Individual Covariate testing - zero SE estimate

questions concerning analysis/theory using programs M-SURGE, E-SURGE and U-CARE

Re: Individual Covariate testing - zero SE estimate

Postby simone77 » Thu Mar 20, 2014 7:14 am

Hi Guillaume,
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.
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Re: Individual Covariate testing - zero SE estimate

Postby Guillaume Souchay » Thu Mar 20, 2014 11:33 am

Hi Simone,

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.

Not exactly. A parameter can be well estimated and at the boundary.
This trick is to investigate if the parameter at the boundary is identifiable or not. If you fix the parameter, if the deviance remains the same, thus, the parameter is not identifiable. Else, it is identifiable and estimated at the boundary.

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...

Yes, this is the point of your problem. To fix the slope was a method to check if the parameter is well identifiable.
To try this trick, it's better to use the "From last model" option, thus, is should avoid other parameter issues and the difference in the deviance value will only be the result of fixing the parameter.
I know that you had some pb with the "from lat model" option, in that case, you should have no pb. You just have to run your model (or retrieve it) and only fix the value to 0.02 (even to 0.01) in the IVFV and run the model. I hope the model can converge.

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?

I understood that you only have 1 measure of the body mass.
I'm trying to explain my point better:
when you are using an individual covariate, you are using the model: logit(Psi)= i + slope*Cov
Thus, the whole variance of Psi is expected to be explained by the covariate.
When you add a individual random effect, you are then using: logit(Psi)= i + slope*Cov + e, with e the random ind effect.
Thus, you are now explaining a great part of variance of psi by your covariate and you have the residual variance in the random effect. Thus, the relationship between Psi and the covariate is quite relaxed.

I don't know if it could solve the problem or not, but it can be tried also to see if the slope is still 0.

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.

Yes, the initial point (slope=0.0)is that the covariate is explaining nothing.

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.

Usually, to deal with parameters at the boundary, the EM(20) option is a good thing. To start from the final value of the model without the covariate(again the From Last Model option), and thus, to only have to estimate the slope with the EM(20) could be helpful. But, unfortunately, you already tried that.

Just to check if there is a problem with the slope itself or something else, did you try to input your covariate on another parameter (e.g. a survival rate)?
If again, the slope is 0 and no SE, then, there might be a problem with the covariate itself (I don't know why but it could be a clue).
If the slope is identifiable, estimated and different from 0, then, the 0 is just reflecting that the body mass doesn't explain variation in the transition you're interested in ... (even if the deviance is decreasing).

Hope it could help ...

Guillaume
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Re: Individual Covariate testing - zero SE estimate

Postby simone77 » Fri Mar 21, 2014 8:28 am

Thank you again for your help. My previous comments are in italic.

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.
Guillaume wrote:Not exactly. A parameter can be well estimated and at the boundary.
This trick is to investigate if the parameter at the boundary is identifiable or not. If you fix the parameter, if the deviance remains the same, thus, the parameter is not identifiable. Else, it is identifiable and estimated at the boundary.

Right. I meant at the boundary and not estimable.

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:Yes, this is the point of your problem. To fix the slope was a method to check if the parameter is well identifiable.
To try this trick, it's better to use the "From last model" option, thus, is should avoid other parameter issues and the difference in the deviance value will only be the result of fixing the parameter.
I know that you had some pb with the "from lat model" option, in that case, you should have no pb. You just have to run your model (or retrieve it) and only fix the value to 0.02 (even to 0.01) in the IVFV and run the model. I hope the model can converge.

I have made several trials slightly changing the value to be fixed and using both "from last model" or "multiple random" options: No way to make it converge. However, beyond understanding clearly if the parameter is estimable or not, I believe the fact the deviance decreases so much is the main question and at the moment I haven't found an answer to this.

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?
Guillaume wrote:I understood that you only have 1 measure of the body mass.
I'm trying to explain my point better:
when you are using an individual covariate, you are using the model: logit(Psi)= i + slope*Cov
Thus, the whole variance of Psi is expected to be explained by the covariate.
When you add a individual random effect, you are then using: logit(Psi)= i + slope*Cov + e, with e the random ind effect.
Thus, you are now explaining a great part of variance of psi by your covariate and you have the residual variance in the random effect. Thus, the relationship between Psi and the covariate is quite relaxed.
I don't know if it could solve the problem or not, but it can be tried also to see if the slope is still 0.

I have tried to add a random effect by modifying the sentence
"a(1).g(2).f(1 2).[i+xind]+a(1).g(2).f(3 4)+a(1).g(1).f(1 2,3 4)+a(2).g(1,2).f(1 2,3 4)" for
"a(1).g(2).f(1 2).[i+xind+ind]+a(1).g(2).f(3 4)+a(1).g(1).f(1 2,3 4)+a(2).g(1,2).f(1 2,3 4)"
The output was exactly the same, no change in deviance and no change in the individual covariate parameter estimate.

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.
Guillaume wrote:Yes, the initial point (slope=0.0)is that the covariate is explaining nothing.

