Is it statistically valid to enter "control" predictors that are theoretically relevant in a linear mixed effects model (aka multilevel model), even if only very weak and non-significant linear relationships were demonstrated beforehand?   The predictors in question could be considered control variables (e.g., age, SES, score 1, score 2). The main aim of the analysis is to examine the relative effects of these between-subjects predictors and a within-subjects predictor (experimental condition) on a continuous DV. Linear mixed effects modelling is being used, as this approach can take into account the non-independent observations.   Linearity was explored through through examining scatterplots, and conducting bivariate Pearson correlations (they yielded small Pearson coefficients that were non-significant). Unsurprising, since only weak and nonsignificant linear relationships were demonstrated in screening, the control variables do not contribute to the variance in the DV when entered into the linear mixed effect model. But dropping them doesn't seem valid given their theoretical relevance. It seems more useful to maintain them in the model as controls to soak up some "noise", and then discuss how that in this particular sample they did not actually contribute to variance in the DV. In addition, I think it makes sense to keep them in the model and check for possible interactions with the main exploratory predictor (condition).  Would this approach be statistically valid?
I have a set of predictors in a linear regression, as well as three control variables. The issue here is that one of my variables of interest is only statistically significant if the control variables are included in the final model. However, the control variables themselves are not statistically significant.  Here is how the multicollinearity of all my variables look like (including control variables):   &gt; vif(lm(return ~ EQ + EFF + SIZE + MOM + MSCR + UMP, data = as.data.frame(port.df)))        EQ      EFF     SIZE      MOM     MSCR      UMP   3.687171 3.481672 2.781901 1.064312 1.438596 1.003408   &gt; vif(lm(return ~ EQ + MOM + MSCR, data = as.data.frame(port.df)))        EQ      MOM     MSCR   1.359992 1.048142 1.412658    My variables of interest are EQ, MOM and MSCR, and the control variables are EFF, SIZE and UMP. EQ is only significant if the three control var are included, and becomes insignificant when they are not:   Here are the coefficients (1rst row) and t-stats (2nd row) when control variables are included (notice that EQ is statistically significant)         intercept           EQ          EFF        SIZE         MOM       MSCR          UMP [1,] 0.005206246 -0.006310531 0.0001229055 0.004125551 0.007738259 0.00473377 5.838596e-06 [2,] 1.866628909 -1.746583234 0.0388823612 1.178460997 2.145062820 2.08131100 1.994863e-01  Now, here is the result of the regression when the control variables are excluded (notice that EQ is NOT statistically significant anymore)         intercept           EQ         MOM       MSCR [1,] 0.007313402 -0.002111833 0.007128606 0.00668364 [2,] 2.652662996 -0.595391117 2.036985378 2.80177366    The problem is that when I include my control variables, all my variables of interest are significant, but my control variables are not.  Which variables should I include in my final model? How should I structure my final model then, given the fact that the model will be used for forecasting?  Thank you,
How to find the last field using 'cut' Can you partition an infinite set, into an infinite number of infinite sets? We moved to a new place where the dryer connection is 3-prong instead of 4-prong. The dryer was originally 4-prong, so we bought a 3-prong cord and installed it. It works fine, except I am not entirely sure if I installed the ground wire correctly.   Originally, there was a green wire on the cord itself, and that was connected to the screw on the top of the first picture. This is, I assume, used to ground the case and prevent shocks when touching the exterior of the dryer.  Now with the 3-pronged plug, there is no ground wire on the cord. So where does the existing green wire in the case go? Do I leave it where it originally was like in the first picture or do I connect it to the central terminal like in the second picture?      There's no bonding strap running from the case to any terminal. I can't tell where the green wire is connected to. If a Matrix Has Only Zero as an Eigen-Value Then It Is Nilpotent The problem is, it seems when I enable a disabled module, the module's schema version in the system table is automatically updated to the latest version supplied by hook_update_N.  So my current module with the schema version -1 is modified to 7106 when I enable the module, and no hook_update_N functions are run.   So when I come to the next step of running database updates, no hook_update_N functions are run because the module thinks it's already the correct version.  The only method I can see is to manually set the module version in hook_enable, however I'll then need to update the module code to remove the hook_enable to make sure it doesn't run if the module is ever re-enabled in the future, so obviously this approach is a bit dirty.  