Take this linear mixed effects model, which is discussed on the CMM website:   $y_{ij} = \beta_0 + \beta_1X_{ij} + \beta_2\bar{X}_j + u_j + e_{ij}$  The variable $X$ is included as both a level 1 and level 2 explanatory variable. The value of $X$ is included for each person $i$ in each group $j$ and it is also included as the mean for each group $j$.  But if $X$ is included as the mean for each group $j$, why would it be necessary to include a random intercept for each group $j$ as well?
I am doing an analysis with 2 groups of patients (control and disease) whose blood pressures have been measured continuously for 24 hours. My first goal is to test the effect of GROUP on BP. In the beginning, I built the mixed effect model with TIME as random effect variable and group as fixed effect model. The model I used is listed below:  mod &lt;- lme(BP ~ factor(GROUP), random=~1+ TIME| ID, data=gdata)   However, the experimenter wants to know the effects of GROUP on the slope of blood pressure changing per hour. In another words, we need to have blood pressure slope, which is the change of blood pressure by time, as response variable in the model. And I generated another model as bellow:  mod &lt;- lme(BP ~ factor(GROUP)*TIME, random=~1+ TIME| ID , data=gdata)   However, in the new model, the time works both as random effect variable and fixed effect variable. I am not sure if this is allowed in the mixed effect model.
Expanding an event group shows more events than labeled when there are new events Which is the recommended way to plot: matplotlib or pylab? Is there a way to draw a sort of connection between subplots in TiKz/pgfplot, like in this ? I'm looking to achieve something like this:    But I would need to draw the "x 2000" line between the plots.  EDIT: So right now I have something like this:    Coming from my main.tex:  \input{aipcheck}  \documentclass[final]{aipproc}  \layoutstyle{8x11single} \usepackage[utf8]{inputenc} \usepackage{algorithm2e} \usepackage{color} \usepackage[usenames,dvipsnames]{xcolor} \usepackage{cleveref} \usepackage{pgfplots}  \pgfplotsset{ tick label style={font=\tiny}, %axis numbers label style={font=\small}, %axis labels legend style={font=\tiny} }  \begin{document}  (...)  \begin{figure}     \centering     \newlength\figureheight      \newlength\figurewidth      \setlength\figureheight{5cm}      \setlength\figurewidth{5cm}     \input{figs/_ddmp2d.tikz} \label{fig2D} \end{figure}   with _ddmp2d.tikz, originally created from matlab2tikz, but already modified, containing:  % This file was created by matlab2tikz v0.3.3. % Copyright (c) 2008--2013, Nico Schlömer &lt;nico.schloemer@gmail.com&gt; % All rights reserved. %  % The latest updates can be retrieved from %   http://www.mathworks.com/matlabcentral/fileexchange/22022-matlab2tikz % where you can also make suggestions and rate matlab2tikz. %  %  %   \begin{tikzpicture}  \begin{axis}[% width=\figurewidth, height=\figureheight, scale only axis, xmin=0, xmax=15, xlabel={Number of iterations}, ymin=0, ymax=16000000000000, name=plot1, after end axis/.append code={\coordinate (a) at (axis description cs:1,0);}]  \addplot [ thick, color=red, dash pattern=on 1pt off 3pt on 3pt off 3pt, forget plot ] table[row sep=crcr]{ 1 15841000000000\\ (...) 15 25160000000\\ }; \addplot [ thick, color=black, dashed, forget plot ] table[row sep=crcr]{ 1 15841000000000\\ (...) 15 52501000000\\ }; \addplot [ thick, color=blue, dotted, forget plot ] table[row sep=crcr]{ 1 15841000000000\\ (...) 15 5324200000\\ }; \addplot [ thick, color=green, solid, forget plot ] table[row sep=crcr]{ 1 15841000000000\\ (...) 