# Extracting p-values from different fit R objects

Let's say you want to extract a p-value and save it as a variable for future use from a linear or generalized linear model – mixed or non! This is something you might want to do if, say, you were calculating Fisher's C from an equation-level Structural Equation Model. Here's how to extract the effect of a variable from multiple different fit models. We'll start with a data set with x, y, z, and a block effect (we'll see who in a moment).

``````
x <- rep(1:10, 2)
y <- rnorm(20, x, 3)
block <- c(rep("a", 10), rep("b", 10))

mydata <- data.frame(x = x, y = y, block = block, z = rnorm(20))
``````

Now, how would you extract the p-value for the parameter fit for z from a linear model object? Simply put, use the t-table from the lm object's summary

``````alm <- lm(y ~ x + z, data = mydata)

summary(alm)\$coefficients
``````
``````##             Estimate Std. Error t value Pr(>|t|)
## (Intercept)   1.1833     1.3496  0.8768 0.392840
## x             0.7416     0.2190  3.3869 0.003506
## z            -0.4021     0.8376 -0.4801 0.637251
``````
``````
# Note that this is a matrix.
# The third row, fourth column is the p value
# you want, so...

p.lm <- summary(alm)\$coefficients[3, 4]

p.lm
``````
``````## [1] 0.6373
``````

That's a linear model, what about a generalized linear model?

``````aglm <- glm(y ~ x + z, data = mydata)

summary(aglm)\$coefficients
``````
``````##             Estimate Std. Error t value Pr(>|t|)
## (Intercept)   1.1833     1.3496  0.8768 0.392840
## x             0.7416     0.2190  3.3869 0.003506
## z            -0.4021     0.8376 -0.4801 0.637251
``````
``````
# Again, is a matrix.
# The third row, fourth column is the p value you
# want, so...

p.glm <- summary(aglm)\$coefficients[3, 4]

p.glm
``````
``````## [1] 0.6373
``````

That's a linear model, what about a generalized linear model?

``````
anls <- nls(y ~ a * x + b * z, data = mydata,
start = list(a = 1, b = 1))

summary(anls)\$coefficients
``````
``````##   Estimate Std. Error t value  Pr(>|t|)
## a   0.9118     0.1007   9.050 4.055e-08
## b  -0.4651     0.8291  -0.561 5.817e-01
``````
``````
# Again, is a matrix.
# The second row, fourth column is the p value you
# want, so...

p.nls <- summary(anls)\$coefficients[2, 4]

p.nls
``````
``````## [1] 0.5817
``````

Great. Now, what if we were running a mixed model? First, let's look at the nlme package. Here, the relevant part of the summary object is the tTable

``````library(nlme)
alme <- lme(y ~ x + z, random = ~1 | block, data = mydata)

summary(alme)\$tTable
``````
``````##               Value Std.Error DF t-value  p-value
## (Intercept)  1.1833    1.3496 16  0.8768 0.393592
## x            0.7416    0.2190 16  3.3869 0.003763
## z           -0.4021    0.8376 16 -0.4801 0.637630
``````
``````
# Again, is a matrix.
# But now the third row, fifth column is the p value
# you want, so...

p.lme <- summary(alme)\$tTable[3, 5]

p.lme
``````
``````## [1] 0.6376
``````

Last, what about lme4? Now, for a linear lmer object, you cannot get a p value. But, if this is a generalizes linear mixed model, you are good to go (as in Shipley 2009). Let's try that here.

``````library(lme4)

almer <- lmer(y ~ x + z + 1 | block, data = mydata)

# no p-value!
summary(almer)@coefs
``````
``````##             Estimate Std. Error t value
## (Intercept)    4.792     0.5823   8.231
``````
``````
# but, for a genearlined linear mixed model
# and yes, I know this is a
# bad model but, you know, demonstration!

aglmer <- lmer(y + 5 ~ x + z + (1 | block),
data = mydata, family = poisson(link = "log"))

summary(aglmer)@coefs
``````
``````##             Estimate Std. Error z value  Pr(>|z|)
## (Intercept)  1.90813    0.16542  11.535 8.812e-31
## x            0.07247    0.02471   2.933 3.362e-03
## z           -0.03193    0.09046  -0.353 7.241e-01
``````
``````
# matrix again!  Third row, fourth column
p.glmer <- summary(aglmer)@coefs[3, 4]

p.glmer
``````
``````## [1] 0.7241
``````

