Re: [R] Predicted values for zero-inflated Poisson

2012-07-10 Thread Laura Lee
Alain-

Thanks again for the response. I guess my question is more related to R, which 
I'm learning as I go along. Could you provide guidance as to how I would code 
this in R?

Thanks,
Laura

From: Alain Zuur [via R] [mailto:ml-node+s789695n4635920...@n4.nabble.com]
Sent: Monday, July 09, 2012 5:20 PM
To: Lee, Laura
Subject: Re: Predicted values for zero-inflated Poisson

Laura Lee laura.lee at ncdenr.gov
Mon Jul 9 22:51:40 CEST 2012

 Previous message: [R] Predicted values for zero-inflated Poisson
 Next message: [R] Lavaan Package - How to Extract Residuals in Data Values
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Thanks for your reply. I do have a copy of Zero Inflated Models and
Generalized Linear Mixed Models with R and have been using that as a guide.
I applied the predict function (type=count) to the dataset for which I
built the model to compare the predicted bycatch numbers to the observed to
ensure I was doing things correctly. When I summed over the new predicted
variable, the value is over 500 whereas there were less than 10 observed.
I'd appreciate any advice regarding what I'm doing wrong.

--
View this message in context: 
http://r.789695.n4.nabble.com/Predicted-values-for-zero-inflated-Poisson-tp4635861p4635916.html
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AFZ:
Laurano...you don't want to compare the count part of the model with raw 
datayou need to compare
the Exp(Y) = (1-pi) * mu with the raw data. Have a look at the Epilogue 
chapterit shows the difference
between mu and (1-pi) * mu.



Alain







--

Dr. Alain F. Zuur
First author of:

1. Analysing Ecological Data (2007).
Zuur, AF, Ieno, EN and Smith, GM. Springer. 680 p.
URL: www.springer.com/0-387-45967-7http://www.springer.com/0-387-45967-7


2. Mixed effects models and extensions in ecology with R. (2009).
Zuur, AF, Ieno, EN, Walker, N, Saveliev, AA, and Smith, GM. Springer.
http://www.springer.com/life+sci/ecology/book/978-0-387-87457-9


3. A Beginner's Guide to R (2009).
Zuur, AF, Ieno, EN, Meesters, EHWG. Springer
http://www.springer.com/statistics/computational/book/978-0-387-93836-3


4. Zero Inflated Models and Generalized Linear Mixed Models with R. (2012) 
Zuur, Saveliev, Ieno.
http://www.highstat.com/book4.htm

Other books: http://www.highstat.com/books.htm


Statistical consultancy, courses, data analysis and software
Highland Statistics Ltd.
6 Laverock road
UK - AB41 6FN Newburgh
Tel: 0044 1358 788177
Email: [hidden email]/user/SendEmail.jtp?type=nodenode=4635920i=0
URL: www.highstat.comhttp://www.highstat.com
URL: www.brodgar.comhttp://www.brodgar.com


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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
Dr. Alain F. Zuur
First author of:

1. Analysing Ecological Data (2007).
Zuur, AF, Ieno, EN and Smith, GM. Springer. 680 p.
URL: www.springer.com/0-387-45967-7http://www.springer.com/0-387-45967-7


2. Mixed effects models and extensions in ecology with R. (2009).
Zuur, AF, Ieno, EN, Walker, N, Saveliev, AA, and Smith, GM. Springer.
http://www.springer.com/life+sci/ecology/book/978-0-387-87457-9


3. A Beginner's Guide to R (2009).
Zuur, AF, Ieno, EN, Meesters, EHWG. Springer
http://www.springer.com/statistics/computational/book/978-0-387-93836-3


Other books: http://www.highstat.com/books.htm


Statistical consultancy, courses, data analysis and software
Highland Statistics Ltd.
6 Laverock road
UK - AB41 6FN Newburgh
Tel: 0044 1358 788177
Email: highs...@highstat.commailto:highs...@highstat.com
URL: www.highstat.comhttp://www.highstat.com
URL: www.brodgar.comhttp://www.brodgar.com


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Laura M. Lee
Senior Stock Assessment Scientist
North Carolina Division of Marine Fisheries
E-Mail: laura@ncdenr.gov
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Re: [R] Predicted values for zero-inflated Poisson

2012-07-10 Thread Achim Zeileis

On Tue, 10 Jul 2012, Laura Lee wrote:


Alain-

Thanks again for the response. I guess my question is more related to R, 
which I'm learning as I go along. Could you provide guidance as to how I 
would code this in R?


