# A Comparison of Regression Modelling Strategies

### Description

Compare two nested modelling strategies and return measures of their relative predictive performance

### Usage

1 2 |

### Arguments

`model` |
the type of regression model. Either "linear" or "logistic". |

`Ntrials` |
number of simulation trials. |

`strat1` |
a list containing the strategy name and strategy-specific parameter values. This modelling strategy is taken as the reference for comparison. |

`strat2` |
a list containing the strategy name and strategy-specific parameter values. This modelling strategy is compared with the reference strategy, strat1. |

`data` |
a list describing the dataset in which the selected modelling strategies
will be compared. If the first object in the list is "norm" or "unif",
the user may submit parameters for generating multivariable simulated
datasets (see details below. Users may specify their own dataset using
the format |

`Nrows` |
the number of rows of observations in simulated datasets of type "norm" or "unif". |

`Ncomp` |
the number of rows of observations in the comparison set. This dataset is
taken to represent the overall population, from which the training set is
sampled. When |

`int` |
logical. If |

`int.adj` |
logical. If |

`trim` |
logical. If |

`output` |
logical. If |

### Details

This is the core function in the apricom package. The *compare* function can be used to compare the performance of two prediction model building approaches for either simulated or user-specified data. For further details, see the apricom user manual.

The following strategies are currently supported: heuristic shrinkage ("heuristic"), split-sample-derived shrinkage ("split"), cross-validation-derived shrinkage ("kcv"), leave-one-out cross-validation-derived shrinkage ("loocv"), bootstrap-derived shrinkage ("boot") and penalized logistic regression using Firth's penalty ("pml.firth"). Furthermore, models built using these methods may be compared with raw models fitted by ordinary least squares estimation ("lsq") or maximum likelihood estimation ("ml").

Strategies should be specified within the "strat1" and "strat2" arguments in the form of a list, starting with the strategy name (as listed above in parentheses), followed by relevant parameters for each respective method. For further details see individual help files for each strategy, and the examples below. Note that in the *compare* function call, the dataset should not be specified within the "strat1" or "strat2" arguments, and instead should only be called within the "data" argument.

### Value

`compare`

returns a list containing the following:

`VR` |
the victory rate of strategy 2 over strategy 1. |

`MPR` |
the median precision ratio over Ntrials comparison trials. |

`PR.IQR` |
the precision ratio interquartile range over |

`VR.trim` |
if |

`MPR.trim` |
if |

`distribution` |
the comparison distribution of strategy 2 vs. strategy 1. This is
the distribution of precision ratios generated from |

`distribution.trim` |
if |

`N.rejected` |
the number of trials excluded from the comparison distribution by trimming |

`strat1` |
modelling strategy 1 |

`strat2` |
modelling strategy 2 |

`shrinkage1` |
If strategy 1 is a shrinkage-after-estimation technique, a vector or matrix containing the shrinkage factor estimated in each trial is returned |

`shrinkage1` |
If strategy 1 is a shrinkage-after-estimation technique, a vector or matrix containing the shrinkage factor estimated in each trial is returned |

### Note

When using `compare`

it is strongly recommended that ideally 10000
comparison trials are used, to give stable estimates. Comparisons with
logistic regression modelling model adjustment strategies are *considerably*
slower than with linear regression, and 1000-5000 trials may be preferred. The
examples provided in this documentation use considerably fewer comparison trials
and yield highly unstable estimates.

### References

Pestman W., Groenwold R. H. H., Teerenstra. S, *"Comparison of
strategies when building linear prediction models."*
Numerical Linear Algebra with Applications (2013)

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 | ```
## Example 1: Comparison of heuristic formula-derived shrinkage against
## a raw least squares model. Data is simulated multivariable random
## normally distributed.The comparison set will have 2000 rows. Here only
## 10 trial replicates are used, but at least 1000 should be used in practice
mu <- c(rep(0, 21))
rho <- 0.5
comp1 <- compare(model = "linear", Ntrials = 10, strat1 = list("lsq"),
strat2 = list("heuristic", DF = 8),
data = list("norm", mu, rho), Nrows = 200, Ncomp = 2000,
int = TRUE, int.adj = FALSE, trim = FALSE, output = TRUE)
## Example 2: A truncated comparison of 10-rep, 10-fold
## cross-validation-derived shrinkage against leave-one-out cross-validation.
## Data is simulated multivariable random uniformly distributed
## (50 rows; 5 predictors with mean=0 ; r^2 = 0.7)
## The comparison set will contain 1000 observations.
mu <- c(rep(0, 6))
rho <- 0.7
comp2 <- compare(model = "linear", Ntrials = 10, strat1 = list("loocv"),
strat2 = list("kcv", k = 10, nreps = 10),data = list("unif", mu, rho),
Nrows = 50, Ncomp = 1000, trim = TRUE)
## Example 3: Comparison of penalized logistic regression with
## Firth's penalty against raw logistic regression model using
## maximum likelihood estimation.
## Note that the logistf package is required for pml.firth.
library(shrink)
data(deepvein)
dv.data <- datashape(deepvein, y = 3, x = 4:11)
set.seed(123)
comp4 <- compare(model = "logistic", Ntrials = 10,
strat1 = list("ml"), strat2 = list("pml.firth"),
data = list("dataset", dv.data), int = TRUE,
int.adj = TRUE, trim = FALSE, output = TRUE)
``` |

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