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Problem

Using R, how can I build a logistic regression model with serial correlation or a general linear mixed model with ARMA?

I cannot use linear regression because I have serial correlation. I cannot use ARMA because I have binary predication target.

I consulted with a statistician and they told me this is my situation. It is a multivariate time series with a univariate, but binary predictor. Simply said, I have multiple independent variables such as heart rate, GIS zone, zone rating, participant id, temp and I want to predict a binary variable called fatigue which is 0 or 1. I'm finding some material in SAS, but need to use R to solve this.

Having suggestions where to start would be immensely useful and how to define the model.

Right now for logistic, I am thinking of something like: 

model <- glm(fatigue ~ participant + hr + temp + zone + zone_rating)

However, this in no way is taking into account my serial correlated data.

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    $\begingroup$ "I cannot use linear regression because I have serial correlation"... This is simply incorrect, nothing prevents from the recovering the condtional exceptation $E[Y|X]$ in this case. Regardless you might want to consider the 'GLS' function in the package 'nlme' which has a correlation argument, where you can speficify the ARMA structure on the errors. $\endgroup$
    – Repmat
    Commented Oct 11, 2016 at 10:09
  • $\begingroup$ Is GLS with a correlation argument a generalized linear mixed model? $\endgroup$
    – GeekyOmega
    Commented Oct 11, 2016 at 13:22

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