I have three independent and one dependent variable in our model. I am using partial least square structural equation modeling to test the relationships. When tested separately, each independent variable has a significant relationship with the dependent variable. But when put together in the model, one of the independent variable becomes insignificant.
What does it mean? What could be the interpretation?
Not just multicollinearity. Sometimes the existing independent variable had just spurious relationship with the dependent one, because it was correlated (in various ways, not just by collinearity) with the new indepent var and not with the dependent: in this case, adding the true relation, the spurious one fades. In other cases, both independent variables have true relationship with the dependent one, but some little correlation relate each other, and the variance of the first var is partially explained by the latter, then reducing its statistical significance
The multi-collinearity problem has occurred where the two independent variables are highly correlated. Need to drop either one because the are redundant of each other.
I checked for multicollinearity, it does not seem to be the case because VIf values are just under 2.
Farhan -
Because of the various ways in which the "independent" variables may interact, in addition to the misleading nature of "significance," it is probably best just to test your model's overall performance if you are looking for the 'best' predictions. ----- However, you might first make sure you are looking for the best predictions, not for explanation, as discussed in the following, where the appendix example is instructive:
Galit Shmueli -
https://www.researchgate.net/publication/48178170_To_Explain_or_to_Predict
You might want to research the terms "model selection," "model validation," and "model testing."
In general, a more complex model may have higher variance, but lower bias, and vice versa for less complex models, as noted in bias-variance tradeoff discussions in the area of "statistical learning." However, I have found that if the less complex model does not use the 'best' regressor (i.e., predictor, independent variable), the estimate of sigma is inflated so that the higher estimated variance of the prediction error may actually be for the less complex case.
Perhaps you could compare your model to other ones which would be consistent with subject matter theory. If you compare them for fit, say graphically/visually, as I am about to suggest, you still need to save out some data for testing, to avoid overfitting. - You could, in many cases, and I am assuming it is practical in your case, though I don't know, compare different models on the same scatterplot by graphing y on the y-axis, and predicted-y on the x-axis. That is included in the following as Figures 5 and 6:
https://www.researchgate.net/publication/313925533_Comparing_Model_Performances_Graphically
I'm not sure how helpful the above may be for you, but I think it might be of some use.
Cheers - Jim
Article To Explain or to Predict?
Method Comparing Model Performances Graphically
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