Thanks four your suggestions.
Guillaume wrote:Did you try to fix the slope to a value of 0.05 to see if the model converges to the same deviance or not? To fix a parameter estimate at the boundary can help to check if this parameter is really estimated or not, and if indeed estimated, by looking at different fixed values of this parameter, you can estimate the 95%CI.
If I understand it correctly: if the parameter suspected to be at the boundary is fixed and the deviance and model rank keeps the same, it would mean that the parameter is really at the boundary and is not estimated.
I have tried it but the model does not converge at all. However, beyond the fact this is a boundary estimate or not (it seems to be for the estimate value it has), to me the point is that the model with and the model without the individual covariate are identical except for one parameter being explained by the individual covariate. If the deviance of the model with the individual covariate has decreased with respect to the model without it, I would believe that the effect of the individual covariate is absorbing deviance. Though, this slope is estimated to be almost zero...
Guillaume wrote:I also have just a suggestion about the modelling with the covariate. You could also try to include an individual random effect in the model to relax a little the strength of the relationship between the survival and to get a estimated of the residual variance.
You could also see if the deviance is still decreasing or being the same than previous models.
I haven't tried this because I am not sure to understand it. The individual covariate only applies for the first interval after first individual capture, i.e. no repeated measures of body mass for each individual exists. Then, on one hand I would believe that my sample size is not big enough to include an individual random effect on state-transition parameter type, on the other, if individual heterogeneity exists, this should be both the model with and without the individual covariate and therefore I don't see how it may help to solve the problem we are talking about. Perhaps you were thinking that repeated measures from a same individual existed, weren't you?
Finally, I have noticed that the initial value (multiple random option) for the individual covariate parameter is always set to zero (it does not vary), I guess there is some reason for that, however I have tried to set it to 0.5, without fixing it. I get again the same identical results as above. However I imagine that for each new iterations cycle after the first one (which has been set to 0.5 in this case) it always set the initial value for the individual covariate to zero. Then, I wonder if this might prevent the multiple random option for the individual covariate to be an effective procedure against local minima. In other words, I am worried about the fact it could exist a local minima for the individual covariate slope close to zero and I cannot get rid of this because for each iteration cycle the correspondent initial value is set always to zero.