Re: Meta-analysis for regression coefficients

Posted by Bruce Weaver on Mar 27, 2013; 1:09am
URL: http://spssx-discussion.165.s1.nabble.com/Meta-analysis-for-regression-coefficients-tp5719057p5719097.html

That looks like a good find, Gene.  I don't have time to read it properly right now, but from a quick glance, it looked like the authors discuss several methods.  I could not tell from my quick look whether the standard meta-analytic method Fleiss describes is one of them.  

Meanwhile, it occurred to me that well weighting by inverse of the variance (where variance = square of the SE) is the most common approach, meta-analysts sometimes weight by sample size instead.  The OP (who seems to have vanished) could take a look at this, for example:

  http://www.um.es/metaanalysis/5015.pdf

Finally, looking at the original post again, I would not include standardized and raw regression coefficients in the same meta-analysis.  And I'd very leery of standardized coefficients even when dealing with them separately.  Why?  These notes I made while reading John Fox's book on GLMs should clarify.

--- Start of note on Fox's book ---

In his book "Applied Regression Analysis and Generalized Linear Models" (2008, Sage), John Fox is very cautious about the use of standardized regression coefficients.  He gives this interesting example.  When two variables are measured on the same scale (e.g.,years of education, and years of employment), then relative impact of the two can be compared directly.  But suppose those two variables differ substantially in the amount of spread.  In that case, comparison of the standardized regression coefficients would likely yield a very different story than comparison of the raw regression coefficients.  Fox then says:

"If expressing coefficients relative to a measure of spread potentially distorts their comparison when two explanatory variables are commensurable [i.e., measured on the same scale], then why should the procedure magically allow us to compare coefficients [for variables] that are measured in different units?" (p. 95)

Good question!

A page later, Fox adds the following:

"A common misuse of standardized coefficients is to employ them to make comparisons of the effects of the same explanatory variable in two or more samples drawn from different populations.  If the explanatory variable in question has different spreads in these samples, then spurious differences between coefficients may result, even when _unstandardized_ coefficients are similar; on the other hand, differences in unstandardized coefficients can be masked by compensating differences in dispersion." (p. 96)

And finally, this comment on whether or not Y has to be standardized:

"The usual practice standardizes the response variable as well, but this is an inessential element of the computation of standardized coefficients, because the _relative_ size of the slope coefficients does not change when Y is rescaled." (p. 95)

--- End of note on Fox's book ---


HTH.

Maguin, Eugene wrote

I think some background reading needs to be done on this topic. As a starting point:

Betsy Jane Becker and Meng-Jia Wu. The Synthesis of Regression Slopes in Meta-Analysis. Statistical Science, 2007, Vol. 22, No. 3, 414–429.

Gene Maguin


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Bruce Weaver
Sent: Monday, March 25, 2013 10:23 PM
To: [hidden email]
Subject: Re: Meta-analysis for regression coefficients

Hi Mark.  Yes, the SE of the *mean* = SD / SQRT(n).  But the OP is talking about regression coefficients, not means.  In matrix notation, the covariance matrix for the coefficients = (X'X)^-1*MS_error.  The terms on the main diagonal of the covariance matrix are the squares of the standard errors (i.e., variance error terms).  In syntax:

compute cov.b = inv(t(x)*x)*ms.e.       /* (X'X)^-1*MS_error .
compute var.b = diag(cov.b).            /* Variances of B .
compute se.b = sqrt(var.b).             /* SE of B .

For other ways of thinking about the formulae, see:

http://www.talkstats.com/showthread.php/5056-Need-some-help-calculating-standard-error-of-multiple-regression-coefficients

HTH.



Mark Miller wrote
> Is it not the case that the SE (standard error of sample) can be
> derived from Std Dev along with Sample Size (N) as  sd / sqrt(N) ??
>
> ... Mark Miller
>
>
> On Mon, Mar 25, 2013 at 3:27 PM, Bruce Weaver <

> bruce.weaver@

> > wrote:
>> Assuming you mean you want to do two meta-analyses, one for each
>> coefficient, then the standard methods should work.  See this article
>> by Fleiss for a nice overview of the standard methods:
>>
>>   http://smm.sagepub.com/content/2/2/121.short
>>
>> By the way, I found this statement in your post rather odd: "Some
>> coefficients were calculated mathematically and I don't have SDs for
>> those coefficients."  Surely they were all calculated mathematically,
>> weren't they?  Anyway, as the Fleiss article shows, you need to have
>> an estimate of the coefficient for each study and the corresponding
>> standard error (SE, not SD).  If the SE is missing, I think you have
>> two choices:  1) exclude those studies, or 2) estimate the missing
>> SEs.  If you opt for 2, then you should probably run the analysis
>> with a range of estimates plugged in as a kind of sensitivity
>> analysis.  How many of them are missing the SE?
>>
>> HTH.
>>
>>
>>
>> Sungeun Chung-2 wrote
>>> Dear SPSS-L experts
>>>
>>> I haven't done meta-analysis before but I need to do it now. I am
>>> trying to teach myself about meta-analysis and would like to have
>>> some wisdom from the experts here.
>>> My problems is that I have results from 16 studies and want to do
>>> meta-analysis for two regression coefficients  My data look like
>>> this:
>>>
>>> study b1 b2 sample size　  coefficients standardized?
>>> S -0.06 0.14 549　  unstandarized
>>> P, T, & H1 0.34 0.04 101　  standardized
>>> P, T, & H2 0.15 -0.1 129　  unstandarized
>>> P, T, & H2 -0.19 0.25 241　  standardized
>>> S & D 0.39 0.07 132　  standardized
>>> T, R, & C 0.39 0.07 132　  standardized
>>> G 0.66 0.31 632　  standardized
>>> G & H 0.02 0.24 506　  standardized
>>> L & W 0.1 0.13 1335　  standardized
>>> L & T 0.25 0.41 232　  standardized
>>> M et al. -0.18 0.18 198　  standardized
>>> E et al. 0.25 -0.01 359　  unstandarized
>>> S et al 1 0.26 0.18 167　  unstandarized
>>> S et al 2 0.01 0.37 167　  unstandarized
>>> N & F 1 0.26 0.12 152　  standardized
>>> N et al 0.09 0.33 520　  standardized
>>>
>>> Some coefficients were calculated mathematically and I don't have
>>> SDs for those coefficients.
>>>
>>> Can I find numbers for overall effects for two variables through
>>> meta-analysis? What are the methods and programs that I can use for
>>> this kind of analysis.
>>> Any help will be greatly appreciated!
>>>
>>> Thanks in advance,
>>>
>>> Sungeun
>>>
>>>
>>> Sungeun Chung, Ph.D. Associate Professor Department of Journalism
>>> and Mass Communication
>>> 40210 Faculty Hall Sungkyunkwan University
>>> 53 Myeongyun-Dong 3-Ga Jongno-Gu, Seoul, Korea 110-745
>>> 82-02-760-0398;Â
>>
>>> chseun@
>>
>>> ;Â
>>
>>> chseun@
>>
>>
>>
>>
>>
>> -----
>> --
>> Bruce Weaver
>>

> bweaver@

>> http://sites.google.com/a/lakeheadu.ca/bweaver/
>>
>> "When all else fails, RTFM."
>>
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-----
--
Bruce Weaver
[hidden email]
http://sites.google.com/a/lakeheadu.ca/bweaver/

"When all else fails, RTFM."

NOTE: My Hotmail account is not monitored regularly.
To send me an e-mail, please use the address shown above.

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