[R-sig-ME] about: GLMM for continuous response

[David Winsemius]

When you responded to me privately, you included useful information and code that could have been assessed by other subscribers of this mailing list. I would encourage you to post that reply to the mailing list as well. I am by no means the most knowledgeable on `lmer` numerical stability questions.

I continue to think that using policy number as a random effect and also number of claims as a fixed effect is incorrect on methodological grounds and may also be the cause of your convergence errors and variations in the parameter estimates.

-- 
David 

On Oct 17, 2015, at 1:24 PM, David Winsemius wrote:

> 
> On Oct 15, 2015, at 6:02 AM, Aslıhan Şentürk Acar wrote:
> 
>> 
>> Dear Sir,
>> 
>> I am a Phd student working on GLMM implementation for continuous response of insurance claim size. I have some problems to implement GLMM in R. I would be very glad if you could answer.
>> 
>> Response variable y_ij: jth claim amount of individual i. People can have just one claim or more than one claim (max. claim number is 136. so j=1,2,...,136).
> 
> What about zero claims? Those are the policy holders who are paying for persons or entities who did have non-zero claims. 
> 
>> 
>> There are 22 000 individuals in the sample. Explanatory variables are (fixed effects): claim number in one year (integer), age(integer), gender (0-1,factor), provience (0-6,factor), package (0-3,factor), marital status (0-1,factor).
>> 
> 
> Including 'claim number' as a fixed effect would seem to be highly questionable. It presumes you could have known in advance who would become the high claim policyholders.
> 
> 
>> *I use only random intercept as random effect.
>> 
>> I am using R 3.0.3, MASS, lme4,nlme and lm4.0 packages.
>> 
>> My questions are:
>> 
>> 
>> 1- I use GLMMPQL (MASS package) that generally converges. But laplace and quadrature never converges. I did not understand the reason. What can be the reason? While implementing GLMM are the individuals that have just one claim problem for model convergence?
>> 
> 
> You should offer actual code samples. I get the impression you are using more than just the glmmPQL function, since ?glmmPQL says options are passed to lme and those are not offered as options in the ?lmeControl page.
> 
>> note: gamma glm, log transform and linear mixed model, gamma GEE all converges.
>> 
>> 2- I simulated gamma distributed response variable and used a few covariates to test convergence error. Laplace converges, Quadrature does not converge again. While PQL gives 0.2632854 for standard deviation of random intercept, glmer (laplace) gives std. dev 1028.16. Why is so huge difference between two methods?
> 
> Wouldn't the data and code be needed for an answer? The FAQ says gamma models can be "difficult": http://glmm.wikidot.com/faq. It makes me wonder whether you have achieved complete separation in one of the models through excessive control for the claim-number variable.
> 
> 
>> 
>> 3- GLMMPQL converges with all explanatory variables. Province and gender are not significant. When I exclude only province GLMMPQL does not converge. But when I exclude gender and both province+gender it converges. Why is this contradiction?
> 
> Wouldn't we need to see the data to answer such a question?
> 
>> 
>> 4- I could not see any paper on GLMM applications for continuous response.
> 
> ???  Gamma is not a continuous response? Log-normal as well?
> 
> https://www.researchgate.net/profile/Jostein_Paulsen/publication/222532925_Fitting_mixed-effects_models_when_data_are_left_truncated/links/0c96052542940503ac000000.pdf
> 
> 
>> I am afraid of doing something wrong but I ca not find any reference. Can you give me any references to understand detail of GLMM implementation for continuous response and general idea for implementation of GLMM.
>> 
> 
> Wouldn't that simply depend on what `family` (or link) argument was offered to your regression function?
> 
>> 5- I do not want to make logarithmic transform and fit linear mixed models, I want to use data on original scale. Do you offer any other distribution exempt gamma GLMM?
> 
> Do you have some descriptive data regarding the response? Seems that insurance claims problems should be using truncated distributions if at all possible. (See the citation above.)  There is often both a minimum and maximum value for coverage.
> 
>> 
>> 
>> I appreciate any help.
>> 
>> Thank you very much.
>> 
>> Best wishes,
>> 
>> Aslihan
>> 
>> 
>> -- 
>> Aslihan Senturk Acar
>> 
>> Research Assistant
>> Hacettepe University
>> Department of Actuarial Sciences
>> Beytepe, Ankara
>> 08600
>> 
>> Phone: (+90) 312 297 6160 / 119
>> Email: aslihans at hacettepe.edu.tr
>> 
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> 
> David Winsemius
> Alameda, CA, USA
> 
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David Winsemius
Alameda, CA, USA