That depends on what exactly you want to predict.

As Alain said: The type=count predictions are probably not interesting 
to you. In the JSS paper accompanying zeroinfl, these correspond to 
exp(x'b) in Equation 8.


More interesting is probably the mean (1 - pi) * exp(x'b) which is the 
expected mean mu_i in Equation 8. This can be obtained as type=response.


Additionally, you might be interested in the individual probabilities for 
counts of 0, 1, 2, ... etc. This corresponds to evaluating Equation 7 
for y = 0, 1, 2, ... which can be obtained via type=prob. And from this 
you could also get the mode or median rather than the mean of the 
distribution.


hth,
Z



Thanks,
Laura

From: Alain Zuur [via R] [mailto:ml-node+s789695n4635920...@n4.nabble.com]
Sent: Monday, July 09, 2012 5:20 PM
To: Lee, Laura
Subject: Re: Predicted values for zero-inflated Poisson

Laura Lee laura.lee at ncdenr.gov
Mon Jul 9 22:51:40 CEST 2012

Previous message: [R] Predicted values for zero-inflated Poisson
Next message: [R] Lavaan Package - How to Extract Residuals in Data Values
Messages sorted by: [ date ] [ thread ] [ subject ] [ author ]

Thanks for your reply. I do have a copy of Zero Inflated Models and
Generalized Linear Mixed Models with R and have been using that as a guide.
I applied the predict function (type=count) to the dataset for which I
built the model to compare the predicted bycatch numbers to the observed to
ensure I was doing things correctly. When I summed over the new predicted
variable, the value is over 500 whereas there were less than 10 observed.
I'd appreciate any advice regarding what I'm doing wrong.

--
View this message in context: 
http://r.789695.n4.nabble.com/Predicted-values-for-zero-inflated-Poisson-tp4635861p4635916.html
Sent from the R help mailing list archive at Nabble.com.




AFZ:
Laurano...you don't want to compare the count part of the model with raw 
datayou need to compare
the Exp(Y) = (1-pi) * mu with the raw data. Have a look at the Epilogue 
chapterit shows the difference
between mu and (1-pi) * mu.



Alain







--

Dr. Alain F. Zuur
First author of:

1. Analysing Ecological Data (2007).
Zuur, AF, Ieno, EN and Smith, GM. Springer. 680 p.
URL: www.springer.com/0-387-45967-7http://www.springer.com/0-387-45967-7


2. Mixed effects models and extensions in ecology with R. (2009).
Zuur, AF, Ieno, EN, Walker, N, Saveliev, AA, and Smith, GM. Springer.
http://www.springer.com/life+sci/ecology/book/978-0-387-87457-9


3. A Beginner's Guide to R (2009).
Zuur, AF, Ieno, EN, Meesters, EHWG. Springer
http://www.springer.com/statistics/computational/book/978-0-387-93836-3


4. Zero Inflated Models and Generalized Linear Mixed Models with R. (2012) 
Zuur, Saveliev, Ieno.
http://www.highstat.com/book4.htm

Other books: http://www.highstat.com/books.htm


Statistical consultancy, courses, data analysis and software
Highland Statistics Ltd.
6 Laverock road
UK - AB41 6FN Newburgh
Tel: 0044 1358 788177
Email: [hidden email]/user/SendEmail.jtp?type=nodenode=4635920i=0
URL: www.highstat.comhttp://www.highstat.com
URL: www.brodgar.comhttp://www.brodgar.com


   [[alternative HTML version deleted]]

__
[hidden email]/user/SendEmail.jtp?type=nodenode=4635920i=1 mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
Dr. Alain F. Zuur
First author of:

1. Analysing Ecological Data (2007).
Zuur, AF, Ieno, EN and Smith, GM. Springer. 680 p.
URL: www.springer.com/0-387-45967-7http://www.springer.com/0-387-45967-7


2. Mixed effects models and extensions in ecology with R. (2009).
Zuur, AF, Ieno, EN, Walker, N, Saveliev, AA, and Smith, GM. Springer.
http://www.springer.com/life+sci/ecology/book/978-0-387-87457-9


3. A Beginner's Guide to R (2009).
Zuur, AF, Ieno, EN, Meesters, EHWG. Springer
http://www.springer.com/statistics/computational/book/978-0-387-93836-3


