Hello Noud,

There's actually a couple of issues to address for your query.

1. If the three subscores/scales/factors representing the mediating variable are related (as you'd expect them to be if all relate to a common construct), then, yes: collinearity can and will account for the results you report. Remember, in OLS regression, the point is to estimate coefficients that form the "best" linear composite (for maximizing R-squared, minimizing sum of squared errors) for that set of variables with that specific sample. Only when IVs are uncorrelated will their regression coefficients track exactly to the magnitude and sign of the zero-order correlations with the DV.

Many regression software packages can compute and report on measures of collinearity (e.g., VIF, or its inverse, tolerance). These may be useful for understanding what's going on with your mediator IVs. As well, with only three scores, inspection of the intercorrelations could also be helpful.

2. It might be worth considering whether a single, factor score would be better used in lieu of the three separate scores that represent your proposed mediator.

Good luck with your work.

Collinearity seems to be the reason for your problem. In addition, check the philosophy behind multiple/ordinary regression. It gives you sufficient insight to make the required decisions.

Noud - 

David's idea about a combined score sounds interesting.  If each separate score is actually a component, however, here is an interesting paper on when that might not be too helpful:

Samaniego, F.J., and Watnik, M.R.(1997), “The Separation Principle in Linear Regression,” Journal of

Statistics Education, Vol 5, Number 3, DOI: 10.1080/10691898.1997.11910599

I like graphics, so I would suggest more graphical analysis.  If you use "graphical residual analysis" to check the closeness of the fit, you can use some kind of cross-validation, perhaps just another sample you can collect, to see if you have fit one sample too closely to "predict" well for the rest of the population. 

Also, if you have a good model, I think that increases your chances of having heteroscedasticity for Y|x, or in multiple regression, Y|predicted-y. (Heteroscedasticity in regression is a feature, not a bug.)  See www.researchgate.net/publication/352134279_When_Would_Heteroscedasticity_in_Regression_Occur. 

Cheers - Jim

Noud - 

Looking at the table you provided on your terms, the intercept term is very important there, and other coefficients add and subtract, much like the Longley data example in section 8 of the second and last link I gave you above.  Those data were highly collinear. I doubt that you will have heteroscedasticity, but having it would likely be a good "sign," not a bad one. 

I am not a fan of, nor an expert on, principle components, but you might want to look into that, especially if you aren't trying to interpret the variables. I don't know.  

You might want to reevaluate the problem from a subject matter perspective: Do you have the best set of variables?  Maybe you need different ones. I emphasize that for prediction, as well as interpretation, and when you might have heteroscedasticity.  I agree with David's saying above that you want variables "...that form the 'best' linear composite..." - as emphasized in the paper at my last link in my previous response. 

Cheers - Jim

Thanks everyone for the replies. Starting with David Morse 's point about using a single factor, I did not mention this, but I have indeed done a separate regression for the full construct (three dimensions combined), but would like additional insight into the three dimensions separately.

James R Knaub I do believe my variables are valid, as they are based on several pieces of extant reputable literature.

I have looked at collinearity statistics (VIF values), which indeed have an average value that has biased the regression model, according to my textbook. So I suppose the multiple regression route does not clearly tell me which of the three dimensions has the largest significant impact on the outcome variable. Is there a better way to measure this? If not, this is an acceptable limitation, as I can support this with all this information.

Would I then not be able to reject the following H0: Not all elements of shopper confusion: (a) irritation, (b) inefficiency and (c) helplessness have negative effects on purchase intention? Since I cannot prove their separate effects.

Noud -

Ah. Looking at those variables, I think that just because they overlap does not mean they can't be looked at separately. I would not have thought I'd be saying this, but perhaps if your question is which variables have "negative effects," I think you can look at them one at a time. I doubt that, for example, two variables with negative impact would together have a positive impact, though with collinearity, one might just look that way in a multiple regression. Maybe separate, single predictor regressions would be better here.

Cheers - Jim

See this link

https://www.investopedia.com/ask/answers/060315/what-difference-between-linear-regression-and-multiple-regression.asp

@Noud @Babak Jamshidi has rightly pointed out that collinearity among your predictors might be suppressing regression effects. Kindly check for collinearity for your variables. Your can also look for bivariate correlations among your variables and ensure they are not highly correlated.

There are a few remedies to deal with multicollinearity. Disturbance is sometimes helpful while dealing with multicollinearity. Also helpful may be keeping the number of degrees of freedom minimum.

The recursive least squares algorithm (RLS) is the recursive application of the well-known least squares (LS) regression algorithm, so that each new data point is taken in account to modify (correct) a previous estimate of the parameters from some linear (or linearized) correlation thought to model the observed system. The method allows for the dynamical application of LS to time series acquired in real-time. As with LS, there may be several correlation equations with the corresponding set of dependent (observed) variables. For the recursive least squares algorithm with forgetting factor (RLS-FF), acquired data is weighted according to its age, with increased weight given to the most recent data.

Years ago, while investigating adaptive control and energetic optimization of aerobic fermenters, I have applied the RLS-FF algorithm to estimate the parameters from the KLa correlation, used to predict the O2 gas-liquid mass-transfer, hence giving increased weight to most recent data. Estimates were improved by imposing sinusoidal disturbance to air flow and agitation speed (manipulated variables). The power dissipated by agitation was accessed by a torque meter (pilot plant). The proposed (adaptive) control algorithm compared favourably with PID. Simulations assessed the effect of numerically generated white Gaussian noise (2-sigma truncated) and of first order delay. This investigation was reported at (MSc Thesis):

Thesis Controlo do Oxigénio Dissolvido em Fermentadores para Minimi...