R help - Mar 2016 - Is there dpois equivalent for zero-inflated Poisson?

Could you clarify what are the parameters and why it?s formulated that way?

-Matti
> On 22 Mar 2016, at 14:17, Thierry Onkelinx <thierry.onkelinx at
inbo.be> wrote:
> 
> Dear Matti,
> 
> What about this?
> 
> dzeroinflpois <- function(x, lambda, zero){
>   ifelse(x == 0, zero, 0) + dpois(x, lambda) / (1 - zero)
> }
> plot(x, dzeroinflpois(x, lambda = 10, zero = 0.2), type = "l")
> 
> 
> 
> ir. Thierry Onkelinx
> Instituut voor natuur- en bosonderzoek / Research Institute for Nature and
Forest
> team Biometrie & Kwaliteitszorg / team Biometrics & Quality
Assurance
> Kliniekstraat 25
> 1070 Anderlecht
> Belgium
> 
> To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to say what
the experiment died of. ~ Sir Ronald Aylmer Fisher
> The plural of anecdote is not data. ~ Roger Brinner 
> The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of data. ~
John Tukey
> 
> 2016-03-22 13:04 GMT+01:00 Matti Viljamaa <mviljamaa at kapsi.fi
<mailto:mviljamaa at kapsi.fi>>:
> I?m doing some optimisation that I first did with normal Poisson (only
parameter theta was estimated), but now I?m doing the same with a zero-inflated
Poisson model which
> gives me two estimated parameters theta and p (p is also pi in some
notation).
> 
> My question is, is there something equivalent to dpois that would use both
of the parameters (or is the p parameter possibly unnecessary)?
> 
> I?m calculating the ?fit? of the Poisson model
> 
> i.e. like
> 
> x = c(0,1,2,3,4,5,6)
> y = c(3062,587,284,103,33,4,2)
> fit1 <- sum(y)*dpois(x, est_theta)
> 
> and then comparing fit1 to the real observations.
>         [[alternative HTML version deleted]]
> 
> ______________________________________________
> R-help at r-project.org <mailto:R-help at r-project.org> mailing list
-- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
<https://stat.ethz.ch/mailman/listinfo/r-help>
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
<http://www.r-project.org/posting-guide.html>
> and provide commented, minimal, self-contained, reproducible code.
> 

	[[alternative HTML version deleted]]

zero = proportion of zero inflation part
lamba = expected value of poisson part

There was a typo in the distribution. It should multiple by (1 - zero)
instead of divide by it.

dzeroinflpois <- function(x, lambda, zero){
  ifelse(x == 0, zero, 0) + dpois(x, lambda) * (1 - zero)
}

ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and
Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium

To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to say
what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of data.
~ John Tukey

