Why use the log_e function as link function for Poisson data in a GLM model

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This has been puzzling me for quite some time.



Suppose I have som data, that I have justefied should be described using a GLM model with a poisson as response.



As for choice of link function, You would normally go for the $log_e $function, and I understand that to be the case. Since we ofte observe, when working with count data. That the effekt of an observation is proportional to the side of size of the observation (ie. The predicter should be multiplicatice)



But would all this be true even if i chose log function such as the $ log_10$. Why do we always turn to the natural logarithm?




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  • What difference would that make? The coefficients would change by a scaling factor of $ln(10)$ (and their standard errors would change by the same factor, so the p-values would be unaltered). Meanwhile the fitted values would all be exactly the same. You could take any present output and convert it to a log-10 link after the fact.
    – Glen_b
    Aug 25 at 3:35















up vote
1
down vote

favorite
1












This has been puzzling me for quite some time.



Suppose I have som data, that I have justefied should be described using a GLM model with a poisson as response.



As for choice of link function, You would normally go for the $log_e $function, and I understand that to be the case. Since we ofte observe, when working with count data. That the effekt of an observation is proportional to the side of size of the observation (ie. The predicter should be multiplicatice)



But would all this be true even if i chose log function such as the $ log_10$. Why do we always turn to the natural logarithm?




statistics




share|cite|improve this question






















  • What difference would that make? The coefficients would change by a scaling factor of $ln(10)$ (and their standard errors would change by the same factor, so the p-values would be unaltered). Meanwhile the fitted values would all be exactly the same. You could take any present output and convert it to a log-10 link after the fact.
    – Glen_b
    Aug 25 at 3:35













up vote
1
down vote

favorite
1









up vote
1
down vote

favorite
1






1





This has been puzzling me for quite some time.



Suppose I have som data, that I have justefied should be described using a GLM model with a poisson as response.



As for choice of link function, You would normally go for the $log_e $function, and I understand that to be the case. Since we ofte observe, when working with count data. That the effekt of an observation is proportional to the side of size of the observation (ie. The predicter should be multiplicatice)



But would all this be true even if i chose log function such as the $ log_10$. Why do we always turn to the natural logarithm?




statistics




share|cite|improve this question














This has been puzzling me for quite some time.



Suppose I have som data, that I have justefied should be described using a GLM model with a poisson as response.



As for choice of link function, You would normally go for the $log_e $function, and I understand that to be the case. Since we ofte observe, when working with count data. That the effekt of an observation is proportional to the side of size of the observation (ie. The predicter should be multiplicatice)



But would all this be true even if i chose log function such as the $ log_10$. Why do we always turn to the natural logarithm?





statistics





share|cite|improve this question













share|cite|improve this question




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edited Aug 23 at 5:35

























asked Aug 23 at 5:14









Viktor Jeppesen

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  • What difference would that make? The coefficients would change by a scaling factor of $ln(10)$ (and their standard errors would change by the same factor, so the p-values would be unaltered). Meanwhile the fitted values would all be exactly the same. You could take any present output and convert it to a log-10 link after the fact.
    – Glen_b
    Aug 25 at 3:35

















  • What difference would that make? The coefficients would change by a scaling factor of $ln(10)$ (and their standard errors would change by the same factor, so the p-values would be unaltered). Meanwhile the fitted values would all be exactly the same. You could take any present output and convert it to a log-10 link after the fact.
    – Glen_b
    Aug 25 at 3:35
















What difference would that make? The coefficients would change by a scaling factor of $ln(10)$ (and their standard errors would change by the same factor, so the p-values would be unaltered). Meanwhile the fitted values would all be exactly the same. You could take any present output and convert it to a log-10 link after the fact.
– Glen_b
Aug 25 at 3:35





What difference would that make? The coefficients would change by a scaling factor of $ln(10)$ (and their standard errors would change by the same factor, so the p-values would be unaltered). Meanwhile the fitted values would all be exactly the same. You could take any present output and convert it to a log-10 link after the fact.
– Glen_b
Aug 25 at 3:35
















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