| Type: | Package |
| Title: | Feasible Solution Algorithm for Finding Best Subsets and Interactions |
| Version: | 0.9.6 |
| Date: | 2020-06-10 |
| Description: | Assists in statistical model building to find optimal and semi-optimal higher order interactions and best subsets. Uses the lm(), glm(), and other R functions to fit models generated from a feasible solution algorithm. Discussed in Subset Selection in Regression, A Miller (2002). Applied and explained for least median of squares in Hawkins (1993) <doi:10.1016/0167-9473(93)90246-P>. The feasible solution algorithm comes up with model forms of a specific type that can have fixed variables, higher order interactions and their lower order terms. |
| License: | GPL-2 |
| LazyData: | TRUE |
| Imports: | parallel, methods, tibble, rPref, tidyr, hash |
| RoxygenNote: | 7.1.0 |
| NeedsCompilation: | no |
| Packaged: | 2020-06-10 17:53:10 UTC; josh |
| Author: | Joshua Lambert [aut, cre], Liyu Gong [aut], Corrine Elliott [aut], Sarah Janse [ctb] |
| Maintainer: | Joshua Lambert <joshua.lambert@uc.edu> |
| Repository: | CRAN |
| Date/Publication: | 2020-06-10 20:20:03 UTC |
FSA: Feasible Solution Algorithm
Description
A function using a Feasible Solution Algorithm to find a set of feasible solutions for a statistical model of a specific form that could include mth-order interactions (Note that these solutions are optimal in the sense that no one swap to any of the variables will increase the criterion function.)
Usage
FSA(
formula,
data,
fitfunc = lm,
fixvar = NULL,
quad = FALSE,
m = 2,
numrs = 1,
cores = 1,
interactions = T,
criterion = AIC,
minmax = "min",
checkfeas = NULL,
var4int = NULL,
min.nonmissing = 1,
return.models = FALSE,
fix.formula = NULL,
...
)
lmFSA(...)
glmFSA(...)
Arguments
formula |
an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted. |
data |
a data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. |
fitfunc |
the method that should be used to fit the model. For Example: lm, glm, or other methods that rely on formula, data, and other inputs. |
fixvar |
variable(s) to fix in the model. Usually a covariate that should always be included (Example: Age, Sex). Will still consider it with interactions. Default is NULL. |
quad |
Include quadratic terms or not. Logical. |
m |
order of terms to include. If interactions is set to TRUE then m is the order of interactions to be considered. For Subset selection (interaction=F), m is the size of the subset to examine. Defaults to 2. |
numrs |
number of random starts to perform. |
cores |
number of cores to use while running. Note: Windows can only use 1 core. See mclapply for details. If function detects a Windows user it will automatically set cores=1. |
interactions |
whether to include interactions in model. Defaults to TRUE. |
criterion |
which criterion function to either maximize or minimize. For linear models one can use: r.squared, adj.r.squared, cv5.lmFSA (5 Fold Cross Validation error), cv10.lmFSA (10 Fold Cross Validation error), apress (Allen's Press Statistic), int.p.val (Interaction P-value), AIC, BIC. |
minmax |
whether to minimize or maximize the criterion function |
checkfeas |
vector of variables that could be a feasible solution. These variables will be used as the last random start. |
var4int |
specification of which variables to check for marginal feasiblilty. Default is NULL |
min.nonmissing |
the combination of predictors will be ignored unless this many of observations are not missing |
return.models |
bool value to specify whether return all the fitted models which have been checked |
fix.formula |
... |
... |
other arguments passed to fitfunc. |
Value
matrix of results
Functions
-
FSA: find best set of variables for statistical models -
lmFSA: alias forFSA(fitfunc=lm,...) -
glmFSA: alias forFSA(fitfunc=glm,...)
Examples
N <- 10 #number of obs
P <- 100 #number of variables
data <- data.frame(matrix(rnorm(N*(P+1)), nrow = N, ncol = P+1))
sln <- FSA(formula = "X101~1", data = data, cores = 1, m = 2,
interactions = FALSE, criterion = AIC, minmax = "min",
numrs = 10)
sln
Return QICu for geepack::geeglm
Description
Computes quasi-likelihood under the independence criterion (QICu)
Usage
QICu.geeglm(gee.obj)
Arguments
gee.obj |
geeglm obj |
An rFSA Criterion Function.
