Warning when using non-normal link function for generalized linear models with fitglme

When I fit my data to a generalized linear model using the function fitglme, I get the following warning:

Warning: The 'Reciprocal' and 'Power' links require the linear predictor to be non-negative. However, the model
assumes that the linear predictor is unconstrained. 

This happens although the data are non-negative, and I do not see any option to tell the fitting function that it should not worry. Question: How do I avoid this warning? (I mean "avoid" not "suppress". A warning usually indicates that something is wrong, so how do I correct it?)

Answer 1

[Ayush]

Hey Kim,

I understand that you are encountering a warning when fitting a generalized linear model using fitglme in MATLAB, specifically when employing 'Reciprocal' or 'Power' link functions. This warning is due to the requirement for the linear predictor to be non-negative, and you're looking for a way to address this issue.

To avoid the warning about the linear predictor being non-negative when using 'Reciprocal' or 'Power' links in "fitglme", consider the following approaches:

1. Transform Predictors: Adjust your predictor variables through transformations (e.g., logarithmic) to ensure the linear predictor remains positive.
2. Change Link Function: If possible, switch to a different link function that doesn't require a strictly positive linear predictor, such as the log link or the identity link.
3. Initial Values: Check and adjust the initial values for the model fitting process to guide it towards a solution that maintains a positive linear predictor.

For more information on the link functions , you can refer to the following MathWorks documentation: https://in.mathworks.com/help/stats/fitglme.html

Hope this helps!

Regards

[Kim Bostroem]

Hi Ayush, thank you so much for your response!

However, I do not understand what I would have to do, really.

Transform Predictors: What do you mean by transforming the predictor? I thought, Generalized linear models are superior to standard linear models of transformed variables, which is why I use them in the first place. Sure, I could transform my dependent variable by log function and then perform a standard linear model fit on the transformed data, but then I would not need special distribution and link functions in the first place. Also, this is not really equivalent to using a Generalized linear model (with the appropriate distribution and link function). Or did I misunderstand you here?

Change Link Function: the log as a link function throws the same warning, as it also requires non-negative data. The identity link is not appropriate for Gamma and InverseGaussian distribution. I would rather stick to their corresponding canonical link functions or at least a best-fit alternative, which is in most cases not the identity function.

Initial Values: This sounds interesting, but how can I accomplish this, using fitglme?

Sorry for being stupid, but may I ask you for some clarification on these issues? I would be very thankful!