Other books: http://www.highstat.com/books.htm


Statistical consultancy, courses, data analysis and software
Highland Statistics Ltd.
6 Laverock road
UK - AB41 6FN Newburgh
Tel: 0044 1358 788177
Email: highs...@highstat.commailto:highs...@highstat.com
URL: www.highstat.comhttp://www.highstat.com
URL: www.brodgar.comhttp://www.brodgar.com


If you reply to this email, your message will be added to the discussion below:
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Re: [R] Predicted values for zero-inflated Poisson

2012-07-10 Thread Laura Lee
I want to predict the number of turtles for different levels of effort and
combinations of covariates. So, for my dataset from which I built the model,
would I compare sum(predict(ZIP,type=response)) to the observed bycatch to
compare numbers? In order to predict for the new data (called effort), would
I use sum(predict(ZIP,newdata=effort,type=response))? I want to be certain
I am understanding the coding--this is my first time using the predict
function.

Thanks,

Laura

-
Laura M. Lee
Senior Stock Assessment Scientist
North Carolina Division of Marine Fisheries
E-Mail: laura@ncdenr.gov
--
View this message in context: 
http://r.789695.n4.nabble.com/Predicted-values-for-zero-inflated-Poisson-tp4635861p4636016.html
Sent from the R help mailing list archive at Nabble.com.

__
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.


Re: [R] Predicted values for zero-inflated Poisson

2012-07-10 Thread Highland Statistics Ltd
*Laura Lee* laura.lee at ncdenr.gov 
mailto:r-help%40r-project.org?Subject=Re%3A%20%5BR%5D%20Predicted%20values%20for%20zero-inflated%20PoissonIn-Reply-To=%3C1341937636301-4636016.post%40n4.nabble.com%3E
/Tue Jul 10 18:27:16 CEST 2012/



I want to predict the number of turtles for different levels of effort and
combinations of covariates. So, for my dataset from which I built the model,
would I compare sum(predict(ZIP,type=response)) to the observed bycatch to
compare numbers? In order to predict for the new data (called effort), would
I use sum(predict(ZIP,newdata=effort,type=response))? I want to be certain
I am understanding the coding--this is my first time using the predict
function.

Thanks,

Laura




Laura
Why do you use the sum? If you use:

PredY - predict(ZIP, type = response) then you have predicted values for 
each of the rows in your effort data frame.
Job done.

You have an offset in your model, isn't it? You will need to choose values for 
this in the data frame effort as well.
Also double check that the offset is only in the count partat least that is 
what I would do.
Note that using an offset means that you assume that if sampling effort is 
doubled, your fish (?) numbers double.




If you fully want to understand what predict is doing, try to do it manually. 
Below is R code from Chapter 7 (Zero Inflation and GLMM with R)






M3 - zeroinfl(ParrotFish ~ Depth + Slope + SQDistRck + DistSed + Swell + Chla 
+ SST,
dist = poisson, link = logit,
data = PF2)

Betas.logistic - coef(M3, model = zero)
X.logistic - model.matrix(M3, model = zero)
eta.logistic   - X.logistic %*% Betas.logistic
p  - exp(eta.logistic) / (1 + exp(eta.logistic))

Betas.log  - coef(M3, model = count)
X.log  - model.matrix(M3, model = count)
eta.log- X.log %*% Betas.log
mu - exp(eta.log)

ExpY   -  mu * (1 - p)
VarY   - (1 - p) * (mu + p * mu^2)



Instead of using model.matrix(M3), you could specify your own data frame with 
covariates.
Your effort. Something like:

M4 - zeroinfl(ParrotFish ~ Depth + Slope   | SST,
dist = poisson, link = logit,
data = PF2)

betapois - coef(M4, model = count)
betaBin  - coef(M4, model = zero)

MyDataPois - data.frame(Depth = blah blah,
  Slope = Blah blah)
MyDataBin  - data.frame(SST =  blah)

Xpois - model.matrix(~ blah blah, data = MyDataPois)
Xbin  - model.matrix(~ blah blah, data = MyDataBin)

eta.Pois - Xpois %*% betapois
eta.Bin - blah blah

mu = blah blah
pi = blah blah

ExpY = ...