# A Quick Note in Weighting with nlme

I’ve been doing a lot of meta-analytic things lately. More on that anon. But one quick thing that came up was variance weighting with mixed models in R, and after a few web searches, I wanted to post this, more as a note-to-self and others than anything. Now, in a simple linear model, weighting by variance or sample size is straightforward.

```#variance
lm(y ~ x, data = dat, weights = 1/v)

#sample size
lm(y ~ x, data = dat, weights = n)
```

You can use the same sort of weights argument with lmer. But, what about if you’re using nlme? There are reasons to do so. Things change a bit, as nlme uses a wide array of weighting functions for the variance to give it some wonderful flexibility – indeed, it’s a reason to use nlme in the first place! But, for such a simple case, to get the equivalent of the above, here’s the tricky little difference. I’m using gls, generalized least squares, but this should work for lme as well.

```#variance
gls(y ~ x, data=dat, weights = ~v)

#sample size
gls(y ~ x, data = dat, weights = ~1/n)
```

OK, end note to self. Thanks to John Griffin for prompting this.

# Missing my Statsy Goodness? Check out #SciFund!

I know, I know, I have been kinda lame about posting here lately. But that’s because my posting muscle has been focused on the new analyses for what makes a succesful #SciFund proposal. I’ve been posting them at the #SciFund blog under the Analysis tag – so check it out. There’s some fun stats, and you get to watch me be a social scientist for a minute. Viva la interdisciplinarity!

# Running R2WinBUGS on a Mac Running OSX

I have long used JAGS to do all of my Bayesian work on my mac. Early on, I tried to figure out how to install WinBUGS and OpenBUGS and their accompanying R libraries on my mac, but, to no avail. I just had too hard of a time getting them running and gave up.

But, it would seem that some things have changed with Wine lately, and it is now possible to not only get WinBUGS itself running nicely on a mac, but to also get R2WinBUGS to run as well. Or at least, so I have discovered after an absolutely heroic (if I do say so myself) effort to get it all running (this was to help out some students I’m teaching who wanted to be able to do the same exercises as their windows colleagues). So, I present the steps that I’ve worked out. I do not promise this will work for everyone – and in fact, if it fails at some point, I want to know about it so that perhaps we can fix it so that more people can get WinBUGS up and running.

Or just run JAGS (step 1} install the latest version, step 2} install rjags in R. Modify your code slightly. Run it. Be happy.)

So, this tutorial works to get the whole WinBUGS shebang running. Note that it hinges on installing the latest development version of Wine, not the stable version (at least as of 1/17/12). If you have previously installed wine using macports, good on you. Now uninstall it with “sudo port uninstall wine”. Otherwise, you will not be able to do this.

Away we go!

1) Have the free version of XCode Installed from http://developer.apple.com/xcode/. You may have to sign up for an apple developer account. Whee! You’re a developer now!

2) Have X11 Installed from your system install disc.

` echo export PATH=/opt/local/bin:/opt/local/sbin:\$PATH\$'n'export MANPATH=/opt/local/man:\$MANPATH | sudo tee -a /etc/profile `

4) Open your terminal and type

` sudo port install wine-devel `

5) Go have a cup of coffe, check facebook, or whatever you do while the install chugs away.

