# How to perform a meta regression with a random effect model?Which model should I use?How to start? (beginner)

I have to perform a meta-regression, using mixed or random effects model, but I don't have any software (except Matlab) and I'm new on this topic (having a relativelly poor statistics background).

Briefly the problem I'm addressing is as follows.

I've collected several effect sized from different studies. In my case, the effect size are percentages of adoption of a specific behaviour.

For example, one study analysed a sample of 100 individuals and concluded that 35 % adopt the behaviour under analysis, whereas another study analysed a sample of 150 individuals and concluded that 45 % adopt the behaviour. My goal is to determine the average of adoption of the behaviour. All the studies are observational (no control groups).

I have to perform a meta-analysis because its study have different characteristics, as for example, the sample size or for instance the average level of education of the sample. Some of the dependent variables are dummy variables.

I read many things about meta analysis/regression but I'm so confused and I don't know how should I start my analysis, which model should I follow, what are the adequate formulation to calculate variance and the weights etc. How the heterogenity is included in the model?

I thought about using this model: y=b0+b1x+b2x+...+u+e (fixed+random effect model)

Is the way I'm thinking correct? Do you have any suggestion for me? If not, what is the step-by-step procedure? (in matlab or excel).

I would appreciate if you could guide me on this analysis.

I'm sorry if I wasn't clear or specific enough.

## 1 Answer

There is a lot to say about what you want to do ! So I will adress what I know:

• First, what you call effect size does not seems to be a standardized effect size. I mean that % from different studies can't be compared that easily. I suggest you consult the classic book of Borenstein et al to learn a bit more about what standardized effect size you should use: Borenstein, M., Hedges, L. V., Higgins, J. P., & Rothstein, H. R. (2011). Introduction to meta-analysis. John Wiley & Sons.

• Second, I think you need to read a bit more about meta-analysis. The terminology is somewhat different from what you can find in classic ANOVA. You will have to decide between a fixed effect and a random effect model. That decision will have strong implications on the way you weight your effect size.Again, read Borenstein et al 2011.

• Finally. for actually doing the analysis, I suggest you take a look at the Metafor package in R (http://www.metafor-project.org/doku.php/metafor) and at this reference article: Viechtbauer, W. 2010. Conducting meta-analyses in R with the metafor package. — Journal of statistical software 36: It will cover some of the question you need to answer before actually doing a model.

Good luck !

• Thank you for your thoughtful comments and the references you provide. Welcome to our site! – whuber Jul 30 '14 at 20:08
• Thank you for your suggestions for reading. I think it will help me. – Catarina Jul 31 '14 at 11:55