This may seem like a foolish question, but it is critical for me to have some expert advice on this.   I am doing some research on students' learning levels in India. I am using R software (ltm package) to calculate student scores (ability estimates as per IRT model).   Features of the data:  No of students: 15,000 Test papers: 3 different forms No of questions in one form: 50  My concern is whether R outputs are reliable enough to publish the results in research community or the results from R software can be questioned, specifically with respect to ltm package. Also if R can handle such large data comfortably without compromising the quality.  I would be very grateful if you could share your inputs and any documentation/research paper/reference you may have.
I am a graduate student in economics who recently converted to R from other very well-known statistical packages (I was using SPSS mainly). My little problem at the moment is that I am the only R user in my class. My classmates use Stata and Gauss and one of my professors even said that R is perfect for engineering, but not for economics. He said that many packages are built by people who know a lot about programming, but not much about economics and therefore are not reliable. He also mentioned the fact that since no money is actually involved in building an R package, there is therefore no incentive to do it correctly (unlike in Stata for example) and that he used R for a time and got some "ridiculous" results in his attempts to estimate some stuff. Moreover, he complained about he random number generator in R which he said was "messy".  I've been using R for just a little more than a month and I must say I have fallen in love with it. All this stuff I am hearing from my professor is just discouraging me.  So my question is: "Is R reliable for the field of economics?".
Modelling the "Moving Sofa" I believe that many of you know about the moving sofa problem; if not you can find the description of the problem .     In this question I am going to rotate the L shaped hall instead of moving a sofa around the corner. By rotating the hall $180^{\circ}$ what remains between the walls will give the shape of the sofa. Like this:    The points on the hall have the following properties:  \begin{eqnarray} A &amp; = &amp; \left( r\cos { \alpha  } ,t\sin { \alpha  }  \right)  \\ { A }' &amp; = &amp; \left( r\cos { \alpha  } +\sqrt { 2 } \cos { \left( \frac { \pi  }{ 4 } +\frac { \alpha  }{ 2 }  \right)  } ,t\sin { \alpha  } +\sqrt { 2 } \sin { \left( \frac { \pi  }{ 4 } +\frac { \alpha  }{ 2 }  \right)  }  \right)  \\ { B } &amp; = &amp; \left( r\cos { \alpha  } -\frac { t\sin { \alpha  }  }{ \tan { \left( \frac { \alpha  }{ 2 }  \right)  }  } ,0 \right)  \\ { B }' &amp; = &amp; \left( r\cos { \alpha  } -\frac { t\sin { \alpha  }  }{ \tan { \left( \frac { \alpha  }{ 2 }  \right)  }  } -\frac { 1 }{ \sin { \left( \frac { \alpha  }{ 2 }  \right)  }  } ,0 \right)  \\ C &amp; = &amp; \left( r\cos { \alpha  } +t\sin { \alpha  } \tan { \left( \frac { \alpha  }{ 2 }  \right)  } ,0 \right)  \\ { C }' &amp; = &amp; \left( r\cos { \alpha  } +t\sin { \alpha  } \tan { \left( \frac { \alpha  }{ 2 }  \right)  } +\frac { 1 }{ \cos { \left( \frac { \alpha  }{ 2 }  \right)  }  } ,0 \right)  \end{eqnarray}  Attention: $\alpha$ is not the angle of $AOC$, it is some angle $ADC$ where $D$ changes location on $x$ axis for $r\neq t$. I am saying this because images can create confusion. Anyways I will change them as soon as possible.  I could consider $r=f(\alpha)$ and $t=g(\alpha)$ but for this question I am going to take $r$ and $t$ as constants. If they were functions of $\alpha$ there would appear some interesting shapes. I experimented for different functions however the areas are more difficult to calculate, that's why I am not going to share. Maybe in the future.  We rotate the hall for $r=t$ in the example above: In this case:   point A moves on a semicircle  The envelope of lines between A' and C' is a circular arc. One has to prove this but I assume that it is true for $r=t$.   