2016-03-22 13:25 GMT+01:00 Matti Viljamaa <mviljamaa at kapsi.fi>:
> Could you clarify what are the parameters and why it?s formulated that way?
>
> -Matti
>
> On 22 Mar 2016, at 14:17, Thierry Onkelinx <thierry.onkelinx at
inbo.be>
> wrote:
>
> Dear Matti,
>
> What about this?
>
> dzeroinflpois <- function(x, lambda, zero){
>   ifelse(x == 0, zero, 0) + dpois(x, lambda) / (1 - zero)
> }
> plot(x, dzeroinflpois(x, lambda = 10, zero = 0.2), type = "l")
>
>
>
> ir. Thierry Onkelinx
> Instituut voor natuur- en bosonderzoek / Research Institute for Nature and
> Forest
> team Biometrie & Kwaliteitszorg / team Biometrics & Quality
Assurance
> Kliniekstraat 25
> 1070 Anderlecht
> Belgium
>
> To call in the statistician after the experiment is done may be no more
> than asking him to perform a post-mortem examination: he may be able to say
> what the experiment died of. ~ Sir Ronald Aylmer Fisher
> The plural of anecdote is not data. ~ Roger Brinner
> The combination of some data and an aching desire for an answer does not
> ensure that a reasonable answer can be extracted from a given body of data.
> ~ John Tukey
>
> 2016-03-22 13:04 GMT+01:00 Matti Viljamaa <mviljamaa at kapsi.fi>:
>
>> I?m doing some optimisation that I first did with normal Poisson (only
>> parameter theta was estimated), but now I?m doing the same with a
>> zero-inflated Poisson model which
>> gives me two estimated parameters theta and p (p is also pi in some
>> notation).
>>
>> My question is, is there something equivalent to dpois that would use
>> both of the parameters (or is the p parameter possibly unnecessary)?
>>
>> I?m calculating the ?fit? of the Poisson model
>>
>> i.e. like
>>
>> x = c(0,1,2,3,4,5,6)
>> y = c(3062,587,284,103,33,4,2)
>> fit1 <- sum(y)*dpois(x, est_theta)
>>
>> and then comparing fit1 to the real observations.
>>         [[alternative HTML version deleted]]
>>
>> ______________________________________________
>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> <http://www.r-project.org/posting-guide.html>
>> and provide commented, minimal, self-contained, reproducible code.
>
>
>
>
	[[alternative HTML version deleted]]

And why is the first term of ifelse(x == 0, zero, 0) + dpois(x, lambda) / (1 -
zero)

ifelse(x == 0, zero, 0)

rather than something corresponding to

zero+(1-zero)e^{-lambda}

https://en.wikipedia.org/wiki/Zero-inflated_model#Zero-inflated_Poisson
> On 22 Mar 2016, at 14:25, Matti Viljamaa <mviljamaa at kapsi.fi>
wrote:
> 
> Could you clarify what are the parameters and why it?s formulated that way?
> 
> -Matti
> 
>> On 22 Mar 2016, at 14:17, Thierry Onkelinx <thierry.onkelinx at
inbo.be <mailto:thierry.onkelinx at inbo.be>> wrote:
>> 
>> Dear Matti,
>> 
>> What about this?
>> 
>> dzeroinflpois <- function(x, lambda, zero){
>>   ifelse(x == 0, zero, 0) + dpois(x, lambda) / (1 - zero)
>> }
>> plot(x, dzeroinflpois(x, lambda = 10, zero = 0.2), type =
"l")
>> 
>> 
>> 
>> ir. Thierry Onkelinx
>> Instituut voor natuur- en bosonderzoek / Research Institute for Nature
and Forest
>> team Biometrie & Kwaliteitszorg / team Biometrics & Quality
Assurance
>> Kliniekstraat 25
>> 1070 Anderlecht
>> Belgium
>> 
>> To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to say what
the experiment died of. ~ Sir Ronald Aylmer Fisher
>> The plural of anecdote is not data. ~ Roger Brinner 
>> The combination of some data and an aching desire for an answer does
not ensure that a reasonable answer can be extracted from a given body of data.
~ John Tukey
>> 
>> 2016-03-22 13:04 GMT+01:00 Matti Viljamaa <mviljamaa at kapsi.fi
<mailto:mviljamaa at kapsi.fi>>:
>> I?m doing some optimisation that I first did with normal Poisson (only
parameter theta was estimated), but now I?m doing the same with a zero-inflated
Poisson model which
>> gives me two estimated parameters theta and p (p is also pi in some
notation).
>> 
>> My question is, is there something equivalent to dpois that would use
both of the parameters (or is the p parameter possibly unnecessary)?
>> 
>> I?m calculating the ?fit? of the Poisson model
>> 
>> i.e. like
>> 
>> x = c(0,1,2,3,4,5,6)
>> y = c(3062,587,284,103,33,4,2)
>> fit1 <- sum(y)*dpois(x, est_theta)
>> 
>> and then comparing fit1 to the real observations.
>>         [[alternative HTML version deleted]]
>> 
>> ______________________________________________
>> R-help at r-project.org <mailto:R-help at r-project.org> mailing
list -- To UNSUBSCRIBE and more, see
>> https://stat.ethz.ch/mailman/listinfo/r-help
<https://stat.ethz.ch/mailman/listinfo/r-help>
>> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
<http://www.r-project.org/posting-guide.html>
>> and provide commented, minimal, self-contained, reproducible code.
>> 
> 
	[[alternative HTML version deleted]]

dpois(0, lambda) == e^(-lambda)