Doing it like this means you fully understand it..:-)
   

Alain




-- 

Dr. Alain F. Zuur
First author of:

1. Analysing Ecological Data (2007).
Zuur, AF, Ieno, EN and Smith, GM. Springer. 680 p.
URL: www.springer.com/0-387-45967-7


2. Mixed effects models and extensions in ecology with R. (2009).
Zuur, AF, Ieno, EN, Walker, N, Saveliev, AA, and Smith, GM. Springer.
http://www.springer.com/life+sci/ecology/book/978-0-387-87457-9


3. A Beginner's Guide to R (2009).
Zuur, AF, Ieno, EN, Meesters, EHWG. Springer
http://www.springer.com/statistics/computational/book/978-0-387-93836-3


4. Zero Inflated Models and Generalized Linear Mixed Models with R. (2012) 
Zuur, Saveliev, Ieno.
http://www.highstat.com/book4.htm

Other books: http://www.highstat.com/books.htm


Statistical consultancy, courses, data analysis and software
Highland Statistics Ltd.
6 Laverock road
UK - AB41 6FN Newburgh
Tel: 0044 1358 788177
Email: highs...@highstat.com
URL: www.highstat.com
URL: www.brodgar.com


[[alternative HTML version deleted]]

__
R-help@r-project.org mailing list
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.


Re: [R] Predicted values for zero-inflated Poisson

2012-07-10 Thread Laura Lee
Alain-

Thanks again for your reply. Yes, the offset for effort is only in the count 
part of the model. Sorry I wasn't clear about why I was using 'sum'...my effort 
data set contains records of trips with the effort given for each trip. I 
thought using sum would get me the total number of turtles predicted for the 
new effort data. I did also log-transform the effort in the new effort data 
before applying predict (correct?). I will try the manual method as you 
recommended to help me understand the code.

Thanks,

Laura

From: Alain Zuur [via R] [mailto:ml-node+s789695n4636025...@n4.nabble.com]
Sent: Tuesday, July 10, 2012 1:52 PM
To: Lee, Laura
Subject: Re: Predicted values for zero-inflated Poisson

*Laura Lee* laura.lee at ncdenr.gov
mailto:r-help%40r-project.org?Subject=Re%3A%20%5BR%5D%20Predicted%20values%20for%20zero-inflated%20PoissonIn-Reply-To=%3C1341937636301-4636016.post%40n4.nabble.com%3E
/Tue Jul 10 18:27:16 CEST 2012/



I want to predict the number of turtles for different levels of effort and
combinations of covariates. So, for my dataset from which I built the model,
would I compare sum(predict(ZIP,type=response)) to the observed bycatch to
compare numbers? In order to predict for the new data (called effort), would
I use sum(predict(ZIP,newdata=effort,type=response))? I want to be certain
I am understanding the coding--this is my first time using the predict
function.

Thanks,

Laura




Laura
Why do you use the sum? If you use:

PredY - predict(ZIP, type = response) then you have predicted values for 
each of the rows in your effort data frame.
Job done.

You have an offset in your model, isn't it? You will need to choose values for 
this in the data frame effort as well.
Also double check that the offset is only in the count partat least that is 
what I would do.
Note that using an offset means that you assume that if sampling effort is 
doubled, your fish (?) numbers double.




If you fully want to understand what predict is doing, try to do it manually. 
Below is R code from Chapter 7 (Zero Inflation and GLMM with R)






M3 - zeroinfl(ParrotFish ~ Depth + Slope + SQDistRck + DistSed + Swell + Chla 
+ SST,
dist = poisson, link = logit,
data = PF2)

Betas.logistic - coef(M3, model = zero)
X.logistic - model.matrix(M3, model = zero)
eta.logistic   - X.logistic %*% Betas.logistic
p  - exp(eta.logistic) / (1 + exp(eta.logistic))

Betas.log  - coef(M3, model = count)
X.log  - model.matrix(M3, model = count)
eta.log- X.log %*% Betas.log
mu - exp(eta.log)

ExpY   -  mu * (1 - p)
VarY   - (1 - p) * (mu + p * mu^2)



Instead of using model.matrix(M3), you could specify your own data frame with 
covariates.
Your effort. Something like:

M4 - zeroinfl(ParrotFish ~ Depth + Slope   | SST,
dist = poisson, link = logit,
data = PF2)

betapois - coef(M4, model = count)
betaBin  - coef(M4, model = zero)

MyDataPois - data.frame(Depth = blah blah,
  Slope = Blah blah)
MyDataBin  - data.frame(SST =  blah)

Xpois - model.matrix(~ blah blah, data = MyDataPois)
Xbin  - model.matrix(~ blah blah, data = MyDataBin)

eta.Pois - Xpois %*% betapois
eta.Bin - blah blah

mu = blah blah
pi = blah blah

ExpY = ...


