Posted by
Maguin, Eugene on
Mar 26, 2013; 1:09pm
URL: http://spssx-discussion.165.s1.nabble.com/Meta-analysis-for-regression-coefficients-tp5719057p5719089.html
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-coefficientsHTH.
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
>>
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