7) Open your terminal, and type

``` cd Downloads wine WinBUGS14.exe ```

8 ) Follow the instructions to install WinBUGS into c:Program Files.

9) Run WinBUGS via the terminal as follows:

` wine ~/.wine/drive_c/Program Files/WinBUGS14/WinBUGS14 `

10) After first running WinBUGS, install the immortality key. Close WinBUGS. Open it again as above and install the patch. Close it. Open it again and WinBUGS away!

11) To now use R2WinBugs fire up R and install the R2WinBUGS library.

12) R2WinBugs should now work normally with one exception. When you use the bugs function, you will need to supply the following additional argument:

` bugs.directory='/Users/YOURUSERNAME/.wine/drive_c/Program Files/WinBUGS14' `

filling in your username where indicated. If you don’t know it, in the terminal type

` ls /Users `

No, ~ will not work for those of you used to it. Don’t ask me why.

# Ecological SEMs and Composite Variables: What, Why, and How

I’m a HUGE fan of Structural Equation Modeling. For those of you unfamiliar with the technique, it’s awesome for three main reasons.

1. It’s a method of teasing apart direct and indirect interactions in your data.
2. It allows you to assess the importance of underlying latent variables that you cannot measure, but for which have measured indicators.
3. As it’s formally presented, with path diagrams showing connections between variables, it’s SUPER easy to link conceptual models with your data. See Grace et al. 2010 for a handy guide to this.

Also, there is a quite simple and intuitive R package for fitting SEMs, lavaan (LAtent VAriable Analysis). Disclaimer, I just hopped on board as a lavaan developer (yay!). I’ve also recently started a small project to find cool examples of SEM in the Ecological literature, and then using the provided information, post the models coded up in lavaan so that others can see how to put some of these models together.

As Ecologists, we often use latent variables to incorporate known measurement error of a quantity – i.e., a latent variable with a single indicator and fixed variance. We’re often not interested in the full power of latent variables – latents with multiple indicators. Typically, this is because we’ve actually measured everything we want to measure. We’re not like political scientists who have to quantify fuzzy things like Democracy, or Authoritarianism, or Gastronomicism. (note, I want to live in a political system driven by gastronomy – a gastronomocracy!)

However, we’re still fascinated by the idea of bundling different variables together into a single causal effect, and maybe evaluating the relative contribution of each of those variables within a model. In SEM, this is known as the creation of a Composite Variable. This composite is still an unmeasured quantity – like a latent variable – but with no error variance, and with “indicators” actually driving the variable, rather than having the unmeasured variable causing the expression of its indicators.

Let me give you an example. Let’s say we want to measure the effect of nutrients on diatom species richness in a stream. You’re particularly concerned about nitrogen. However, you can’t bring water samples back to the lab, so, you’re relying on some moderately accurate nitrogen color strips, the biomass of algae (more algae = more nitrogen!), and your lab tech, Stu, who claims he can taste nitrogen in water (and has been proved to be stunningly accurate in the past). In this case, you have a latent variable. The true nitrogen content of the water is causing the readings by these three different indicators.

A composite variable is a different beast. Let’s say we have the same scenario. But, now you have really good measurements of nitrogen. In fact, you have good measurements of both ammonium (NH4) and nitrate (NO3). You want to estimate a “nitrogen effect”, but, you know that both of these different forms of N will contribute to the effect in a slightly different way. You could just construct a model with effects going from both NO3 and NH4 to species richness. If you want to represent the total “Nitrogen Effect” in your model, however, and evaluate the effect of each form of nitrogen on its total effect, you would create a composite. The differences become clear when looking at the path diagram of each case.

Here, I’m adopting the custom of observed variables in squares, latent variables in ovals, and composite variables in hexagons. Note that, as indicators of nitrogen in the latent variable model, each observed indicator has some additional variation due to factors other than nitrogen – Î´i. There is no such error in the composite variable model. Also, I’m showing that the error in the Nitrogen Effect in the composite variable model is indeed set to 0. There are sometimes reasons where that shouldn’t be 0, but that’s another topic for another time.

This may still seem abstract to you. So, let’s look at an example in practice. One way we often use composites is to bring together a linear and nonlinear effect of a single variable. For example, we know that often nutrient supply rates have a humped shape effect on species richness – i.e., the highest richness happens at intermediate supply rates. One nice example of that is in a paper by Cardinale et al. in 2009 looking at relationships between manipulated nutrient supply, species richness, and algal productivity. To capture that relationship with a composite variable, one would have a ‘nitrogen effect’ affected by N and N2. This nitrogen effect would then affect local species richness.

So, how would you code this model up in lavaan, and then evaluate it.

Well, hey, the data from this paper are freely available, so, let’s use this as an example. For a full replication of the model presented in the paper see here. However, Cardinale et al. didn’t use any composite variables, so, let’s create a model of our own capturing the Nitrogen-Richness relationship while also accounting for local species richness being influenced by regional species richness.

In the figure above, we have the relationship between resource supply rate and local species richness on an agar plate to the left. Separate lines are for separate streams. The black line is the average fit with the supplied equation. On the right, we have a path diagram representing this relationship, as well as the influence of regional species richness.

So, we have a path diagram. Now comes the tricky part. Coding. One thing about the current version of lavaan (0.4-8) is that it does not have a way to represent composite variables. This will change in the future (believe me), but, it may take a while, so, let me walk you through the tricks of incorporating latent variables now. Basically, there are four steps.

1. Define the variable as a regression, where the composite is determined by it’s causal variables. Also, fix one of the effects to 1. This gives your composite variable a scale.
2. Specify that the composite has an error variance of 0.
3. Now treat the composite as a latent variable. It’s indicators are it’s response variables. This may seem odd. However, it’s all just ways of specifying causal pathways – an indicator pathway and a regression pathway have the same meaning in terms of causality. The software just needs something specified so that it doesn’t go looking for our composite variable in our data. Hence, defining it as a latent variable whose indicators are endogenous responses. I actually find this helpful, as it also makes me think more carefully about what a composite variable is, and how too many responses may make my model not identified.
4. Lastly, because we don’t want to fix the effect of our composite on its response to 1, we’ll have to include an argument in the fitting function that makes it not force the first latent variable loading to be set to 1. We’ll also have to specify that we then want the variance of the response to latent variables freely estimated. Yeah, I know. Note: this all can play havoc when you have both latent and composite variables, so be careful. See here for an example.
5. Everything else – other regression relationships, showing that nonlinearities are derived quantities, etc.

OK, that’s a lot. How’s it work in practice? Below is the code to fit the model in the path diagram. I’ve labeled the steps in comments, and, included the regional ~ local richness relationship as well as the relationship showing that logN2 was derived from logN. Note, this is a centered squared variable. And, yes, all nitrogen values have been log transformed here.

