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I have a very simple structural model, with 11 exogenous constructs predicting 1 endogenous latent variable. I examined my structural model with PLS, and I got very poor results - none of the 11 paths is significant, none of the t-values and p values pass the minimum threhold. However, when I included only 3 exogenous constructs predicting the one endogenous construct, the 3 t-values are then all significant. I have no problem with the measurement model, so I reported the structural model evaluation with the 11 exogenous constructs. But in this way I cannot reach the findings of the 3 significant paths, as they are only significant when all the other 8 constructs are eliminated.

My questions are:

  1. How should I report the results to reach the right conclusion (3 significant paths)? Because as far as I know, the complete model should be examined and reported, elimination of constructs should not be done unless the constructs have issues at measurement model evaluation.

  2. In my case when no single path is significant, what is the right way to eliminate constructs in evaluating structural model? (For example, should we eliminate one by one to see whether there's improvement in t-values?)

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How should I report the results to reach the right conclusion (3 significant paths)? Because as far as I know, the complete model should be examined and reported, elimination of constructs should not be done unless the constructs have issues at measurement model evaluation.

You cannot report only the model where the 3 paths are significant unless you have clear theoretical justification for excluding the other 8 constructs. In PLS-SEM (and SEM generally), constructs that pass the measurement model should remain in the structural model, and they cannot be removed solely because their structural paths are nonsignificant as doing so would inflate the Type I error.

In my case when no single path is significant, what is the right way to eliminate constructs in evaluating structural model? (For example, should we eliminate one by one to see whether there's improvement in t-values?).

The correct approach in PLS-SEM is that you should NOT eliminate constructs based on insignificant structural paths, and you should definitely not remove them one by one to “improve” t-values. That strategy is statistically inappropriate because it turns SEM into a stepwise regression procedure, which produces biased coefficients and inflated Type I error. Generally speaking constructs may only be removed when:

  1. There here are measurement model problems (e.g., low loadings, low reliability, poor discriminant validity).
  2. You have theoretical justification for excluding them.
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I am new to SEM, so will keep to general model building principles. In building a regression model, for example, you can take an additive approach and decide on independent variable inclusion based on change in AIC or BIC (or based on log-likelihood). The most parsimonious model may not be best (there are other discussions on that), so logically relevant variables may be included also. Following these principles, you shouldn't be designing your model on what's significant or not, but whether variables add information to the model.

Another aspect to check: missingness in one independent variable can influence the model if you're using list-wise deletion (ie. the model only takes complete cases). I believe this is default in the Lavaan package in R

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