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POWhich function/package for robust linear regression works with glmulti (i.e., behaves like glm)?
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<h1>Background: Multi-model inference with glmulti</h1> <a href="http://www.jstatsoft.org/v34/i12/paper" rel="noreferrer">glmulti</a> is a R function/package for automated model selection for general linear models that constructs all possible general linear models given a dependent variable and a set of predictors, fits them via the classic <a href="http://stat.ethz.ch/R-manual/R-patched/library/stats/html/glm.html" rel="noreferrer">glm</a> function and allows then for multi-model inference (e.g., using model weights derived from AICc, BIC). glmulti works in theory also with any other function that returns coefficients, the log-likelihood of the model and the number of free parameters (and maybe other information?) in the same format that glm does. <h1>My goal: Multi-model inference with robust errors</h1> I would like to use glmulti with robust modeling of the errors of a quantitative dependent variable to guard against the effect out outliers. For example, I could assume that the errors in the linear model are distributed as a <a href="http://en.wikipedia.org/wiki/Student%27s_t-distribution" rel="noreferrer">t distribution</a> instead of as a normal distribution. With its kurtosis parameter the t distribution can have heavy tails and is thus more robust to outliers (as compared to the normal distribution). However, I'm not committed to using the t distribution approach. I'm happy with any approach that gives back a log-likelihood and thus works with the multimodel approach in glmulti. But that means, that unfortunately I cannot use the well-known robust linear models in R (e.g., lmRob from <a href="http://cran.r-project.org/web/packages/robust/" rel="noreferrer">robust</a> or lmrob from <a href="http://cran.r-project.org/web/packages/robustbase/" rel="noreferrer">robustbase</a>) because they do not operate under the log-likelihood framework and thus cannot work with glmulti. <h1>The problem: I can't find a robust regression function that works with glmulti</h1> The only robust linear regression function for R I found that operates under the log-likelihood framework is heavyLm (from the <a href="http://cran.r-project.org/web/packages/heavy/index.html" rel="noreferrer">heavy</a> package); it models the errors with a t distribution. Unfortunately, heavyLm does not work with glmulti (at least not out of the box) because it has no S3 method for loglik (and possibly other things). To illustrate: <pre><code>library(glmulti) library(heavy) </code></pre> Using the dataset stackloss <pre><code>head(stackloss) </code></pre> Regular Gaussian linear model: <pre><code>summary(glm(stack.loss ~ ., data = stackloss)) </code></pre> Multi-model inference with glmulti using glm's default Gaussian link function <pre><code>stackloss.glmulti <- glmulti(stack.loss ~ ., data = stackloss, level=1, crit=bic) print(stackloss.glmulti) plot(stackloss.glmulti) </code></pre> Linear model with t distributed error (default is df=4) <pre><code>summary(heavyLm(stack.loss ~ ., data = stackloss)) </code></pre> Multi-model inference with glmulti calling heavyLm as the fitting function <pre><code>stackloss.heavyLm.glmulti <- glmulti(stack.loss ~ ., data = stackloss, level=1, crit=bic, fitfunction=heavyLm) </code></pre> gives the following error: <pre><code> Initialization... Error in UseMethod("logLik") : no applicable method for 'logLik' applied to an object of class "heavyLm". </code></pre> If I define the following function, <pre><code>logLik.heavyLm <- function(x){x$logLik} </code></pre> glmulti can get the log-likelihood, but then the next error occurs: <pre><code> Initialization... Error in .jcall(molly, "V", "supplyErrorDF", as.integer(attr(logLik(fitfunc(as.formula(paste(y, : method supplyErrorDF with signature ([I)V not found </code></pre> <h1>The question: Which function/package for robust linear regression works with glmulti (i.e., behaves like glm)?</h1> There is probably a way to define further functions to get heavyLm working with glmulti, but before embarking on this journey I wanted to ask whether anybody <ul> <li>knows of a robust linear regression function that (a) operates under the log-likelihood framework and (b) behaves like glm (and will thus work with glmulti out-of-the-box).</li> <li>got heavyLm already working with glmulti.</li> </ul> Any help is very much appreciated!
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<r><glm><robust>
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Which function/package for robust linear regression works with glmulti (i.e., behaves like glm)?
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