# model algebra especification

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### Joaquín Aldabe

Aug 3, 2022, 3:10:50 PMAug 3
Dear all, I am working with an N-mixture model with random effects and want to check if I am writing the algebra correctly. I have several bird counts (samples) in each ranch (or farm), so farm identity is the random intercept (beta0,R). Is this the correct sequence of equations?  I also want to explain how the Poisson and Binomial processes connect to estimate Ni but can´t figure out how the model works. I appreciate comments in this regard too.

Thanks so much. Joaquín.

--
Joaquín Aldabe

Departamento de Sistemas Agrarios y Paisajes Culturales
Centro Universitario de la Región Este, Universidad de la República, Uruguay
Ruta 15 (y Ruta 9), Km 28.500, Departamento de Rocha

### Marc Kery

Aug 4, 2022, 4:02:23 AMAug 4

Dear Joaquin,

mostly correct, but:

• i in the first line should be a subscript
• Also in the first line, you need a subscript i for lambda
• Line 2: make a twiddle instead of the equal sign
• Line 3: you want the I to be a subscript for lambda and then I think you need a plus sign in the latter parts of that line
• Line 4: make this a twiddle instead of an equal sign

Otherwise, it looks good to me.

Best regards --- Marc

Gesendet: Mittwoch, 3. August 2022 21:11
Betreff: [unmarked] model algebra especification

Dear all, I am working with an N-mixture model with random effects and want to check if I am writing the algebra correctly. I have several bird counts (samples) in each ranch (or farm), so farm identity is the random intercept (beta0,R). Is this the correct sequence of equations?  I also want to explain how the Poisson and Binomial processes connect to estimate Ni but can´t figure out how the model works. I appreciate comments in this regard too.

Thanks so much. Joaquín.

--

Joaquín Aldabe

Departamento de Sistemas Agrarios y Paisajes Culturales
Centro Universitario de la Región Este, Universidad de la República, Uruguay

Ruta 15 (y Ruta 9), Km 28.500, Departamento de Rocha

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### joaquin...@gmail.com

Aug 4, 2022, 9:51:05 AMAug 4
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Thanks Marc! in line 4 I want to express a interaction between Year and Management. That´s why I used a X. Do you knwo how to algebraically express that?

Best,
Joaquín

### Marc Kery

Aug 4, 2022, 9:55:15 AMAug 4
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Dear Joaquin,

If you send me the BUGS language code offline I can make an attempt. I realize now that you may also need some index t for year perhaps.

Thanks and best regards  -- Marc

### joaquin...@gmail.com

Aug 4, 2022, 12:39:06 PMAug 4
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Hi Marc, I used ubms package. So I don´t have BUGS code. My data consists on 11 ranches. In each ranch I sampled several fields or paddocks. I did this in two different years. In year 1, all ranches had the same management, while in year 2, 6 ranches had changed their management. So, I have 5 ranches as control (no changes in management) and 6 ranches that changed management (treatment). So I´m assessing if year affected treated ranches but not control ranches. That´s why I´m interested in assessing the interaction term..

Hope this helps to figure out the algebra.

Thanks so much!

Joaquín.

### Marc Kery

Aug 4, 2022, 2:47:26 PMAug 4
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Dear Joaquin,

OK, thanks. Question back:
• so what's the unit in the experiment ? The field/paddock ?
• And how did you organize the data for the two years ? Stack them on top of each other ?
Thanks and best regards  -- Marc

Sent: Thursday, August 4, 2022 18:39
Subject: Re: [unmarked] model algebra especification

### joaquin...@gmail.com

Aug 4, 2022, 2:52:26 PMAug 4

Hi Marc, the unit in the experiment is the field, that is nested in ranch (i.e. several fields were sampled in each ranch). I put Year as a variable (column) with two levels (year 1 and year 2). I want to know if year has a effect on field abundance at control and treatment ranches. I attached the dataset. Let me know if you need further explanation or information.

Thanks so much for your time!

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