[R-meta] Dependant variable in Meta Analysis

[Viechtbauer, Wolfgang (SP)]

Dear Tarun,

What exactly do you mean by 'beta coefficient'? A standardized regression coefficient? In the (very unlikely) case that the model includes no other predictors and is just a standard regression model, then the standardized regression coefficient for that single predictor is actually identical to the correlation beteen the predictor and the outcome and converting this correlation via Fisher's r-to-z transformation is fine (and then 1/(n-3) can be used as the corresponding sampling variance). However, if there are other predictors in the model, then the standardized regression coefficient is not a simple correlation and while one can still apply Fisher's r-to-z transformation to the coefficient, it will not have a variance of 1/(n-3) and assuming so would be wrong.

Why don't you just meta-analyze the 'beta coefficients' directly? If these coefficients reflect percentage change, it sounds like they are 'unitless' and comparable across studies. Then you get the pooled estimate of the percentage change directly from the model.

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org]
>On Behalf Of Tarun Khanna
>Sent: Thursday, 04 June, 2020 13:41
>To: r-sig-meta-analysis using r-project.org
>Subject: [R-meta] Dependant variable in Meta Analysis
>
>Dear All,
>
>I am conducting a meta analysis of reduction in energy consumption in
>households that have been exposed to certain behavioural interventions in
>trials. The beta coefficients in the regressions in my the original studies
>can ususally be interpreted as percentage change in electricity consumption.
>To do the meta analysis I am converting these beta coefficients to Fisher's
>Z. My problem is that Fisher's Z is not as easy to interpret as percentage
>change in energy consumption.
>
>Question 1: Is it possible to do the meta anlysis using the beta
>coefficients coming from the original studies so that the results remain
>easy to interpret?
>
>Question 2: Is it sensible to convert the final Fisher's Z estimates back to
>the dependant variable coming from the studies?
>
>Sorry if this question sounds too basic.
>
>Best
>
>Tarun
>Tarun Khanna
>PhD Researcher
>Hertie School
>
>Friedrichstraße 180
>10117 Berlin ∙ Germany
>khanna using hertie-school.org ∙ www.hertie-school.org