Feasible Solution Algorithm for Finding Best Subsets and Interactions.

Overview

Our article "rFSA: An R Package for Finding Best Subsets and Interactions" was published in the R Journal in December 2018. The article outlines The Feasible Solution Algorithm (FSA) and the R package rFSA.

rFSA

To use the R package, rFSA, the user must know how they wish to model the data (method) and how the will evaluate the fit of the models that will be checked (criterion function).

Example (mtcars)

In R, a commond test dataset to analyze is mtcars. For this example we will use multiple linear regression to fit the model and Adjusted R Squared to asses the model fit on the response(Miles Per Gallon).

data(mtcars)
help(mtcars)

For this example, let us assume that we have already found that the weight(wt) and the number of cylinders(cyc) in a car are statistically signficant predictors of Miles Per Gallon(mpg) for that car. And, let's say that we wish to explore two-way interactions for inclusion in or model with wt and cyc.

To do this with rFSA, we could run the following code:

install.packages(rFSA) #or devtools::install_github("joshuawlambert/rFSA")
library(rFSA)
data(mtcars)

set.seed(123)

fsaFit<-FSA(
  formula="mpg~wt+cyl", #Model that you wish to compare new models to. The variable to the left of the '~' will be used as the response variable in all model fits
  data=mtcars, #specify dataset 
  fitfunc = lm, #method you wish to use 
  fixvar = c('wt','cyl'), # variables that should be fixed in every model that is considered 
  m = 2, #order of interaction or subset to consider
  numrs = 10, #number of random starts to do 
  interactions = TRUE, #If TRUE, then the m variables under condsideration will be added to the model with a '*' between them, if FALSE then the m variables will be added to the model with a '+' between them. Basically, do you want to look for interactions or best subsets.
  criterion = adj.r.squared, #Criterion function used to asses model fit
  minmax = "max" #Should Criterion function be minimized ('min') or maximized ('max').
  
)

fsaFit #shows results from running FSA
print(fsaFit) #shows results from running FSA
summary(fsaFit) #shows summary from all models found by FSA
plot(fsaFit) #plots diagnostic plots for all models found by FSA
fitted(fsaFit) #fitted values from all models found by FSA
predict(fsaFit) #predicted values from all models found by FSA, can also add newdata command.

As we can see from print(fsaFit), from the 10 random starts there were 2 feasible solutions (FS). The two feasible included an interaction between hpwt and dratcarb. Each of these FS happened 9 and 1 respectively. After looking at summary(fsaFit) we can see that hp and wt interaction is statistically significant (p-value<0.01) and drat and carb interaction is marginally significant (p-value ~= 0.06). If we wished to find interactions that were significant, we could change criterion=int.p.val and minmax = "min". Doing so, will yeild one FS: hp*wt.

Following up these results with sufficient checks into model fit and diagnositic plots is .

Other options for the FSA function in rFSA include:

cores = 1  #*FOR LINUX USERS ONLY* uses parallel package to use multiple cores if available. 
quad = FALSE #should quadratic terms be considered by rFSA (example: wt^2)
checkfeas = NULL #Choose a starting place for FSA. If used, should be a vector same length as m from above. Example: c('wt','cyc')
var4int = NULL #Variable to fix in interaction. Useful when considering 3 or more way interactions.
min.nonmissing = 1 #Don't consider models that have less than or equal to this number of observations
return.models = FALSE #should all models that are checked be returned? Useful when you want to ploc criterion history.

see `help(FSA)' for more details.

Visualizing Interactions

Visualizing interactions can be quite difficult depending on the types of variables that are involved in the relationship. The goal of rFSA is not to assist the user in visualizing the interaction, but the authors recognize that visual tools are often quite useful conveying the results from a statistical model.

We have found the sjPlot package to be very useful for plotting 2-way interactions. More information about the sjPlot package can be found here: http://www.strengejacke.de/sjPlot/.

For the mtcars example above, the two interactions that were found can be plotted very easy using the sjPlot function plot_model with the type="int" option. Below is some example code:

library(sjPlot)
library(rFSA)
fit<-rFSA::fitmodels(fsaFit)
sjPlot::plot_model(fit[[2]],type = "int")
sjPlot::plot_model(fit[[3]],type = "int")