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I think this question has been answered in bits and pieces here and there, but I am still a bit unsure about what the best approach for this is: how to compare two coefficients from a multiple linear regression to see if the effect strengths are significantly different.

For example, I am interested in relating attitude (IV1) and behavioral control (IV2) to the medication adherence (DV). I found that standardized betas were 0.30 and 0.19 for attitude and behavioral control, respectively. Is it reasonable to say the attitude is the strongest predictor of medication adherence? If so, how can I test whether its effect is significantly different from those of the other predictors? I am using SPSS v19.

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    $\begingroup$ With just one dependent variable, your model is more simply described as multiple regression rather than multivariate. Indeed, increasingly "multiple" although a harmless term is superfluous; having two or more predictors is not a big deal. Note that "IV" to many means instrumental variable; it is by no means a universal abbreviation across statistical science. $\endgroup$
    – Nick Cox
    Commented Feb 27, 2014 at 14:15
  • $\begingroup$ Nick you are right. Sorry for this. DO you have any idea for doing such a analysis to compare standfsrdized betas? $\endgroup$
    – Amir
    Commented Feb 27, 2014 at 14:18
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    $\begingroup$ Just about any decent regression text warns that trying to get at the separate effects of predictors is difficult if not impossible. They act as a team, pulling together or against each other. Comparing relative strength is completely straightforward only if the predictors (you say dependent variables) are uncorrelated. $\endgroup$
    – Nick Cox
    Commented Feb 27, 2014 at 14:22
  • $\begingroup$ Dear Nick, So you mean that i have done already? and no need to compare? $\endgroup$
    – Amir
    Commented Feb 27, 2014 at 14:27
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    $\begingroup$ Yes and no. Using standardized coefficients clearly adjusts for different measurement units and different variability. Beyond that what you seem to want is difficult to establish. $\endgroup$
    – Nick Cox
    Commented Feb 27, 2014 at 14:30

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In econometrics there's a concept of economic significance. In a nutshell it's a product of beta and the standard error of the variable. You compare these products.

UPDATE: I think @MaartenBuis is right that you are already doing this. In a model $y=X\beta+\varepsilon$, the economic significance of a variable $x_i$ is $std[x_i]\cdot\beta_i$. This product has the same unit of measure as $y$. The meaning is that one standard deviation of the variable causes this much change in $y$. There is no statistical test here to compare them. Since independent variables are correlated, you can't simply add up the significances to the total variance of $y$. So this economic significance metric is sort of qualitative.

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    $\begingroup$ The OP said that (s)he was comparing standardized coefficients, so (s)he is already doing that. As an aside, I would define economic significance differently as substantively meaningful, but that is a different story. $\endgroup$ Commented Feb 27, 2014 at 14:00
  • $\begingroup$ Dear Aksakal Thanks. Could you please let me know who compare these regressions? $\endgroup$
    – Amir
    Commented Feb 27, 2014 at 14:04
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    $\begingroup$ I have never seen economic significance defined like that. Do you have any references for that use? In my experience, economic significance means something akin to "the estimated effect size / coefficient is relevant from a policy and / or theory perspective, and is not only a statistical curiosity". $\endgroup$
    – KOE
    Commented Apr 2, 2014 at 18:47
  • $\begingroup$ I seriously question the use of standard errors or standard deviations in assessing "significance". Standardized estimates have a number of problems. $\endgroup$ Commented May 3, 2014 at 12:25

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