I'm hoping there's a better solution? How to get only filename using sed How can I get only the filename using sed? I've this  out_file=$(echo $in_file|sed "s/\(.*\.\).*/\1mp4/g")   But I get the path too /root/video.mp4, and I want only video.mp4. Let $x_1 = 2$, and define $$x_{n+1} = \frac{1}{2} \left(x_n + \frac{2}{x_n}\right).$$ Show that $x_n^2$ is always greater than or equal to $2$, and then use this to prove that $x_n − x_{n+1} ≥ 0$. Conclude that $\lim x_n = \sqrt2$.   My question:  So I know how to do this problem but I don't know how to prove that $x_n &gt;0$ for all $n\in \mathbb{N}$. Using wired and wireless headphones simultaneously? I have 1 android device, 1 wired headphones, 1 wireless headphones, 2 ppl willing to watch film.  When I connect both of headphones only wired work.  Is it possible to use both of headphones simultaneously? I'm using Xubuntu 14.04 64 bit. I know that question been asked a billion times, but all of them consist of editing following file:  /etc/polkit-1/localauthority/50-local.d/com.ubuntu.enable-hibernate.pkla   That file does not exist on my system. I tried com.xubuntu.enable-hibernate.pkla but doesn't exist either, locate command doesn't find it. Check synchronously if file/directory exists in Node.js How to merge cells vertically Is it possible to create a table like this one?    The usual structure of tables I use looks like this:  \begin{table}[H]     \begin{adjustbox}{width=\textwidth,center}     % \begin{adjustbox}{center}         \begin{tabular}{lll}             \hline             \multicolumn{1}{l}{\head{XXX}} &amp; \multicolumn{1}{l}{\head{XXX}} &amp; \multicolumn{1}{l}{\head{XXX}} \\             \hline             \ttfamily xxx &amp; \ttfamily xxx &amp; \ttfamily xxx \\             \hline         \end{tabular}     \end{adjustbox}     \vspace{ - 05 mm}     \caption{xxx}     \label{tab:xxx} \end{table} Is there a case insensitive version of the  jQuery selector or should I do the work manually by looping over all elements and comparing their .text() to my string? Prime/Maximal Ideals in $\mathbb{Z}[\sqrt d]$ Can internal forces do work? I want to show that for each $n \in \mathbb N$ it holds that $$\sum_{k = 0}^\infty \frac{n^k}{k!} \vert k - n \vert = 2n \frac{n^n}{n!}.$$ But I have absolutely no idea how to do that. I tried to split the series like this:  $$\sum_{k = 0}^\infty \frac{n^k}{k!} \vert k - n \vert = \sum_{k = 0}^{n - 1} \frac{n^k}{k!}(n - k) + \sum_{k = n + 1}^\infty \frac{n^k}{k!} (k - n)$$ Now I want to show that $\sum_{k = 0}^{n - 1} \frac{n^k}{k!}(n - k) = \sum_{k = n + 1}^\infty \frac{n^k}{k!} (k - n) = n \frac{n^n}{n!}$ holds. But I got no idea how to achieve that. I tried to use induction but things became pretty messy and I don't think it will work like that. On the other hand I got the idea that it might have to do with $\exp$ or binomial coefficients but I don't see where I can facilitate that. I would appreciate some hints :) Baking lots of bread - keeping a yeast starter Like many people sheltering-at-home, I'm baking . My yeast supply is running low, and I'm not sure I'll be able to get more on demand. I'd like a simple way to make sure I have yeast on hand for my next batch. Could you all recommend a method for storing a starter culture?  Specifically:   How should I store it (how much? where? I have a fridge ~4C and a wine cooler ~13C)  How often should I feed it? With what? Should I divide the culture when feeding?  How much should I use when baking? Can I treat it like dry active yeast, or does it need more/less time?   For some other context, I'm a novice at making bread (I've made it a few times, and others in my family make it more often). I see lots of advice on sourdough starters, but am interested in something that's a replacement for dry active yeast (unless sourdough starters are actually easier to maintain). I found a  that was similar, but it focused on long-term storage of yeast and the answers did not describe how to use the starter.  Your advice is appreciated. put (a) and (b) to one in subfigures IP tables - changes not persisting What exactly does ARM sell to vendors? Assumptions:   Computer architecture: Describes how the different modules of a processor interact with each other. A computer architecture is defined using vhdl files Computer Organization: Describes the physical layout of the processor modules on silicon. A computer organization is defined using a set of photo masks (and manufacturing process eg chemical, that goes at each step) Computer Organization, therefore, requires that the fab process be taken into account. ARM is not in the fabrication business, therefore it does not sell photo masks.     My question(s):   What exactly is ARM selling to a vendor (eg: freescale)? For a SoC (System On Chip), (eg: ), which part is ARM and which is Freescale? Who did the integration? $K \subset \mathbb{R}^n$ is compact iff it is closed and bounded I want to prove $\Leftarrow$.  I just need one more step, now. If I find a compact set that contains K, then it will finish the proof. Rudin take a k-cell to do that, but before it he proves that every k-cell is compact, and I think I can take a more simple compact to do this step. I has thinked in the closed ball, but don't know how to prove that it is compact. Can anyone help me to find this set, if it really exists? Thanks.