The wikipedia formula is
ifelse(x == 0, zero + dpois(0, lambda) * (1-zero), dpois(x, lambda) *
(1-zero))

or

ifelse(x == 0, zero + dpois(x, lambda) * (1-zero), dpois(x, lambda) *
(1-zero))

so we can move the dpois() out of the ifelse()

ifelse(x == 0, zero, 0)  + dpois(x, lambda) * (1-zero)



ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and
Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium

To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to say
what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of data.
~ John Tukey

2016-03-22 13:50 GMT+01:00 Matti Viljamaa <mviljamaa at kapsi.fi>:
> And why is the first term of ifelse(x == 0, zero, 0) + dpois(x, lambda) /
> (1 - zero)
>
> ifelse(x == 0, zero, 0)
>
> rather than something corresponding to
>
> zero+(1-zero)e^{-lambda}
>
> https://en.wikipedia.org/wiki/Zero-inflated_model#Zero-inflated_Poisson
>
> On 22 Mar 2016, at 14:25, Matti Viljamaa <mviljamaa at kapsi.fi>
wrote:
>
> Could you clarify what are the parameters and why it?s formulated that way?
>
> -Matti
>
> On 22 Mar 2016, at 14:17, Thierry Onkelinx <thierry.onkelinx at
inbo.be>
> wrote:
>
> Dear Matti,
>
> What about this?
>
> dzeroinflpois <- function(x, lambda, zero){
>   ifelse(x == 0, zero, 0) + dpois(x, lambda) / (1 - zero)
> }
> plot(x, dzeroinflpois(x, lambda = 10, zero = 0.2), type = "l")
>
>
>
> ir. Thierry Onkelinx
> Instituut voor natuur- en bosonderzoek / Research Institute for Nature and
> Forest
> team Biometrie & Kwaliteitszorg / team Biometrics & Quality
Assurance
> Kliniekstraat 25
> 1070 Anderlecht
> Belgium
>
> To call in the statistician after the experiment is done may be no more
> than asking him to perform a post-mortem examination: he may be able to say
> what the experiment died of. ~ Sir Ronald Aylmer Fisher
> The plural of anecdote is not data. ~ Roger Brinner
> The combination of some data and an aching desire for an answer does not
> ensure that a reasonable answer can be extracted from a given body of data.
> ~ John Tukey
>
> 2016-03-22 13:04 GMT+01:00 Matti Viljamaa <mviljamaa at kapsi.fi>:
>
>> I?m doing some optimisation that I first did with normal Poisson (only
>> parameter theta was estimated), but now I?m doing the same with a
>> zero-inflated Poisson model which
>> gives me two estimated parameters theta and p (p is also pi in some
>> notation).
>>
>> My question is, is there something equivalent to dpois that would use
>> both of the parameters (or is the p parameter possibly unnecessary)?
>>
>> I?m calculating the ?fit? of the Poisson model
>>
>> i.e. like
>>
>> x = c(0,1,2,3,4,5,6)
>> y = c(3062,587,284,103,33,4,2)
>> fit1 <- sum(y)*dpois(x, est_theta)
>>
>> and then comparing fit1 to the real observations.
>>         [[alternative HTML version deleted]]
>>
>> ______________________________________________
>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> <http://www.r-project.org/posting-guide.html>
>> and provide commented, minimal, self-contained, reproducible code.
>
>
>
>
	[[alternative HTML version deleted]]