Hey Kathleen

Im not sure what kind of a meta-analysis you are conducting, but know that you can easily transform SEM to standard deviation (SD) which is often used for conducting meta-analyses.

https://stats.stackexchange.com/questions/15505/converting-standard-error-to-standard-deviation

Somewhere around my office I have a book entitled "Meta-Analytic Structural Equation Modelling" by Suzanne Jak (2015). It would be worth looking at.

1. You can use a structural equation approach to meta-analysis, as suggested by Gordon. I recommend another book by Mike Cheung: https://www.amazon.de/Meta-Analysis-Structural-Equation-Modeling-Approach/dp/1119993431. For this, you would use the individual correlation matrices of the primary studies to generate a meta-analytical variance-covariance matrix and run SEM on that. This method is preferable to first meta-analysing the bilateral relation and using the matrix of those relations as input to SEM.

2. You can use the output of SEM as you would treat any regression method for inclusion in meta-analysis. Hence, you can use the regression coefficients (or its derivative: partial correlation) and run the meta-analysis on that. Check the first question here: http://www.erim.eur.nl/research-facilities/meta-essentials/frequently-asked-questions/ (disclaimer: I wrote the answer). This is based on the work of Ariel Aloe and others: DOIs: 10.1080/00221309.2013.853021 and 10.3102/1076998610396901

Good luck!

Robert

PS: I think Martin Bjørn Stausholm misunderstood your question as referring to standard errors. His answer is absolutely correct (I think) but doesn't relate to structural equation modelling (SEM)

Hello !

Thank you all for your answers, there are very helpful. Gordon L Warren, I will check the book of Suzanne Jak, I didn’t know about it.

However, I started reading the book of Mike Cheung, but it is still difficult for me to really understand what metrics I should code for my meta-analysis. I saw he was also talking about the individual correlation matrices but I don’t know how to code them for my metaSEM.

A concrete example to be clearer: let’s say I want to do a meta-analysis on the relationships between 3 variables: the consumer satisfaction, trust and loyalty for example. I have found several articles studying these relationships, through SEM model. However, there are often other variables in their analysis, that I don’t want to include in my final model. And my issue is that, within the individual correlation matrices you are talking about, all the variables of the study are considered. so how should I code this?

So far, I started coding my articles by reporting the following metrics for every relationship I am interested in and that are analyzed in the articles (between an independent and dependent variable in my model): beta coefficient (or also called path coefficient, parameter estimate…), the t-value, the SE, the C.R., the R² of the dependent variable, the p-value, the Cronbach alphas of the measures used. I also reported the correlation coefficient of the two variables of interest, extracted from the correlation matrix. But this matrix is not always provided in all the studies.

What do you think about that? Is it enough to run a MetaSEM?

Thank you again Robert Suurmond for you precious help, I try to self-educate myself on this subject but it’s not always easy 😊

Have a nice day,

Kathleen

Hi Kathleen Desveaud

Well, looks like you are well on your way if you've made it this far.

In order to work with the individual correlation matrices, you have to re-create it based on the one provided in the study. You have to make sure that they are always in the same format (and I guess they are usually reported in different order, different other vars etc). So, for example:

Trust 1

Loyalty 0.20 1

Satisfaction 0.10 0.30 1

Do this for all the studies (repeat exact structure), put it without the labels into a text file and you can import that into metaSEM in R. In my experience, you can always ask Mike himself if you can't figure it out yourself.

However, if not all studies report correlation matrices, you either have to obtain them from the authors or stick with meta-analyzing regression coefficients themselves. I think you've coded the right stuff to calculate the (semi-)partial correlation, see the Ariel Aloe stuff I was referring to earlier.

Good luck!

Hello!

Thank you very much Robert Suurmond ! I will look at the articles you gave me, on the use of regression coefficients for a meta-analysis.

Regarding the correlation matrix: If we take the last example, let say we have an article, where there are only 2 out of the 3 variables of interest (satisfaction and loyalty), and the correlation coefficient extracted from the matrix of the article is 0,3. (The other coefficients in the matrix of the article are for variables I’m not interested in). My re-created matrix would be:

Trust na

Loyalty na 1

Satisfaction na 0,3 1

Right?

Instead of coding directly this re-created matrix for each article, I coded with a line for each relation studied in the different articles, and the single correlation coefficient associated with the 2 variables (like in the following table, in the image file). I will be able to recreate later the matrices for each articles the way you proposed.

For the 2nd article (given in example in the picture), my re-created matrix will be then:

Trust 1

Loyalty 0,6 1

Satisfaction 0,5 0,7 1

What do you think about this way of coding?

Another question: most on the time, correlation coefficients are presented in a matrix used to assess convergent and discriminant validity for the research variables. Is it correct to extract the coefficients from this matrix? Are they comparable with a r coefficient or a Spearman coefficient? All are correlation coefficients, but since they are called with different names, it’s often difficult to know if there are the same.

Plus, do you advise me to code the p-value for the correlation coefficients?

Thanks again for your precious help 😊

Have a nice day!

Kathleen

Hi Kathleen Desveaud ,

~Sorry for the tardiness.

The matrices you propose appear to be correct. As long as you are able to recreate the matrix from the long format of the data as you present it, you will be fine. This will require some manual labor, unfortunately, and this may be prone to errors. Last time I checked there was no way to use this long format to create the matrix automatically in metaSEM, but someone with computer/R skills may be able to do that for you.

Regarding the correlation coefficients: yes, these are all fine as they represent the correlation between two variables. You would have an issue if they used rotated factor analysis to construct the variables, as this may lead to orthogonality (zero correlation) by default between these variables. But I'm assuming that won't be the case for your vars.

No need to code the p-value, as the p-value depends solely on sample size for a correlation. The way metaSEM works is that is uses the study-level sample size to weigh each individual correlation matrix and create a variance-covariance matrix. The cells of the latter are then weighted depending on how many studies (observations) are available for each relationship. This is a massive improvement over 'standard' MASEM, in whihc the harmonic mean of the sample size is taken to weigh each cell, even if that cell has not been measured by that many (or few) observations.

Good luck,

Robert

Thank you very much for your answer, it's really helpful ! :) If I find a way to recreate the matrix automatically in R, I will let you know :)

Just to be sure that I am on the right path...

I had a look at the MetaSEM package of Mike Cheung and it seems that the key metrics to conduct a MetaSEM are the effect size, the sampling variance and the predictors.

For the effect sizes I coded correlation coefficient and the Beta value (with its t-value, SE and CR). I will have then to transform the Beta values into correlation coefficient for the studies where the correlation coefficients are missing.

For the sampling variance, so far I coded the R² of the dependant variable (for the relationship of interest). I also coded the AVE of the variables I'm interested in. Is it correct ? Is there another metrics I should code for the sampling variance?

Finally for the predictors I don't really know how to code. So far I reported the number of predictors in the model for the dependant variable of my relationship. What do you think?

Thanks and have a nice day :)

Kathleen

There is a collection of functions for conducting meta-analysis using a structural equation modeling (SEM) approach via OpenMx is provided by the metaSEM package. you can read the introdunction of this package.Hope this will helpful to you @ Kathleen Desveaud

hi, Kathleen Desveaud I am doing a meta-analysis regarding the effect of customer satisfaction on loyalty and I have the exact problem as yours. most articles did not provide R-value and I am stuck in effect size and coding like you. can you share with me what did you code for effect size at the end and the procedure?