How can factor-levels be automatically chosen in R to maximize the number of positive coefficients in a regression model?

Question

I am performing simple (first-order terms) linear regression on data having several categorical variables (i.e. factors), and it is often desired that for each factor, one of the levels should add nothing to the regressand, and the other levels should add positive values to the regressand. When I perform a regression analyses, however, I often get a lot of negative coefficients.

Is there a non-manual way of choosing which levels of a factor should be used as regressor variables in order to maximize the number of positive coefficients in the equation? In other words, how can I get R to do this (somewhat tedious) task for me?

Answer 1

Here is an attampt of doing what you wanted.

 # Setting up some sample data
 require(dummies)
 df <- data.frame(categorial=rep(c(1,2,3), each=20), x=rnorm(60))
 flevels <- dummy(df$categorial)
 df$categorial <- factor(df$categorial)

 df$y=20 + df$x*3 + flevels%*%c(3,1,2) + rnorm(60)*2

I use a regression in order to obtain the minimum factor level and then reorder:

 # Now we start with trying to find the minimum cateogry. However, note that this does not work in every context!
 summary(helpreg <- lm(y~x+factor(categorial) - 1, data=df))

     Coefficients:
                         Estimate Std. Error t value Pr(>|t|)    
     x                     2.9944     0.2334   12.83   <2e-16 ***
     factor(categorial)1  22.9640     0.4472   51.35   <2e-16 ***
     factor(categorial)2  21.0720     0.4390   48.00   <2e-16 ***
     factor(categorial)3  22.1300     0.4364   50.71   <2e-16 ***

Then I start to sort out the minimum:

 factors <- grep('categorial', names(coef(helpreg))) # --- replace categorial with your variable name

 minimumf <- which(coef(helpreg)[factors]==min(coef(helpreg)[factors]))

This is then releveled

 df$categorial <- relevel(df$categorial, ref=minimumf)

And in my case it works - probably it works for you as well....

 summary(lm(y~x+factor(categorial), data=df))

                           Estimate Std. Error t value Pr(>|t|)    
       (Intercept)          21.0720     0.4390  48.003  < 2e-16 ***
       x                     2.9944     0.2334  12.828  < 2e-16 ***
       factor(categorial)1   1.8920     0.6341   2.984  0.00421 ** 
       factor(categorial)3   1.0580     0.6193   1.708  0.09310 . 

Comments of course highly appreciated!

Answer 2

Thanks to whuber's comment, and Seb's answer, I have put together the following function which I believe does what I want. Hopefully it will be useful to someone. Comments are welcome.

# take a dataframe, and re-level it such that the levels of the factors are
# assigned positive coefficients by lm()
# NOTE: this currently only works for model-forms that don't include
#       interaction terms.
auto_relevel <- function(df, model_form)
{
    # get list of categorical variables in df
    catvar_indices <- get_catvar_indices(df)

    # loop over categorical variables
    df_colnames <- attr(df, 'names')
    model_form_zeroicept <- paste(model_form, "- 1")
    for (i in catvar_indices) {
        catvar_name = df_colnames[i]
        all_levels = attr(df[[i]], "levels")
        temp_model <- lm(model_form_zeroicept, data=df)

        # If at least one of the levels' coefficients is less than zero, then
        # choose the one w/min coeff to be the new base-level

        # put a space after catvar_name so that it doesn't match longer level-names
        catvar_name <- paste(catvar_name, " ", sep="")
        factors <- grep(catvar_name, names(coef(temp_model)))
        coeffs <- coef(temp_model)[factors]
        # remove NA's from coeffs
        coeffs2 <- coeffs[! is.na(coeffs)]

        if (any(coeffs2 < 0)) {            
            # find out where this factor is in *all_levels*
            chosen_level_name <- names(coeffs2)[which(coeffs2==min(coeffs2))]
            stripped_level_name <- unlist(strsplit(chosen_level_name," "))[2] # strip factor name
            # add an initial space (to match all_levels)
            stripped_level_name <- paste(" ", stripped_level_name, sep="")
            min_level_index <- which(all_levels == stripped_level_name)
            df[[i]] <- relevel(df[[i]], ref=min_level_index)
        }
    }

    return(df)
}