Hello, I have conducted simple linear regression for four time points, always on the same sample. My time points are 10 years apart and now I wish to compare the slopes / betas / regression coefficient.
I have found a method for comparing correlation coefficients, which are equal to my simple regression betas. It is described in this article ( https://psycnet.apa.org/record/1992-15158-001) and elaborated here ( https://psych.unl.edu/psycrs/statpage/biv_corr_comp_eg.pdf) and recommended here ( http://core.ecu.edu/psyc/wuenschk/docs30/CompareCorrCoeff.pdf).
My question is: can I use this method for comparing correlation coefficients, is it statistically sound or is there other (possibly more rigorous) solution to my problem?
Thank you so much in advance!
Linda
Bruce suggested multilevel models. That should be relatively easy in R. Usually the starting point is the lme4 package. There are many other options - including bayesian packages such as brms (which uses lme4 style syntax for defining models). I'm not sure what the outcome is and whether you'd need something like a generalised multilevel linear model (logistic, Poisson etc).
It seems like you'd need time points nested in units - something like this:
library(lme4)
model.out
Hello Linda Coufalová. I would use a multilevel model (aka., HLM or mixed model) approach with the repeated measures clustered within subjects. Include the X*Time interaction to test for heterogeneity of the slopes over time. What software are you using? HTH.
Yes, Fisher z transformation is the key to solving your task if you want to compare correlation coefficients.
But maybe you can formulate your hypothesis in a different way, so then another solution would be more appropriate.
Hi Bruce Weaver , thank you so much for your answer. I am using R. I had been thinking about including the interaction of time, but I have troubles imagining what would the clustering of measures within subjects look like in my data. Suppose I have four data sets, each measuring my dependent variable and explanatory variable. How would I combine them into one using the clustering you are proposing?
Thank you so much in advance for any further guidance.
I am not a useR, so others will be better able to give specific advice. But a Google search on yields a lot of useful looking resources. In addition to the overall interaction term, I suggest you look for info on interaction contrasts too. Good luck.
Linda Coufalová : the data file should have one column giving the data set identifier, one column identifying the subject (with different identifiers for different subjects, even if from different data sets), one column for the time, one column for your X and one for your Y. And as many lines as observations — so called "long format".
Then, using the lmer syntax, you should be able to model what you need. For instance
lmer( Y ~ X + time + X:time + (1|Subject) + (1|DataSet) )
could be a model, that tests interaction and main effects of time and X, taking into account the repeated measures (1|Subject) and the DataSet (as a random effect).
Of course, you'll have to think on how to include each predictor in your model. Typically, with four datasets, you may well consider them as fixed-effects instead of random-effects...
Good luck,
Bruce suggested multilevel models. That should be relatively easy in R. Usually the starting point is the lme4 package. There are many other options - including bayesian packages such as brms (which uses lme4 style syntax for defining models). I'm not sure what the outcome is and whether you'd need something like a generalised multilevel linear model (logistic, Poisson etc).
It seems like you'd need time points nested in units - something like this:
library(lme4)
model.out
Thank you, Thom Baguley , I am already trying it out in nlme package for R (because I found really nice youtube tutorial providing me with a basic insight into this package). I have been nesting my observations by units so far, getting quite satisfying results (random = X ~ unit).
What you are suggesting seems like a good direction, thank you so much. Do you think that this way of writing it would work in nlme as well? (random = X ~ unit/time_point) ?
In nlme, as far as I remember, if you write random = X ~ unit, you introduce not only a random intercept, but also a random slope in your model. Are you sure it is what you need?
If you use time_point as anover level of random effects, you will not be able to use them as a X variable to study changes with time... So that's seem strange.
Of course, without detailed explaination on your experimental design and your variables, these two remarks are just guesses, but they illustrate also that it is really hard to give good advices without a clear explaination of your setting and question... Some advices may even appear counterproductive in some cases...
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