Description
rFSA Criterion Function to compute Adjusted R-Squared.
Usage
adj.r.squared(model, name = "Adj R Squared")
Arguments
model |
lm or glm fit to be passed. |
name |
passed to print.FSA |
An rFSA Criterion Function.
Description
rFSA Criterion Function to Allen's Press Statistic.
Usage
apress(model, name = "PRESS")
Arguments
model |
lm or glm fit to be passed. |
name |
passed to print.FSA |
An rFSA Criterion Function.
Description
rFSA Criterion Function to compute the Bhattacharyya distance.
Usage
bdist(model, name = "B Distance")
Arguments
model |
lm or glm fit to be passed. |
name |
passed to print.FSA |
Examples
#To use Bhattacharyya Distance and FSA the response must be binary, and you must
#be considering searching for two way continuous interactions.
data(mtcars)
fit<-FSA(formula = "am~gear*hp",data = mtcars,
fitfunc = glm,family="binomial",m = 2,cores=1,
interactions = TRUE,criterion = bdist,minmax = "max")
Model fitting function for FSA solutions
Description
Model fitting function for FSA solutions
Usage
fitmodels(object, ...)
Arguments
object |
FSA object to construct models on. |
... |
other parameters passed to lm or glm. See help(lm) or help(glm) for other potential arguements. |
Value
list of FSA models that have been fitted.
Examples
#use mtcars package see help(mtcars)
data(mtcars)
colnames(mtcars)
fit<-lmFSA(formula="mpg~hp*wt",data=mtcars,fixvar="hp",
quad=FALSE,m=2,numrs=10,save_solutions=FALSE,cores=1)
fitmodels(fit)
Fitted Values for FSA solutions
Description
Fitted Values for FSA solutions
Usage
## S3 method for class 'FSA'
fitted(object, ...)
Arguments
object |
FSA object to get fitted values from. |
... |
other parameters passed to fitmodels or fitted function. See help(fitmodels) or help(fitted) for assistance. |
Value
list of fitted values from each FSA model.
Examples
#use mtcars package see help(mtcars)
data(mtcars)
colnames(mtcars)
fit<-lmFSA(formula="mpg~hp*wt",data=mtcars,fixvar="hp",
quad=FALSE,m=2,numrs=10,save_solutions=FALSE,cores=1)
fitted(fit)
An rFSA Criterion Function.
Description
rFSA Criterion Function to compute Liklihood Ratio Test Statistics p-value for the largest order interation term.
Usage
int.p.val(model, name = "Interaction P-Value")
Arguments
model |
lm or glm fit to be passed. |
name |
passed to print.FSA |
List all included Criteria function for lmFSA and glmFSA.
Description
List all included Criteria function for lmFSA and glmFSA.
Usage
list.criterion()
Value
list of functions and whether lmFSA or glmFSA work with those functions.
Examples
list.criterion()
Return maximum absolute residual from a model
Description
Return maximum absolute residual from a model
Usage
max_abs_resid(model)
Arguments
model |
model obj |
Variables to include in the >1st step of an mth order interaction model determined from the Feasible Soution Alorithm.
Description
Finds the swaps available given a current position given previous picks.
Usage
nextswap(curpos, n, prevpos, quad)
Arguments
curpos |
A vector of length greater than 2 of what current explantory varialbes are being used in the model. |
n |
The number of explanatory variables in available to swap. |
prevpos |
A vector of previous best spots |
quad |
Whether to include quadratic terms. ie (x1*x1) as potential swaps. |
Value
a matrix with the possible forms by column.
pFSA: Pareto Feasible Solution Algorithm
Description
A function using a Feasible Solution Algorithm to estimate a set of models which are on the Pareto frontiers for chosen criteria
Usage
pFSA(
numFronts = 2,
pselExpr = NULL,
plot.it = TRUE,
formula,
data,
fitfunc = lm,
fixvar = NULL,
quad = FALSE,
m = 2,
numrs = 1,
cores = 1,
interactions = T,
criterion = AIC,
minmax = "min",
checkfeas = NULL,
var4int = NULL,
min.nonmissing = 1,
return.models = FALSE,
fix.formula = NULL,
...
