I am unsure whether turning count data into density still makes Poisson as the appropriate distribution for modelling.  If a given response data are, for example, counts of animals, then such data are best modelled using a Poisson (or quasi-Poisson) distribution.  If the response data are continuous (but bound by zero), then the gamma distribution is likely appropriate.  But what happens when data from counts are turned into density (number of animals per unit area) or encounter rate (number of animals per unit of effort)? Is Poisson distribution still appropriate? Or would one need to use a gamma (or some other) distribution?  I assume it should still be Poisson (or quasi-Poisson, in case of overdispersion).
I am carrying out research to look at differences in fish density and fish species richness when using two different underwater visual census methods. My data was originally count data but then typically this is changed to fish density but I have still decided to use a Poisson GLM, which I hope is right.   model1 &lt;- glm(g_den ~ method + site + depth, poisson)   My 3 predictor variables are method, site and depth which I ordered as factors when I input them.   My response variables are grouper species richness, grouper density and the same for other fish groups. I am aware that density is not an integer and it is numerical data e.g 1.34849. I am now however getting this error:      In dpois(y, mu, log = TRUE) : non-integer x = 0.037500   I've been reading up and many people suggest using an offset, is this the most advisable thing to do?
For which $n$ is the sum: $$\sum_{k=0}^{n}10^k$$ a prime number? Are they finite? An irreducible $f\in \mathbb{Z}[x]$, whose image in every $(\mathbb{Z}/p\mathbb{Z})[x]$ has a root? Problem: Is there an irreducible $f\in \mathbb{Z}[x]$, whose image in every $(\mathbb{Z}/p\mathbb{Z})[x]$ has a root for $p$ prime? If there is, what is the minimal degree possible?   I can only prove that $x^2-c$ is impossible, by quadratic reciprocity and Chinese remainder theorem. Even the case of $a x^2 - c$ is unknown to me.  Meanwhile, if $f$ is not required  to be irreducible, but only have no root in $\mathbb{Z}$, then $(x^2-a)(x^2-b)(x^2-ab)$ is a solution for non-sqaure $a,b,ab$, since if both $a,b$ are not squares in $\mathbb{Z}/p\mathbb{Z}$, then $ab$ is a square. Yet I still don't know if this is of minimal degree.  Also, it is natural to pose generalizations   When $p$ is not necessarily prime (equivalently for all prime powers). When $p$ is odd prime. When $p$ represents sufficiently large primes (equivalently all but a finite number left). I can show that the following limit exists but I am having difficulties to find it. It is $$\lim_{n\to \infty} \sum_{k=1}^n \frac{k^n}{n^n}$$ Can someone please help me? Suppose $A$ is a $n \times n$ constant matrix. How can I prove $\det(e^A) = e^{\displaystyle \sum_{\lambda_i\in\sigma(A)} \lambda_i}$,  where $\sigma(A)$ is the multiset of eigenvalues of $A$?  The following matlab code shows this is true in $n = 3$ case:  A = rand(3) detA = exp(sum(eig(A))) detmA = det(expm(A)) Travel to Cuba as dual citizen (USA+other)? I was looking at the decomposition of Fibonacci numbers using the definition of $F_n = F_{n-1} + F_{n-2}$, and noted the pattern in the coefficients of the terms were Fibonacci numbers. It appears to hold, and I believe it's true, but I haven't seen a proof for it. Does one exist?  $F_n = 1F_{n-1} + 1F_{n-2}$ $F_n = 2F_{n-2} + 1F_{n-3}$ $F_n = 3F_{n-3} + 2F_{n-4}$ $F_n = 5F_{n-4} + 3F_{n-5}$ etc  This can be generalized to $F_n = F_xF_{n-(x-1)}+F_{x-1}F_{n-x}$ Format a number with optional decimal places in Excel I have numbers in cells in Excel. I want the numbers formatted so that if they have decimal places they show to a maximum of two, and if they have no decimal places it doesn't show any.  For example.    15 should be formatted as 15, NOT 15.00 14.3453453 should be formatted as 14.35 12.1 should be formatted as 12.1  0 should be formatted as 0   The closest custom format code I've come up with is 0.##. Unfortunately this formats 15.00 as 15. (note the extra decimal point).  