Linear combinations

[saver...@hotmail.com]

Hi all, sorry this is a bit of a simple question - I'm confused with exactly how linear combinations work when there are covariates included in the model. 

 

For my model fm5 I have created a linear combinations matrix based on the ovenbird example. Basically what I am interested in calculating is the estimated abundance at set distances from a release site. The covariate 'Location' however is a category, so I just wanted to check if  the code I have used below is correct: 

 

> fm5<-pcount(~start~Location+Prox.Release.Site..m.,umf,K=5)

>(lc<-linearComb(fm5, type = "state",

+ + matrix(c(1, 1, 0, 1, 1, 10), 2, 3, byrow = TRUE)))

 Linear combination(s) of Abundance estimate(s)

 

  Estimate    SE (Intercept) LocationRelease.Area Prox.Release.Site..m.

1    1.054 0.594           1                    1                     0

2    0.906 0.526           1                    1                    10

Also I have run a separate model, this one however has more covariates present (most of which are categories), and I am unsure how to get the linear combinations matrix to work as I keep getting an error message: 

fm6<-pcount(~temp+duration+start+wind~Location+Dominant.Veg, umf, K=60)

> (lc<-linearComb(fm6, type = "state",

+ matrix(c(1, 0, 0, 1, 0, 0), 2, 3, byrow = TRUE)))

Error: ncol(coefficients) == length(obj@estimates) is not TRUE

Can anyone explain how linear combinations work and how to create the matrices correctly?

Thanks a lot,

Sarah

[erikw...@gmail.com]

Hi Sarah,

Linear combinations are discussed in several areas including the FAQ as well as a vignette (page 3). I found these links helpful. Not sure how categorical covariates are handled but I've always been under the impression we should backTransform() linear combination estimates to make sensible interpretations. I believe linear combos are point estimates; if you are interested in estimating abundance at a range of distances from x, then I believe predict() would help and you could visualize the relationship with plot() and include confidence intervals. I'll watch this thread as I'm interested in this question as well.

Erik

[Richard Chandler]

Hi Sarah,

I recommend using predict() instead of linearComb() because predict() is just a wrapper around linearComb(), and it should be easier to use. These methods basically just plug the estimates into the (log- or logit-)linear equation. predict() will create the dummy variables and the design matrix for you -- linearComb() will not. 

Richard  

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[saver...@hotmail.com]

Hi Eric & Richard,

Thanks for your reply, really appreciate it. When using 'predict' is there a way of having the estimated abundance values? 

Sarah  

[erikw...@gmail.com]

Hi Sarah,

Indeed, predict() can estimate abundance ('state') along a gradient of covariate values that are supplied by a new data.frame. There are a bunch of good examples spattered about the listserve and vignettes.

Not sure what your data looks like but you would start with something similar to this:

newdataframe<- data.frame(Location=factor(c("A","B","C")), Prox.Release.Site..m = seq(0,1), length=100) #assign your covariate values

predict(fm5, newdata = newdataframe, type = "state")

You can sum the predicted values to get total estimated abundance and plot() Predicted ~ Prox.Release.Site..m to visualize predicted relationships.