)
Arguments
numFronts |
integer number of estimated frontiers to return |
pselExpr |
expression used by function psel to estimate pareto frontiers. help(psel). |
plot.it |
TRUE/FALSE for whether to plot the pareto frontiers |
formula |
an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted. |
data |
a data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. |
fitfunc |
the method that should be used to fit the model. For Example: lm, glm, or other methods that rely on formula, data, and other inputs. |
fixvar |
variable(s) to fix in the model. Usually a covariate that should always be included (Example: Age, Sex). Will still consider it with interactions. Default is NULL. |
quad |
Include quadratic terms or not. Logical. |
m |
order of terms to include. If interactions is set to TRUE then m is the order of interactions to be considered. For Subset selection (interaction=F), m is the size of the subset to examine. Defaults to 2. |
numrs |
number of random starts to perform. |
cores |
number of cores to use while running. Note: Windows can only use 1 core. See mclapply for details. If function detects a Windows user it will automatically set cores=1. |
interactions |
whether to include interactions in model. Defaults to TRUE. |
criterion |
which criterion function to either maximize or minimize. For linear models one can use: r.squared, adj.r.squared, cv5.lmFSA (5 Fold Cross Validation error), cv10.lmFSA (10 Fold Cross Validation error), apress (Allen's Press Statistic), int.p.val (Interaction P-value), AIC, BIC. |
minmax |
whether to minimize or maximize the criterion function |
checkfeas |
vector of variables that could be a feasible solution. These variables will be used as the last random start. |
var4int |
specification of which variables to check for marginal feasiblilty. Default is NULL |
min.nonmissing |
the combination of predictors will be ignored unless this many of observations are not missing |
return.models |
bool value to specify whether return all the fitted models which have been checked |
fix.formula |
... |
... |
see arguments taken by function FSA or other functions. help(FSA). |
Value
list of a matrix of all models obtained from FSA (fits) and their criteria. Also a matrix of the estimated frontiers that were requested. The Key column in fits, and pbound refers to the column number of the variables contined in the model fit. For instance, Key="42,96" would refer to the model which contains the variable in the 42nd column and 96th column of the designated dataset.
Examples
N <- 1000 #number of obs
P <- 100 #number of variables
data <- data.frame(matrix(rnorm(N*(P+1)), nrow = N, ncol = P+1))
sln <- pFSA(formula = "X101~1", data = data, m = 2, criterion = c(max_abs_resid,r.squared),
minmax = c("min","max"),numrs = 10,numFronts = 2,
pselExpr =rPref::low(max_abs_resid)*rPref::high(r.squared),plot.it = TRUE)
Diagnostic Plots for FSA solutions
Description
Diagnostic Plots for FSA solutions
Usage
## S3 method for class 'FSA'
plot(x, ask = F, easy = T, ...)
Arguments
x |
FSA object to see diagnostic plots on. |
ask |
logical; if TRUE, the user is asked before each plot. See help(plot.lm). |
easy |
logical; should diagnostic plots be presented in easy to read format? |
... |
arguments to be passed to other functions. |
Value
diagnostic plots to plot window.
Examples
#use mtcars package see help(mtcars)
data(mtcars)
colnames(mtcars)
fit<-lmFSA(formula="mpg~hp*wt",data=mtcars,fixvar="hp",
quad=FALSE,m=2,numrs=10,save_solutions=FALSE,cores=1)
plot(x=fit)
Prediction function for FSA solutions
Description
Prediction function for FSA solutions
Usage
## S3 method for class 'FSA'
predict(object, ...)
Arguments
object |
FSA object to conduct predictions on. |
... |
other parameters passed to fitmodels or predict functions. See help(fitmodels) or help(predict) for assistance. |
Value
list of predicted values from each FSA model.
Examples
#use mtcars package see help(mtcars)
data(mtcars)
colnames(mtcars)
fit<-lmFSA(formula="mpg~hp*wt",data=mtcars,fixvar="hp",
quad=FALSE,m=2,numrs=10,save_solutions=FALSE,cores=1)
predict(fit)
predict(fit,newdata=mtcars[1:15,])
Printing function for FSA solutions
Description
Printing function for FSA solutions
Usage
## S3 method for class 'FSA'
print(x, ...)
