I tested a structural model, where gender (A) and another variable (B) predict Y. However, I found that male students were significantly (0.7 year) older than female participants in the sample. This means that A is correlated with C. Thus, I controled for C by including C as the third predictor? Yet, C does not predict Y. I wonder whether it is correct, to exclude C from the final model (on condition that it does not affect the model fit)?
Lukasz, I disagree with Manas (though machine learning could have a different answer than my usual work). The basic reasoning is that "not significant" is not the same as "zero in the population," so omitting it could lead to a mis-specified model. And that misspecification won't necessarily show up in fit statistics.
Unless your model is so complex or your sample size is so small that identification is a challenge, leave in variables that you had reason to put in in the first place.
Pat
In my research on machine learning using neural network, i miscalculated an attribute and added to the result though when i view its neural diagram that attribute doesn't influence my response variable so we take it as superfluous attribute and try to minimize such attribute using dimensionality reduction technique. so accordingly u should remove it as it is superfluous or try to make subset and see if that subset influence value is greater than individual predictor.
Lukasz, I disagree with Manas (though machine learning could have a different answer than my usual work). The basic reasoning is that "not significant" is not the same as "zero in the population," so omitting it could lead to a mis-specified model. And that misspecification won't necessarily show up in fit statistics.
Unless your model is so complex or your sample size is so small that identification is a challenge, leave in variables that you had reason to put in in the first place.
Pat
If both models (including C and without C) show a similar model fit and you cannot very well argue for one or the other you should rather present them both as possible and reasonable solutions.
I fully agree to the things Pat said. However, I would question the apriori reasonableness to include C as a control variable just because it is correlated with A.
A variable has to be included if it is related to the IV AND can be expected to affect Y. Similarly it has to be included it is a supposed common cause of A and Y.
Hence, because this theoretical baseline is missing I would exclude it from the model (or would not have included it).
Just my 2c
Best,
Holger
Holger,
I'm not sure that holds. Certainly it should be considered in the case you describe to avoid the omitted variable problem (though even that, I argue, depends on the conceptual model of the relations). But a predictor of Y that is causally unrelated to X can have other benefits. In particular, it can reducing the residual variance of Y and potentially improving power to detect an effect of X, depending on how that balances with the loss of a residual df.
Pat
Pat, thanks for completing the picture. Of course that's correct. I had in mind consistent estimation of the causal effect.
But please note, that Lukasz included a covariate just because it was related to the IV (not DV). In my point of view, this is not a reason to include it.
Having said that, occasionally, we want to include covariates not because we think they are potential confounders but because of a "one may never know"... In such a case I follow Les Hayduk's approch to include it as covarying predictors with fixed -to-zero effects. The fit tells than of these effects should be estimated.
Holger
You inserted the variable C for a reason (theoretical or otherwise), so you should leave it in.
What you can do is to decide whether or not the variable has any effect. You can accomplish this by fixing the regression coefficient to 0 and to test if this leads to a significant decrease in modelfit (compared to the original model fit). If so, the model in which the coefficient is estimated freely is the preffered model. If not, the model in which the coefficient is 0 is the preferred model, so that you can assume the variable has no effect.
The message is: don't look at the significance of individual parameters, judge complete models.
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