If my second assumption is correct the area of sofa is $A= 2r-\frac { \pi r^{ 2 } }{ 2 } +\frac { \pi  }{ 2 } $. The maximum area is reached when $r = 2/\pi$ and it's value is: $$A = 2/\pi+\pi/2 = 2,207416099$$  which matches with Hammersley's sofa. The shape is also similar or same:    Now I am going to increase $t$ with respect to $r$. For $r=2/\pi$ and $t=0.77$:    Well, this looks like .   I believe thearea can be maximized by finding the equations of envelopes above and below the sofa. Look at  where @Aretino has computed the area below $ABC$.   I don't know enough to find equations for envelopes. I am afraid that I will make mistakes. I considered to calculate area by counting number of pixels in it, but this is not a good idea because for optimizing the area I have to create many images.  I will give a bounty of 200 for whom calculates the maximum area. As I said the most difficult part of the problem is to find equations of envelopes. @Aretino did it.  PLUS: Could following be the longest sofa where $(r,t)=((\sqrt 5+1)/2,1)$ ?   If you want to investigate further or use animation for educational purposes here is the Geogebra file:      Ok, I had some free time and I count number of pixels in the sofa and I am sure that I have something bigger than Hammersley's constant.  First, I made a simulation for Hammersley's sofa where $r=t=2/\pi$ and exported the image to png in 300 dpi (6484x3342 pixels) and using Gimp counted number of pixels which have exactly same value. For Hammersley I got $3039086$ pixels.   For the second case $r=0.59$ and $t=0.66$ and I got $3052780$ pixels. To calculate area for this case:  $$\frac{3052780}{3039086}(2/\pi + \pi/2)=2.217362628$$  which is slightly less than Gerver's constant which is $2.2195$. Here is the sofa: For example:     The word rarely turns up outside of those contexts.      The word turns up rarely outside of those contexts.   Which one is correct and why? What is the limit of this sequence? How does it relate to the exponential function? Find $$\lim_{n\to\infty} \left(1+\frac{x^2}{n^2}\right)^n$$   I particular, I am hoping to find the above to be $1+x^kg(x/n)$ where $g(\cdot)$ is a function with uniformly bounded derivatives.  Edit: I'm trying to prove a result that would be true if  $(1+x^2/n^2)^n -1 = x^kO(x/n).$ How can I draw annotated braces over and under math expressions? What LaTeX markup would one have to write to produce a result similar to the image below?    Please excuse my Paint-and-mouse drawing skills. :-) Where to place log4j.xml How to export SVG without lines, polylines and polygons? Automatic code reindent button How do I upgrade from 12.10 to 13.04? How much electronics and other valuables can I bring duty-free when going to India? I am planning to travel to India (COK airport, Kerala) from United States. I want to take my laptop as well as my tablet (iPad). Am I allowed to take both in my backpack with my documents related my work. I think I am allowed to take only one computer as per the rule. Will the customs consider my iPad as a computer?  What all I can take?   One of my friends took 2 laptops (1 work and 1 personal) and had trouble at the airport.  Also I am planning to take some wristwatches (7 of them, each avg price is 45 $). I read in a website that I can take stuff up to max 35000 INR. Is that true? In that case, how will I manage my stuff? Cleaning polygon after using dissolve to repair geometry in QGIS? I'm trying to obtain the boundaries of shapefile, thus to clean the inside as a matter of speaking. While I had expected that dissolve while get me a proper polygon, unfortunately it still has some remainders. How could I get rid of them?  Does QGIS have a tool similar to Repair Geometry?  