How to assess the influence of 2 factors and their interaction on correlations between a collection of traits?

04 April 2018 5 10K Report

I am trying to statistically measure the effect of 2 binary factors (sex and a developmental factor) and their interaction on the correlations between 7 phenotypic traits.

Tools (such as cocor package) only allow for pairwise comparison of correlations (based on correlation coefficient and sample sizes) and then won't let me measure the interactive effects of my factors on the correlations.

The only solution I found so far is to run linear models and, to test the influence of the factor (F) on the correlation between 2 traits (T1 and T2), I use one of the trait as the response variable and test for the interaction between the other trait and the factor (supposed to show me how this factor affects the quality of the regression between my two traits). This solution is great because it also allows me to test for the interactive influence of my 2 factors on the relation between the different traits.

My main problem is that the result of the interaction in the linear models differs when I switch T1 and T2 in the models while, fundamentally, whether or not my factor significantly affects the quality of a regression should have the same answer if I test :

T1 = FxT2

T2 = FxT1

Any explanation or trick to go through this problem, or any suggestion for a better statistical approach of question?

Thanks

Heiko Breitsohl

Florent,

you can do this using a structural equation model, where you specify a "multi-group model" based on the four groups resulting from the two factors [unless this is a within-group design, in which case they are other solutions.] You can then test whether the correlations are equal across groups.

Z. A. Al-Hemyari

Hi Florent

Please refer to:

1. Landau, S. and Everitt, B. S.(2004). A Handbook of Statistical analyses using SPSS.

2.Howitt, D. and Cramer, D.(2008). Introduction to SPSS.

Regards,

Zuhair

Salma Omar Bleed

Hi Florent

I agree with prof. Al-Hemyari : you can refer to:

SPSS Statistical Analyses using SPSS

I attached the book here

Florent Pittet

Thank you all for your answers.

Thank you Pr Al-Hemyari, if you have a more specific statistical technique I should refer to, in the handbook, I'd be glad to have a look at it. I am not a user of this IBM software anymore but once I know for sure the right modelling technique I can apply it to a different stat environment.

Heiko, thank you so much for your suggestion, I never ran any structural equation model so I am reading about it and will possibly come back to you with further questions.

In parallel, I am currently being helped by a statistician who directs me to using multi-response modelling as in the Chapter 5 of the following document:

https://cran.r-project.org/web/packages/MCMCglmm/vignettes/CourseNotes.pdf

I anyway, I will give updates so that this basic and seemingly redundant question does not remain unanswered.

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