Interesting problem, I don't have an answer but have an example that may increase your understanding? My first thought was something's wrong, not to try and explain why it may be greater than 1. So I did some searching and found this example of where r-hat can yield unusual answer in a vector problem - hope it helps and doesn't make more complicated? I think there is something in there that might help?

Let’s suppose, just to make this discussion more concrete, that rˆ is at 36.0° (counterclockwise from the +x direction in the x-y plane)

The fact that a unit vector has a magnitude 1, with no units, means that if you multiply a unit vector by a scalar, the resulting vector has a magnitude equal to the value- with-units of the scalar. So for instance if you multiply a vector (r-hat) by 5.00 m/s, you get a

Velocity vector 5.00(m/s)rˆ which has a magnitude of 5.00 m/s and points in the same direction as the unit vector rˆ . Thus, in the case at hand, 5.00(m/s)rˆ, means 5.00 m/s at 36.0°. The message here is mixing vectors and scalers (data) can yield anomalous results

Hi John:

- Did you use covariates? Did you scaled them?

- Consider changing the parametrizacion. Sometimes you can improve the convergence .

- What's the magnitude of p? As you know, with very low p values, the results would be inconsistent.

Jose