I referred to the fact that the initial starting value for the individual covariate parameter seems to be always zero (by watching the value in the IVFV after setting the multiple random option). I wondered if this may hamper the ability to use multiple random initial values as a way to deal with local minima. Imagine there is a local minima for that parameter being very close to zero: if for every iterations cycle it starts again from zero, you might not be able to "jump" far from that region of the likelihood and then not able to find other minima. However, I guess there is some explanation for this, perhaps Rémi may give an answer to this.

Guillaume wrote:Usually, to deal with parameters at the boundary, the EM(20) option is a good thing. To start from the final value of the model without the covariate(again the From Last Model option), and thus, to only have to estimate the slope with the EM(20) could be helpful. But, unfortunately, you already tried that. Just to check if there is a problem with the slope itself or something else, did you try to input your covariate on another parameter (e.g. a survival rate)?
If again, the slope is 0 and no SE, then, there might be a problem with the covariate itself (I don't know why but it could be a clue).
If the slope is identifiable, estimated and different from 0, then, the 0 is just reflecting that the body mass doesn't explain variation in the transition you're interested in ... (even if the deviance is decreasing)..

Yes. I have tried to use it in survival instead of state-transition, it works, the correspondent parameter for body mass is estimable. I believe this confirms there is nothing wrong with the individual covariate per se, however I don't see the link with the body mass not being related to the state-transition parameter.
Hope to find some explanation to this.
simone77
 
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Re: Individual Covariate testing - zero SE estimate

Postby Guillaume Souchay » Fri Mar 21, 2014 9:00 am

Hi Simone,
sorry not to be able to be more helpful. It is now exceeding my abilities.

That only one parameter can have such a great effect on deviance is quite strange, but maybe there is a more mathematical explaination.

I think Remy is still busy with the E-SURGE workshop. But I hope he will be able to help you after.

Guillaume
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Re: Individual Covariate testing - zero SE estimate

Postby CHOQUET » Mon Mar 24, 2014 8:27 am

One clarrification:

a value of -50 for a slope doesn't mean that the slope is zero because
the slope is not straightly backtransformed. The backtransformation is
on the intercept + slope * value.
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Re: Individual Covariate testing - zero SE estimate

Postby simone77 » Mon Mar 24, 2014 10:50 am

CHOQUET wrote:One clarrification:

a value of -50 for a slope doesn't mean that the slope is zero because
the slope is not straightly backtransformed. The backtransformation is
on the intercept + slope * value.


Hi Rémi,

Thank you for making me see this important point. OK, then by considering this sentence in GEMACO used for Transition step 2 (seroconversion rate):
a(1).g(2).f(1 2).[i+xind]+a(1).g(2).f(3 4)+a(1).g(1).f(1 2,3 4)+a(2).g(1,2).f(1 2,3 4)
(as I am modelling trap dependence, state 1 & 2 corresponds to sero- whereas 3 & 4 to sero+)

I have taken as intercept the first parameter of step 2 and as slope the last parameter of transition (in the IVFV window the slope for the individual covariate corresponds to that parameter) and computed the seroconversion rate by using this formula:
Psero- ->sero+=e^(int+slope*StMassi)/(1+e^(int+slope*StMassi))
where StMass corresponds to the standardized value of Mass.
Up to here, everything right?

By plotting these values against the Body mass on the real scale I get this:
Image

suggesting an almost entirely bivariate response of seroconversion rate to body mass variation.
Could be it related to the lack of SE estimate?
Do you have any suggestion on how to handle this situation?
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Re: Individual Covariate testing - zero SE estimate

Postby CHOQUET » Wed Mar 26, 2014 6:24 am

One stupid question: did you look for the correct beta in the output file ?
The order of the mathematical parameter is the order of display of parameters in the IVFV.

Rémi
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Re: Individual Covariate testing - zero SE estimate

Postby simone77 » Wed Mar 26, 2014 7:39 am

CHOQUET wrote:One stupid question: did you look for the correct beta in the output file ?
The order of the mathematical parameter is the order of display of parameters in the IVFV.

This is what I have in the IVFV:
Image
And these are the betas (first nine are not shown, they refer to Initial State):
Image
Then for this equation:
Psero- ->sero+=e^(int+slope*StMassi)/(1+e^(int+slope*StMassi))
I have used the parameter no. 14 (5 in the Transition IVFV) as the intercept and parameter no. 39 (30 in the Transition IVFV) for the slope.
The 25th parameter is non-estimable as it corresponds to the probability a previously seen individual has to be captured (I have tried to fix it and the result does not change).
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Re: Individual Covariate testing - zero SE estimate

Postby CHOQUET » Wed Mar 26, 2014 11:01 am

39 has a value of 1.35 !!
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Re: Individual Covariate testing - zero SE estimate

Postby simone77 » Wed Mar 26, 2014 1:15 pm

CHOQUET wrote:39 has a value of 1.35 !!

You are watching at the row number of excel, not at the parameter index number.
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