Re: Meta-analysis for regression coefficients

Posted by Bruce Weaver on Mar 26, 2013; 2:22am
URL: http://spssx-discussion.165.s1.nabble.com/Meta-analysis-for-regression-coefficients-tp5719057p5719080.html

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 <[hidden email]> 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 Â
>> 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?Â
>> 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
> [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.
>
> --
> View this message in context: http://spssx-discussion.1045642.n5.nabble.com/Meta-analysis-for-regression-coefficients-tp5719057p5719077.html
> Sent from the SPSSX Discussion mailing list archive at Nabble.com.
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> [hidden email] (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD