summary() output carefully because the residual covariance matrix at the structural level often reveals misspecifications that classic SEM hides under the carpet of global fit indices.
When SAM is the right choice (and when it is not)
SAM is most defensible when at least one of the following conditions holds: your sample is small relative to model complexity (a common rule of thumb is fewer than ten cases per estimated parameter); you have prior evidence that your measurement model is well-established (validated scales with replicated factor structure); your structural model is exploratory or you intend to test several competing structural specifications; or you have encountered convergence failures, Heywood cases, or improper solutions with traditional SEM. In all these scenarios, isolating the measurement model protects your construct definitions from contamination by structural uncertainty.
Conversely, SAM is not the right tool when your measurement model itself is the substantive question (for example, in measurement invariance testing across groups), when your indicators legitimately load on multiple factors due to theoretical reasons, or when your sample is large enough and your model simple enough that classic SEM converges cleanly. In those cases the joint estimation of traditional SEM uses the data more efficiently and the standard errors are exact, not corrected.
Reporting SAM results transparently
Because SAM is still a relatively new approach, reviewers may not be familiar with it. A reporting section that anticipates their questions reduces friction. State explicitly that you used SAM, cite Rosseel and Loh's methodological papers, justify the choice (sample size, prior evidence on the measurement model, observed problems with classic SEM), and report fit indices for both the measurement step and the structural step. If you ran both classic SEM and SAM as a sensitivity check (which I generally recommend), include the comparison in a supplementary table. Confidence intervals for structural coefficients should be reported with their bootstrap version when feasible, since the two-step nature of SAM makes asymptotic standard errors slightly anti-conservative. For the broader context of factor analysis decisions that precede any SEM workflow, my complete guide to exploratory factor analysis is a useful companion reading.
If you are validating an instrument or fitting an SEM with a tight sample and are unsure whether to use joint estimation or SAM, my statistical consulting reviews the measurement model first, before moving to the structural part. You can see the full process in the questionnaire validation service.