Summarizing cross-validation-based inference

Summary method for cv.ncvreg objects

Usage

# S3 method for class 'cv.ncvreg'
summary(object, ...)

# S3 method for class 'summary.cv.ncvreg'
print(x, digits, ...)

Arguments

object: A cv.ncvreg or cv.ncvsurv object.
...: Further arguments passed to or from other methods.
x: A summary.cv.ncvreg object.
digits: Number of digits past the decimal point to print out. Can be a vector specifying different display digits for each of the five non-integer printed values.

Value

An object with S3 class summary.cv.ncvreg. The class has its own print method and contains the following list elements:

penalty: The penalty used by ncvreg.
model: Either "linear" or "logistic", depending on the family option in ncvreg.
n: Number of instances
p: Number of regression coefficients (not including the intercept).
min: The index of lambda with the smallest cross-validation error.
lambda: The sequence of lambda values used by cv.ncvreg.
cve: Cross-validation error (deviance).
r.squared: Proportion of variance explained by the model, as estimated by cross-validation. For models outside of linear regression, the Cox-Snell approach to defining R-squared is used.
snr: Signal to noise ratio, as estimated by cross-validation.
sigma: For linear regression models, the scale parameter estimate.
pe: For logistic regression models, the prediction error (misclassification error).

References

Breheny P and Huang J. (2011) Coordinate descent algorithms for nonconvex penalized regression, with applications to biological feature selection. Annals of Applied Statistics, 5: 232-253. doi:10.1214/10-AOAS388

Author

Patrick Breheny

Examples

# Linear regression --------------------------------------------------
data(Prostate)
cvfit <- cv.ncvreg(Prostate$X, Prostate$y)
summary(cvfit)
#> MCP-penalized linear regression with n=97, p=8
#> At minimum cross-validation error (lambda=0.0276):
#> -------------------------------------------------
#>   Nonzero coefficients: 7
#>   Cross-validation error (deviance): 0.54
#>   R-squared: 0.59
#>   Signal-to-noise ratio: 1.45
#>   Scale estimate (sigma): 0.734
#> MCP-penalized linear regression with n=97, p=8
#> At lambda=0.0276:
#> -------------------------------------------------
#>   Nonzero coefficients         :   7
#>   Expected nonzero coefficients:   2.67
#>   Average mfdr (7 features)    :   0.382
#> 
#>          Estimate      z      mfdr Selected
#> lcavol   0.569546  8.956   < 1e-04        *
#> svi      0.752400  4.156 0.0035352        *
#> lweight  0.614420  3.512 0.0325374        *
#> age     -0.020913 -2.077 0.6160315        *
#> pgg45    0.005324  2.004 0.6506811        *
#> lcp     -0.104960 -1.958 0.6707274        *
#> lbph     0.097353  1.884 0.7009923        *

# Logistic regression ------------------------------------------------
data(Heart)
cvfit <- cv.ncvreg(Heart$X, Heart$y, family="binomial")
summary(cvfit)
#> MCP-penalized logistic regression with n=462, p=9
#> At minimum cross-validation error (lambda=0.0270):
#> -------------------------------------------------
#>   Nonzero coefficients: 5
#>   Cross-validation error (deviance): 1.06
#>   R-squared: 0.21
#>   Signal-to-noise ratio: 0.26
#>   Prediction error: 0.271
#> MCP-penalized logistic regression with n=462, p=9
#> At lambda=0.0270:
#> -------------------------------------------------
#>   Nonzero coefficients         :   5
#>   Expected nonzero coefficients:   0.21
#>   Average mfdr (5 features)    :   0.042
#> 
#>         Estimate     z      mfdr Selected
#> age      0.05109 5.946   < 1e-04        *
#> famhist  0.90619 4.143 0.0022421        *
#> tobacco  0.07012 3.328 0.0435944        *
#> typea    0.03045 3.169 0.0707198        *
#> ldl      0.13459 3.062 0.0959303        *

# Cox regression -----------------------------------------------------
data(Lung)
cvfit <- cv.ncvsurv(Lung$X, Lung$y)
summary(cvfit)
#> MCP-penalized Cox regression with n=137, p=8
#> At minimum cross-validation error (lambda=0.1276):
#> -------------------------------------------------
#>   Nonzero coefficients: 3
#>   Cross-validation error (deviance): 7.53
#>   R-squared: 0.29
#>   Signal-to-noise ratio: 0.41
#> MCP-penalized Cox regression with n=137, p=8
#> At lambda=0.1276:
#> -------------------------------------------------
#>   Nonzero coefficients         :   3
#>   Expected nonzero coefficients:   1.28
#>   Average mfdr (3 features)    :   0.426
#> 
#>          Estimate      z    mfdr Selected
#> karno    -0.03318 -6.589 < 1e-04        *
#> squamous -0.38295 -2.732 0.59462        *
#> adeno     0.33542  2.585 0.68452        *