```#simple SA model with N and regional SR using a composite
#Variables: logN = log nutrient supply rate, logNcen2 = log supply rate squared
# SA = Species richness on a patch of Agar, SR = stream-wide richness
compositeModel<-'
#1) define the composite, scale to logN

#2) Specify 0 error variance
Nitrogen ~~ 0*Nitrogen

#3) now, because we need to represent this as a latent variable
#show how species richness is an _indicator_ of nitrogen
Nitrogen =~ SA

#4) BUT, make sure the variance of SA is estimated
SA ~~ SA

#Regional Richness also has an effect
SA ~ SR

#And account for the derivation of the square term from the linear term
logNcen2 ~ logN
'

# we specify std.lv=T so that the Nitrogen-SA relationship isn't fixed to 1
compositeFit <- sem(compositeModel, data=cards, std.lv=T)```

Great! It should fit just fine. I'm not going to focus on the regional relationship, as it is predictable and positive. Moreover, when we look at the results, two things immediately pop out at us about the effect of nutrient supply rate.

```                   Estimate  Std.err  Z-value  P(>|z|)
Latent variables:
Nitrogen =~
SA                0.362    0.438    0.827    0.408

Regressions:
Nitrogen ~
logN              1.000
logNcen2         -1.311    1.373   -0.955    0.340```

Wait, what? The Nitrogen effect was not detectably different from 0? Nor was there a nonlinear effect? What's going on here?

What's going on is that the scale of the composite is affecting our results. We've set it to 1. Whenever you are fixing scales, you should always check and see, what would happen if you changed which path was set to 1. So, we can simply set the scale to the nonlinear variable, refit the model, and see if this makes a difference. If it doesn't, then that means there is no nitrogen effect at all!

So, change

`Nitrogen ~ 1*logN + logNcen2`

to

`Nitrogen ~ logN + 1*logNcen2`

And, now let's see the resultsâ€¦..

