This error message indicates that the distribution's estimated mean falls outside its valid range when using the estimated parameters of the model to estimate the mean. For example, in a binomial response (logistic) model, this error appears if the estimated binomial mean, p, is less than zero or greater than one. In a Poisson model, it appears if the estimated Poisson mean, λ, is less than zero.

There is no single cause for this error message that can be readily seen by examining the data or model specification. However, the error often happens when the default link function is not used. For example, when the response has a binomial distribution, the default logit link maps any value of the linear predictor (x'β) into the valid range for the binomial mean (0≤p≤1) which usually avoids this error. But if you instead use the log link function, such as when trying to model a relative risk, this error message occurs when the linear predictor is positive for some observation resulting in an estimated mean greater than one. Similarly, the use of the identity link does not ensure valid mean values for response distributions having bounded ranges of their means such the binomial, Poisson, gamma, and others. When using nondefault link functions, the estimated mean may remain in its valid range for a given model and a particular set of data, but any change in the model or data may result in an invalid estimated mean for one or more observations.

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