Doing it like this means you fully understand it..:-)


Alain




--

Dr. Alain F. Zuur
First author of:

1. Analysing Ecological Data (2007).
Zuur, AF, Ieno, EN and Smith, GM. Springer. 680 p.
URL: www.springer.com/0-387-45967-7http://www.springer.com/0-387-45967-7


2. Mixed effects models and extensions in ecology with R. (2009).
Zuur, AF, Ieno, EN, Walker, N, Saveliev, AA, and Smith, GM. Springer.
http://www.springer.com/life+sci/ecology/book/978-0-387-87457-9


3. A Beginner's Guide to R (2009).
Zuur, AF, Ieno, EN, Meesters, EHWG. Springer
http://www.springer.com/statistics/computational/book/978-0-387-93836-3


4. Zero Inflated Models and Generalized Linear Mixed Models with R. (2012) 
Zuur, Saveliev, Ieno.
http://www.highstat.com/book4.htm

Other books: http://www.highstat.com/books.htm


Statistical consultancy, courses, data analysis and software
Highland Statistics Ltd.
6 Laverock road
UK - AB41 6FN Newburgh
Tel: 0044 1358 788177
Email: [hidden email]/user/SendEmail.jtp?type=nodenode=4636025i=0
URL: www.highstat.comhttp://www.highstat.com
URL: www.brodgar.comhttp://www.brodgar.com


[[alternative HTML version deleted]]

__
[hidden email]/user/SendEmail.jtp?type=nodenode=4636025i=1 mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
Dr. Alain F. Zuur
First author of:

1. Analysing Ecological Data (2007).
Zuur, AF, Ieno, EN and Smith, GM. Springer. 680 p.
URL: 

[R] Predicted values for zero-inflated Poisson

2012-07-09 Thread Lee, Laura
Hi all-

I fit a zero-inflated Poisson model to model bycatch rates using an offset term 
for effort. I need to apply the fitted model to a datasets of varying levels of 
effort to predict the associated levels of bycatch. I am seeking assistance as 
to the correct way to code this.

Thanks in advance!

Laura





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__
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and provide commented, minimal, self-contained, reproducible code.


Re: [R] Predicted values for zero-inflated Poisson

2012-07-09 Thread Alain Zuur

Lee, Laura wrote
 
 Hi all-
 
 I fit a zero-inflated Poisson model to model bycatch rates using an offset
 term for effort. I need to apply the fitted model to a datasets of varying
 levels of effort to predict the associated levels of bycatch. I am seeking
 assistance as to the correct way to code this.
 
 
 ---
 Just use the function zeroinfl from the pscl package...fit your
 model...extract the estimated parameters, specify a data frame with
 variables for which you want to make predictions (including values for
 your offset), use model.matrix to convert it into the correct format and
 calculate your fitted values.
 
 You can also use the function predict.
 
 You can either predict the binary (pi) and count parts (mu), or the
 predicted values for the ZIP ((1-pi)*mu)..or better...both. 
 
 
 For detailed examples and code see: 
 
 Zero Inflated Models and Generalized Linear Mixed Models with R. (2012) 
 Zuur, Saveliev, Ieno.
 
 http://www.highstat.com/book4.htm
 
 
 Alain
 
 -- 
 
 Dr. Alain F. Zuur
 First author of:
 
 1. Analysing Ecological Data (2007).
 Zuur, AF, Ieno, EN and Smith, GM. Springer. 680 p.
 URL: www.springer.com/0-387-45967-7
 
 
 2. Mixed effects models and extensions in ecology with R. (2009).
 Zuur, AF, Ieno, EN, Walker, N, Saveliev, AA, and Smith, GM. Springer.
 http://www.springer.com/life+sci/ecology/book/978-0-387-87457-9
 
 
 3. A Beginner's Guide to R (2009).
 Zuur, AF, Ieno, EN, Meesters, EHWG. Springer
 http://www.springer.com/statistics/computational/book/978-0-387-93836-3
 
 
 4. Zero Inflated Models and Generalized Linear Mixed Models with R. (2012)
 Zuur, Saveliev, Ieno.
 http://www.highstat.com/book4.htm
 
 Other books: http://www.highstat.com/books.htm
 
 
 Statistical consultancy, courses, data analysis and software
 Highland Statistics Ltd.
 6 Laverock road
 UK - AB41 6FN Newburgh
 Tel: 0044 1358 788177
 Email: highs...@highstat.com
 URL: www.highstat.com
 URL: www.brodgar.com
 
 
 
 
 Thanks in advance!
 