```                   Estimate  Std.err  Z-value  P(>|z|)
Latent variables:
Nitrogen =~
SA               -0.474    0.239   -1.989    0.047

Regressions:
Nitrogen ~
logN             -0.763    0.799   -0.955    0.340
logNcen2          1.000```

Ah HA! Not only is the linear effect not different from 0, but now we see that fixing the nonlinear effect allows the nutrient signal to come through.

But wait, you may say, that effect is negative? Well, remember that the scale of the nitrogen effect is the same as the nonlinear scale. And, a positive hump-shaped relationship will have a negative squared term. So, given how we've setup the model, yes, that should be negative.

*whew!* That was a lot. And this for a very simile model involving composites and nonlinearities. I thought I'd throw that out as it's a common use of composites, and interpreting nonlinearities in SEMs is always a little tricky and worth bending your brain around. Other uses of composites include summing up a lot of linear quantities, a composite for the application of treatments, and more. But, this should give you a good sense of what they are, how to code them in lavaan, and how to use them in the future.

For a more in depth treatment of this topic, and latent variables versus composites, I urge you to check out this excellent piece by Jim Grace and Ken Bollen. Happy model fitting!

# Extra! Extra! Get Your gridExtra!

The more I use it, the deeper I fall in love with ggplot2. I know, some of you have heard me kvel about it ad nauseum (oh, yiddish and latin in one sentence – extra points!). But the graphs really look great, and once you wrap your head around a few concepts, it’s surprisingly easy to make it do most anything you want.

Except for one thing.

One thing I loved about the old R plotting functions was the ability to setup panels easily, and fill them with totally different graphs. Ye olde par(mfrow=c(2,2)) for a 2 x 2 grid, for example.

Enter gridExtra. Let the games begin.

What exactly do I mean? Let’s say I’m working with the soil chemistry data in the vegan package. First, maybe I just want to eyeball the historgrams of both the hummus depth and bare soil columns.

To do this in ggplot2, and with a single commend to put them in a single window, first you need to melt the data with reshape2 so that the column names are actually grouping variables, and then you can plot it. In the process, you create an additional data frame. And, you also have to do some extra specifying of scales, facets, etc. etc. Here’s the code and graphs.

```library(ggplot2) #for plotting
library(reshape2) #for data reshaping

library(vegan) #for the data
data(varechem)

#First, reshape the data so that Hummus depth and Bare soil are your grouping variables
vMelt<-melt(varechem, measure.vars=c("Humdepth", "Baresoil"))

#Now plot it.  Use fill to color things differently, facet_wrap to split this into two panels,
#And don't forget that the x scales are different - otherwise things look odd
qplot(value, data=vMelt, fill=variable)+facet_wrap( facets=~variable, scale="free_x")
```

This produces a nice graph. But, man, I had to think about reshaping things, and all of those scales? What if I just wanted to make two historgrams, and slam 'em together. This is where gridExtra is really nice. Through its function grid.arrange, you can make a multi-paneled graph using ggplot2 plots, lattice plots, and more (although, not regular R plots...I think).

So, let's see the same example, but with gridExtra.

```library(gridExtra)

#make two separate ggplot2 objects
humDist<-qplot(Humdepth, data=varechem, fill=I("red"))
bareDist<-qplot(Baresoil, data=varechem, fill=I("blue"))

#Now use grid.arrange to put them all into one figure.
#Note the use of ncol to specify two columns.  Things are nicely flexible here.
grid.arrange(humDist, bareDist, ncol=2)
```

"Oh, what a trivial problem," you may now be saying. But, if you want to, say, plot up 5 different correlations, or, say, the same scatterplot with 4 different model fits, this is a life-saver - if nothing else, in terms of readability of your code for later use.

