Dear Charllote,

Although, the SEM packages are quite flexible I think for such kind of repeated measures and multiple response variables, you can find more suitable and easy approaches as for example the class of multivariate covariance generalized linear models. This class will provide you a more flexible modelling of the covariance between and within response variables and also the possibility to deal with non-Gaussian response variables. You can find useful to have a look at this paper

http://onlinelibrary.wiley.com/doi/10.1111/rssc.12145/full

and the associated R package

https://cran.r-project.org/web/packages/mcglm/index.html

All the best

Dear Wagner,

Thanks for your quick response. Your mcglm package seems very interesting for multivariate analyses (which I performed using the MCMCglmm package), especially with non-standard covariance structures. However, as far as I understand, it does not deal with path analysis models, in which an exogenous variable can influence an endogenous variable both directly and through other endogenous variables.This is precisely what I am struggling with. Do you have any insight as to how to perform such path analysis on longitudinal data using mcglm or another package?

Best,

Charlotte

In general the mcglm can deal with the same data structure that the MCMCglmm package. You are right, in path analysis you can use an non-observable variable as covariate for another response variable, but this option is not possible using mcglm.

I did not get this requirement in your first question. I pain attention only to the longitudinal and multivariate analysis.

Best

Well, I am not planning to use latent variables through structural equation modelling, but rather to perform a path analysis on observed variables, as in the attached diagram. Could mcglm handle that?

Hi Charlotte,

It is a really good question, I am not sure.

I did not implement the mcglm package for this kind of analysis.

However, if your traits are observed I think you can fit this model easily using mcglm.

It is not exactly the same model, because it will compute all possible correlations, i.e. in your example a four by four correlation matrix. In your model you have just one covariance between trait1 and trait2.

From correlation to covariance you just have to re parametrized the model.

Please, have a look at the attached code and let me know if it works for your data.

All the best!

Hi Wagner,

I ran your script on my data and got similar results to those obtained with SEM, as it should be since the covariance parameters I constrained to zero are relatively low. That's a good start!

Now I am playing with this to adapt it to repeated measures. I assume I should combine the identity matrix with other matrices describing the variance structure (e.g. one matrix for individuals and one matrix for years), but I do not understand how these should be passed to the "matrix_pred" argument. Additionally, I am not sure how to code the different levels of covariance between variables. To be honest, a sample code in the R help file and/or the supporting paper who have been great (and it's not too late for the former :-))

I also tried  to make trait3 a binomial variable. According to the error message, the Cholesky factorization failed. Is it just that it cannot compute the model or did I do something wrong?

Thanks a lot for your time!

Hi Charlotte,

Indeed, the paper is under review. Probably, it will be published soon.

In the attached code, I include a more complex model.

The trait3 is binary and you have a repeated measures structure.

You can include basically any symmetric matrix in the linear predictor.

Suppose, you have two matrix Z1 and Z2 that you want to include in the matrix linear predictor for all of your 4 response variable. So, the linear_pred arguments will receive a list like this

matrix_pred = list(c(Z0, Z1), c(Z0, Z1), c(Z0, Z1), c(Z0, Z1))

If you have more just include

matrix_pred = list(c(Z0, Z1), c(Z0, Z1), c(Z0, Z1), c(Z0, Z1, Z3, Z4, ...))

You can use different matrix linear predictor for each response variable, as well.

However, the correlation between response variable cannot depend on covariates in a regression model fashion.

All the best

Hi Walter,

Great! I can definitely define the matrices myself, I just wasn't sure how to specify them in the model. And the convergence problem with binary data probably came from how I simulated the binary data.

btw, I also posted the question on Cross Validated (link below), so if you want to get credit there for your solution to my problem, feel free to post your last script with your explanations. Else, I will post your answer myself, of course citing you.

Thanks a lot for your help! I will let you know if we publish this.

http://stats.stackexchange.com/questions/234217/how-to-model-longitudinal-data-in-a-path-analysis

Hello Charlotte Récapet ,

I had been trying to solve a similar problem as yours (repeated measures in time with varying times, and a binomial output response in a path analysis). I can follow the R script very well however, when I try to add the repeated measures structure into the analysis with the the Z1 (100x100 matrix as in the example R script), I come across with non-matching dimensions problem. I don't think I am doing anything wrong. Could you please let me know if you also came across with the same error, or else how you approached this problem?

Many thanks in advance.

Wagner Hugo Bonat many thanks for the R script file.

Sebnem