 Laura
 
 
 
 
 
   [[alternative HTML version deleted]]
 
 __
 R-help@ mailing list
 https://stat.ethz.ch/mailman/listinfo/r-help
 PLEASE do read the posting guide
 http://www.R-project.org/posting-guide.html
 and provide commented, minimal, self-contained, reproducible code.
 


-
Dr. Alain F. Zuur
First author of:

1. Analysing Ecological Data (2007).
Zuur, AF, Ieno, EN and Smith, GM. Springer. 680 p.
URL: www.springer.com/0-387-45967-7


2. Mixed effects models and extensions in ecology with R. (2009).
Zuur, AF, Ieno, EN, Walker, N, Saveliev, AA, and Smith, GM. Springer.
http://www.springer.com/life+sci/ecology/book/978-0-387-87457-9


3. A Beginner's Guide to R (2009).
Zuur, AF, Ieno, EN, Meesters, EHWG. Springer
http://www.springer.com/statistics/computational/book/978-0-387-93836-3


Other books: http://www.highstat.com/books.htm


Statistical consultancy, courses, data analysis and software
Highland Statistics Ltd.
6 Laverock road
UK - AB41 6FN Newburgh
Tel: 0044 1358 788177
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Re: [R] Predicted values for zero-inflated Poisson

2012-07-09 Thread Laura Lee
Thanks for your reply. I do have a copy of Zero Inflated Models and
Generalized Linear Mixed Models with R and have been using that as a guide.
I applied the predict function (type=count) to the dataset for which I
built the model to compare the predicted bycatch numbers to the observed to
ensure I was doing things correctly. When I summed over the new predicted
variable, the value is over 500 whereas there were less than 10 observed.
I'd appreciate any advice regarding what I'm doing wrong.  

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Re: [R] Predicted values for zero-inflated Poisson

2012-07-09 Thread Highland Statistics Ltd
Laura Lee laura.lee at ncdenr.gov
Mon Jul 9 22:51:40 CEST 2012

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Thanks for your reply. I do have a copy of Zero Inflated Models and
Generalized Linear Mixed Models with R and have been using that as a guide.
I applied the predict function (type=count) to the dataset for which I
built the model to compare the predicted bycatch numbers to the observed to
ensure I was doing things correctly. When I summed over the new predicted
variable, the value is over 500 whereas there were less than 10 observed.
I'd appreciate any advice regarding what I'm doing wrong.

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View this message in context: 
http://r.789695.n4.nabble.com/Predicted-values-for-zero-inflated-Poisson-tp4635861p4635916.html
Sent from the R help mailing list archive at Nabble.com.




AFZ:
Laurano...you don't want to compare the count part of the model with raw 
datayou need to compare
the Exp(Y) = (1-pi) * mu with the raw data. Have a look at the Epilogue 
chapterit shows the difference
between mu and (1-pi) * mu.



Alain







-- 

Dr. Alain F. Zuur
First author of:

1. Analysing Ecological Data (2007).
Zuur, AF, Ieno, EN and Smith, GM. Springer. 680 p.
URL: www.springer.com/0-387-45967-7


2. Mixed effects models and extensions in ecology with R. (2009).
Zuur, AF, Ieno, EN, Walker, N, Saveliev, AA, and Smith, GM. Springer.
http://www.springer.com/life+sci/ecology/book/978-0-387-87457-9


3. A Beginner's Guide to R (2009).
Zuur, AF, Ieno, EN, Meesters, EHWG. Springer
http://www.springer.com/statistics/computational/book/978-0-387-93836-3


4. Zero Inflated Models and Generalized Linear Mixed Models with R. (2012) 
Zuur, Saveliev, Ieno.
http://www.highstat.com/book4.htm

Other books: http://www.highstat.com/books.htm


Statistical consultancy, courses, data analysis and software
Highland Statistics Ltd.
6 Laverock road
UK - AB41 6FN Newburgh
Tel: 0044 1358 788177
Email: highs...@highstat.com
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