Here's the source    Result below: How can I import an obj sequence into blender? I have an obj sequence of a fluid simulation from Realflow. I've found a few tools that can import an obj sequence into blender, but most are outdated and don't work. Are there any scripts or plug-ins that can do that? Real Analysis, Existence of a Limit Boundedly:$|\int_0^b\frac{sin(ax)}{x}dx | \le c$ I need to show that there exists a $c$ such that $|\int_0^b\frac{sin(ax)}{x}dx | \le c$, where $a$ is any real number, and $b$ is any real number greater than 0. Also I need to show that the smallest $c$ possible is $c=\int_0^\pi\frac{sinx}{x}dx$. I know that $\int_0^\infty \frac{sin(ax)}{x}dx = sig(a)\frac{\pi}{2}$ where $sig(a)$ literally just means positive one or negative one, depending on the sign of $a$. I think the fourier tranform of the characteristic function on the interval $(0,a)$ is $\frac{sin(ax)}{x}$. After that, I am unsure about how to proceed. Thanks for your help! If I call finalize() on an object from my program code, will the JVM still run the method again when the garbage collector processes this object?  This would be an approximate example:  MyObject m = new MyObject();  m.finalize();  m = null;  System.gc()   Would the explicit call to finalize() make the JVM's garbage collector not to run the finalize() method on object m? Proof that $a\mid b \land b\mid c \Rightarrow a\mid c $ I am trying to prove:     $a\mid b \land b\mid c \Rightarrow a\mid c $   $a\mid b$ means that a divides b if there is an integer k, that $b=k\cdot a$  Please give me a hint on how to start, because I have no idea. Is the composition of two injective functions injective? What is a combo update and how is it different than the regular update? What is a combo update and how is it different from a normal update? Do you think that "was going to be" or "would be" could be used as past tense of will?     I thought this book was going to be your choice.        I thought this book would be your choice.   Do these two sentences basically mean the same thing or are they slightly different? In my cover letter I want to write that I am a graduate student in statistics. But I am not sure about the "in". So what is correct?     I am a graduate student in statistics.      I am a graduate student of statistics. Prove that $\displaystyle \sum^{n}_{r=0}(-1)^r\cdot \large\frac{\binom{n}{r}}{\binom{r+3}{r}} = \frac{3!}{2(n+3)}$   $\bf{My\; Try::}$ We can write $$\frac{\binom{n}{r}}{\binom{r+3}{r}} = \frac{n!}{r!\times (n-r)!}\times \frac{r!\times 3!}{(r+3)!} = \frac{3!\times n!}{(n-r)!\times (r+3)!}$$  So our sum is $$ 3!\sum^{n}_{r=0}(-1)^r\frac{n!}{(n-r)!\times (r+3)!} = \frac{3!}{(n+1)(n+2)(n+3)}\sum^{n}_{r=0}(-1)^r\frac{(n+3)!}{(r+3)!\times (n-r)!}$$  So we get Sum $$ \frac{3!}{(n+1)(n+2)(n+3)}\sum^{n}_{r=0}(-1)^r\binom{n+3}{r+3} = -\frac{3!}{(n+1)(n+2)}\sum^{n}_{r=0}(-1)^{r+3}\binom{n+3}{r+3}$$  $$  = -\frac{3!}{(n+1)(n+2)(n+3)}\left[-\binom{n+3}{3}+\binom{n+3}{4}-\binom{n+3}{5}--.......+(-1)^{n+3}\binom{n+3}{n+3}\right]$$  $$=-\frac{3!}{(n+1)(n+2)(n+3)}\left[\binom{n+3}{0}-\binom{n+3}{1}+\binom{n+3}{2}-\binom{n+3}{3}+\binom{n+3}{4}-\binom{n+3}{5}--.......+(-1)^{n+3}\binom{n+3}{n+3}\right]+\frac{3!}{(n+1)(n+2)(n+3)}\left[\binom{n+3}{0}-\binom{n+3}{1}+\binom{n+3}{2}\right]$$  So we get $$ = \frac{3!}{(n+1)(n+2)(n+3)}\left[1-(n+3)+\frac{(n+3)(n+2)}{2}\right] = \frac{3!}{(n+1)(n+2)}\times \frac{n^2+3n+2}{2} = \frac{3!}{(n+1)(n+2)(n+3)}\times \frac{(n+1)(n+2)}{2} = \frac{3!}{2(n+3)}$$  Can we prove it Using Combinatorial way,bcz above method is very lengthy  If yes then plz explain here  Thanks How can I install a different version of Python using apt-get?  Obviously I realise I can install using the source tar ball, however I would prefer not to install from source and instead use the package manager, as that's what it's there for. Surely somewhere reputable builds .deb files for the latest Python releases (why python.org don't is beyond me) that I can reference.   What do I need to do to reference them and what issues might it create when upgrading to the next version?  If there is no way except for building from source, is there a (pseudo) package that I can can install that will provide all of the dependencies needed without having to find and install each individually? So that I don't get:  The necessary bits to build these optional modules were not found: _bz2                  _curses               _curses_panel       _dbm                  _gdbm                 _lzma               _sqlite3              _ssl                  _tkinter            readline              zlib