To further complicate the issue, the spreadsheet is a result of an export from SQL Server Reporting Services. So no macros are possible. Oh well, it looks like 0.## is my best bet, and they can just live with the extra period. What conditions need to be fulfilled to enter the Schengen zone visa free? Change Windows sound volume via the command line Is it possible to change the volume in Windows XP via the command line? Sending Email via gmail smtp server in JAVA Find a recurrence relation for the number of ternary strings of length n that do not contain two consecutive 0s or two consecutive 1s. Note: Problem from "Kenneth Rosen's DM and it's applications" and solution from "Students solution guide for use with ... applications"  Let P(n) be the number of strings not containg two containing two consecutive zeros or two consecutive ones.  I got the answer  P(n)=P(n-1)+2P(n-2)+2P(n-3)+...+2P(0) +2  but then the book says the sequence also satisfies the recurrence relation  P(n)=2P(n-1)+P(n-2). I am not able to understand this part. What is the use of the Dot Product of two vectors? In eevee, shadows are clipped by camera distance I am embedding a PDF file inside my LaTeX-generated PDF file using embedfile:  \usepackage{embedfile} \embedfile{myfile.pdf}   I would like to also insert a link that the user can click on to open the attachment.  Is there any way to do that? Is Pikachu's gender ever confirmed? I was recently having a discussion about Pokémon, and it came up that none of us were sure whether Ash's Pikachu in the series was male or female. Some (myself included) always thought it was male, whereas others could've sworn it was female.  Was there ever any canon evidence to point in one direction or another? Best way to do multi-row insert in Oracle? How does one get the MinionPro \qoppa? Since I have switched to the 2014 texlive, one issue is not working: the character \qoppa. The command is defined in polutonikogreek in babel. It is an archaic greek letter, but was used also in classic times for the number 90.  The glyph is available in the cmr font and in MinionPro and in the beautiful MinionMath font of Johannes Küster. I want the latter. In MinionPro/MinionMath, it is unicode character 03d9 (formerly u+03DE, it recently changed, as it turns out), see   How do I get the glyph into latex? I tried  \def\testqoppa{\begingroup\fontfamily{MinionPro}\fontencoding{LGR}\selectfont\char19\endgroup}   and   \def\testqoppab{\begingroup\fontfamily{minionmath}\fontencoding{LGR}\selectfont\char19\endgroup}   But all this gives the cmr glyph, because latex complains  LaTeX Font Warning: Font shape `LGR/MinionPro/m/n' undefined LaTeX Font Warning: Font shape `LGR/minionmath/m/n' undefined (Font)              using `LGR/cmr/m/n' instead on input line 571.   This seems like a beginner error from my side. Can somebody help me to get it right? I need \qoppa only in two places, so a nasty trick is also sufficient. The MinionMath font is installed and is working for all other purposes. Here is an extract of the .cls file:  \usepackage[fullfamily,textlf, opticals, swash, onlytext]{MinionPro} \usepackage[extraops,textcomp,withamsmath,amssymb]{minionmath} \usepackage{amsmath}             \usepackage{minionamsmath} \usepackage[polutonikogreek,greek,latin,french,italian,german,british]{babel} Would it better the community if we got compensated for posts? Even with minuscule alt coins? If we are effectively generating more traffic to Stack Exchange sites, would it become a better community if users were compensated somehow besides rep points? Even with minuscule alt coins? When is it appropriate to create an entity instead of a new content type? What is the benefit to creating new entity types over just building a new content type?    It seems a bit overkill to do all of the custom coding that is required to create a new entity when you have all of the CRUD and Views functionality already built into content types. What are some CD Ripping Programs you can use on Ubuntu? What are some CD ripping programs for Ubuntu? Can you list the Pros? What are the Cons? For each program there should be a screenshot, sources to install, and instructions to install and use.