15 551920000\\ }; \addplot [ thick, color=green, solid, forget plot ] table[row sep=crcr]{ 3 0\\ 3 16000000000000\\ };  \addplot [ thick, color=blue, dotted, forget plot ] table[row sep=crcr]{ 4 0\\ 4 16000000000000\\ }; \addplot [ thick, color=black, dashed, forget plot ] table[row sep=crcr]{ 5 0\\ 5 16000000000000\\ }; \addplot [ thick, color=red, dash pattern=on 1pt off 3pt on 3pt off 3pt, forget plot ] table[row sep=crcr]{ 8 0\\ 8 16000000000000\\ }; \end{axis}  \begin{scope}[xshift=5cm] \begin{axis}[% width=0.35\figurewidth, height=\figureheight, scale only axis, xmin=995, xmax=1000, xtick={997,998,999,1000}, xticklabels={$997$,$998$,$999$,$1000$}, ymin=0, ymax=8000000000, at=(plot1.right of south east), anchor=left of south west, yticklabel pos=right, axis x discontinuity=crunch, after end axis/.append code={\coordinate (b) at (axis description cs:0,1);} ] \addplot [ thick, color=red, dash pattern=on 1pt off 3pt on 3pt off 3pt ] table[row sep=crcr]{ 995 6093100000\\ 996 6093100000\\ 997 6093100000\\ 998 6093100000\\ 999 6093100000\\ 1000 6093100000\\ };  \addplot [ thick, color=black, dashed ] table[row sep=crcr]{ 995 1577100000\\ 996 1598000000\\ 997 1598500000\\ 998 1628600000\\ 999 1631000000\\ 1000 1595900000\\ };  \addplot [ thick, color=blue, dotted ] table[row sep=crcr]{ 995 2592000000\\ 996 2591900000\\ 997 2591700000\\ 998 2591600000\\ 999 2591500000\\ 1000 2591400000\\ };  \addplot [ thick, color=green, solid ] table[row sep=crcr]{ 995 391810000\\ 996 391810000\\ 997 391810000\\ 998 391810000\\ 999 391810000\\ 1000 391810000\\ };  \end{axis} \draw[gray] (a) -- (b) node[pos=0.5,sloped,fill=white] {$\times$2000}; \end{scope}  \end{tikzpicture}% If $a^\phi = 1$ then the order of $a$ divides $\phi$ Purpose of else and finally in exception handling Convergence of $\sum\limits_{n=2}^\infty \frac{1}{n^\alpha \ln^\beta (n)} $ for nonnegative $\alpha$ and $\beta$ Study the convergence of the following series: $$\sum_{n=2}^\infty \frac{1}{n^\alpha \cdot\ln^\beta(n)} \text{ where }\alpha,\beta \geq 0 $$   Applying d'Alembert criterion I have that $$ \lim_{n\to\infty} \frac{n^\alpha  \ln^\beta(n)}{(n+1)^\alpha  \ln^\beta (n+1)} = \lim_{n\to\infty} \left(\frac{n}{n+1}\right)^\alpha\left(\frac{\ln(n)}{\ln (n+1)}\right)^\beta = 1$$ so the nature of the series is inconclusive.  If $\alpha = \beta = 0$, then the series diverges, since $\sum_{n=2}^\infty 1 = \infty$.  Should I study the rest of the cases (i.e. if $\alpha = 0, \beta &gt; 0$ the root test and the ratio test are also inconclusive). What is the best form to study the series?.  Thanks in advance After upgrading to Ubuntu 14.04 from 12.04 I have duplicate entries in dash.    How can I get rid of them? Adding a comment should not make me fail the review audit Isle vs. Island Copy Physics To Multiple Objects What algorithm is used by computers to calculate logarithms? Using QGIS 3 graphical modeler I created a model with a variety of input parameters (> 10). When starting the model, a nice user interface is generated. But the arrangement of the GUI elements is totally confused and apparently unpredictable during creating the model. It does neither seem to depend on the arrangement of input parameters in the graphical modeler nor on the chronological order in which the input parameters are added to the model.   Is there a way that let's me arrange the GUI elements in the order I desire? Highlight elements in the matrix Proving that the Hopf map $S^3 \to S^2$ is a submersion I need to show that the Hopf map $H : S^3 \to S^2$ is a submersion. There are many ways to define it, but for now I've gone with the restriction of the function $F : \mathbb{R}^4 \to \mathbb{R}^3$ mapping $$(x,y,u,v)\mapsto (2(xu+yv), 2(xv-yu), x^2+y^2-u^2-v^2).