This is all well and good, but, simple. Let's get into more fun multi-panel figures. Let's say we wanted a bivariate scatter-plot of Hummus Depth and Bare Soil with a linear fit. But, we also wanted to plot the histograms of each variable in adjacent panels. Oh, and flip the histogram of whatever is on the y-axis. Sexy, no? This is pretty straightforward. We can use the ggplot2 objects we already have, flip the co-ordinates on one, create a bivariate plot with a fit, and fill in one final panel with something blank.

```#First, the correlation.  I'm using size just to make bigger points.  And then I'll add a smoothed fit.
corPlot<-qplot(Humdepth, Baresoil, data=varechem, size=I(3))+stat_smooth(method="lm")

#OK, we'll need a blank panel.  gridExtra can make all sorts of shapes, so, let's make a white box
blankPanel<-grid.rect(gp=gpar(col="white"))

#Now put it all together, but don't forget to flip the Baresoil histogram
grid.arrange(humDist, blankPanel, corPlot, bareDist, ncol=2)
```

Nice. Note the use of the grid.rect. gridExtra is loaded with all sorts of interesting ways to place shapes and other objects into your plots - including my favorite - grid.table, for when you don't want to deal with text.

```a<-anova(lm(Baresoil ~ Humdepth, data=varechem))
grid.table(round(a, digits=3))
```

Or, heck, if you want to make that part of the above plot, use tableGrob instead of grid.table, and then slot it in where the blank panel is. The possibilities are pretty endless!

UPDATE: Be sure to see Karthik's comment below about alternatively using viewports. Quite flexible, and very nice, if a hair more complex.

Thanks to Jim, I’ve been using R in the shell more and more – in concert with vi. It’s been fun, and nice to integrate my workflows all on the server (although I haven’t had to do much graphing yet – I’m sure I’ll start kvetching then and return to a nice gui).

One thing that has frustrated me is that large dumps of output – say, a list composed of elements that are 100 lines each – just whip past me without an ability to scroll through more slowly. The page function helps somewhat, but, it gets wonky when looking at S4 objects. I wanted something more efficient that used – something more…well, like more! So i peered into page, and whipped up a more function that some of you may find useful. Of course, I’m sure that there is a simpler way, but, when all else fails…write it yourself!

```more<-function(x, pager=getOption("pager")){
#put everything into a local file using sink
file <- tempfile("Rpage.")
sink(file)
show(x)
sink()

#use file.show as you can use the default R pager
file.show(file, title = "", delete.file = TRUE, pager = pager)
}
```

# RStudio – An IDE for the Masses!

I’ll admit it. There’s one thing that always makes me sad working on a mac. R. How does R make me sad on a mac? I look over at my compatriots in Windows using fun Integrated Development Environments (IDEs) like Tinn-R, and I sigh. On the other hand, I just had the sad little text editor and shell. Sure, it was enough, and I had wrung some sweet sweet code from that simple setup, but windows would get lost, I’d lose track of what file was where, what plot window was open, and would sometimes even forget which instance of R I was working in when I was working on two projects at the same time (one for simulation, one for analysis).

I mean, sure, I could go through the rigamarole of doing everything through some flavor of Emacs like a 31337 h4X0r. But my Emacs days are behind me. I would have preferred a simpler solution.

So when I saw news of a new, cross-platform, free, lovely IDE called RStudio hit R-bloggers and the Twitterverse, I rejoiced.

But would it be just a kludgy piece of bunk, or a nice, smooth, user experience? I figured I’d give it a whirl. I hopped on over to the website, and had a pleasant easy download experience. Then I fired it up, and ran an old analysis. After fiddling around a little just to get my feet on the ground (which took only a minute or two – the whole thing was quite intuitive), I was pretty pleased. The interface was clean, simple, and purty.

Oh! Quite the little interface, there! Click to get a larger view.

And some features – such as image exporting – were like a dream. So easy, in fact, that I decided to confront it with the problem of exporting an image for publication at the proper image quality (something which is always a bit of a hassle in R normally). But to my delight, no problem. Just fiddled with the size a little bit, and presto! High quality pub-ready image.

So, overall, I’m impressed. And with a Twitter feed, blog, and interactive support forum, I think it looks like this IDE is going to be a great tool for science. So go check it out!