Arguments
x |
FSA object to print details about. |
... |
arguments to be passed to other functions. |
Value
list of Feasible Solution Formula's, Original Fitted model formula and criterion function and times converged to details.
Examples
#use mtcars package see help(mtcars)
data(mtcars)
colnames(mtcars)
fit<-lmFSA(formula="mpg~hp*wt",data=mtcars,fixvar="hp",
quad=FALSE,m=2,numrs=10,save_solutions=FALSE,cores=1)
print(fit)
An rFSA Criterion Function.
Description
rFSA Criterion Function to compute R squared.
Usage
r.squared(model, name = "R Squared")
Arguments
model |
lm or glm fit to be passed. |
name |
passed to print.FSA |
An rFSA Criterion Function.
Description
rFSA Criterion Function to compute Root Mean Squared Error.
Usage
rmse(model, name = "RMSE")
Arguments
model |
lm or glm fit to be passed. |
name |
passed to print.FSA |
Summary function for FSA solutions
Description
Summary function for FSA solutions
Usage
## S3 method for class 'FSA'
summary(object, ...)
Arguments
object |
FSA object to see summaries on. |
... |
arguments to be passed to other functions. |
Value
list of summarized lm or glm output.
Examples
#use mtcars package see help(mtcars)
data(mtcars)
colnames(mtcars)
fit<-lmFSA(formula="mpg~hp*wt",data=mtcars,fixvar="hp",
quad=FALSE,m=2,numrs=10,save_solutions=FALSE,cores=1)
summary(fit)
Variables to include in first steip of an mth order interaction model determined from the Feasible Soution Alorithm.
Description
Finds the swaps available given a current position.
Usage
swaps(cur, n, quad = FALSE, yindex)
Arguments
cur |
A vector of length greater than 2 of what current explantory varialbes are being used in the model. |
n |
The number of explanatory variables in available to swap. |
quad |
Whether to include quadratic terms. ie (x1*x1) as potential swaps. |
yindex |
index of response variable. |
Value
a matrix with the possible forms by column.
twFSA
Description
A function for termwise feasiblity
Usage
twFSA(
formula,
data,
fitfunc = lm,
fixvar = NULL,
quad = FALSE,
cores = 1,
criterion = AIC,
minmax = "min",
checkfeas = NULL,
var4int = NULL,
min.nonmissing = 1,
...
)
Arguments
formula |
an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted. |
data |
a data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. |
fitfunc |
the method that should be used to fit the model. For Example: lm, glm, or other methods that rely on formula, data, and other inputs. |
fixvar |
variable(s) to fix in the model. Usually a covariate that should always be included (Example: Age, Sex). Will still consider it with interactions. Default is NULL. |
quad |
Include quadratic terms or not. Logical. |
cores |
number of cores to use while running. Note: Windows can only use 1 core. See mclapply for details. If function detects a Windows user it will automatically set cores=1. |
criterion |
which criterion function to either maximize or minimize. For linear models one can use: r.squared, adj.r.squared, cv5.lmFSA (5 Fold Cross Validation error), cv10.lmFSA (10 Fold Cross Validation error), apress (Allen's Press Statistic), int.p.val (Interaction P-value), AIC, BIC. |
minmax |
whether to minimize or maximize the criterion function |
checkfeas |
vector of variables that could be a feasible solution. These variables will be used as the last random start. |
var4int |
specification of which variables to check for marginal feasiblilty. Default is NULL |
min.nonmissing |
the combination of predictors will be ignored unless this many of observations are not missing |
... |
other arguments passed to fitfunc. |
Value
matrix of results
An rFSA Internal Function.
Description
rFSA function to compute the maximum value from a vector with NA's.
Usage
which.max.na(vec)
Arguments
vec |
Vector to be passed. |
An rFSA Internal Function.
Description
rFSA function to compute the minimum value from a vector with NA's.
Usage
which.min.na(vec)
Arguments
vec |
Vector to be passed. |