$$ It wasn't too bad to show that $F$ is a submersion, but is there a way to go from here to show that $H$ is a submersion? I can write down $H$ as the composition $$S^3 \overset{\iota}{\hookrightarrow} \mathbb{R}^4 \overset{F}{\to} \mathbb{R}^3 \overset{\pi}{\to} S^2,$$ and define $\pi(p) = p/\lVert p\rVert$, but I don't really know where to go after computing the Jacobian of $\pi$, and I don't know if this will even work for my purposes (I don't see how to argue that the composition of the corresponding differentials here isn't rank $1$ — I know $d\iota$ has trivial kernel but things seem to break down once I get to $d\pi$). I'm really just trying to avoid having to compute the Jacobian of $H$ with respect to the stereographic projections and show that that beast of a thing is full rank. Am I on the right track, or is there a better way? Formatting OGR VRT file to convert CSV to KML? Output two sided, but only on recto page -- occasional images on verso I am preparing a thesis. In order to reduce the number of physical sheets of paper, I need to print certain figures/tables on the verso side. However the university regs state that, while figs/tables may appear on the verso, the body text must appear on the recto side.  I would like to therefore output the vast bulk of the work on the recto page, but with occasional verso pages. Ideally they would be numbered as a "subpage" of the preceeding recto page (e.g. 131, 131a, 132...) or similar.  The approach which I will tentatively adopt is to use a "twoside" flag, then have "empty" and non-numbered verso pages until a page with content is required.   I'm sure I'm not the first person to have had a similar issue, but am unable to imagine other ways of posing the question. What techniques have been used to repeat geometry or other detail to the infinite horizon? When I composed my     I would have liked to have the camera pitch up enough to show the horizon, except I didn't have enough geometry to extend the cobblestone street and the sidewalk all the way to infinity (mostly because that would require infinite stuff).  Even in that shot it is clear that I need to widen the "sidewalk" to cover up the "sky"box.    Contrast with     where the ray tracer can use the procedurally replicated geometry.   is a failed attempt at faking out the horizon, even with low detail.  It fails because lighting's interaction with the geometry gives it away.  Some techniques that prevent you from having to deal with infinity include   put the scene in a box (usually a room) put the scene in a canyon (which is just a box without a top so you can see the relatively featureless sky) route the road into a tunnel, or around a corner and hide the horizon with other geometry (which is really just a variant on the canyon). have no detail on the ground at all (flat color or gradient)   Those are all dodging the question of interest to me:  What techniques have people used in blender to fake various kinds of detail repeating into the distance (instead of just obstructing the view of infinity)? how to sort file by DD-MM-YYYY dates in a file containing :  ... 18-11-2018:othercharacters 10-11-2018:othercharacters 03-10-2018:othercharacters 30-10-2018:othercharacters 27-09-2018:othercharacters 03-12-2018:othercharacters ...   the command :  sort -t- -k2 -k1    does not sort by date, what am I missing ? Why is rm allowed to delete a file under ownership of a different user? From the post  I understand that rm just needs write permission on directory to remove the file. But I find it hard to digest the behaviour where we can easily delete a file who owner and group different.  I tried the following  mtk : my username abc : created a new user  $ ls -l file -rw-rw-r-- 1 mtk mtk       0 Aug 31 15:40 file $ sudo chown abc file $ sudo chgrp abc file $ ls -l file -rw-rw-r-- 1 abc abc       0 Aug 31 15:40 file $ rm file $ ls -l file &lt;deleted&gt;   I was thinking this shouldn't have been allowed. A user should be able to delete only files under his ownership? Can someone shed light on why this is permitted? and what is the way to avoid this? I can think only restricting the write permission of the parent directory to dis-allow surprised deletes of file. shorter proof of generalized mediant inequality?