Summary method for ncvreg objects

Inferential summaries for ncvreg and ncvsurv objects based on local marginal false discovery rates.

Usage

# S3 method for class 'ncvreg'
summary(object, lambda, which, number, cutoff, sort = TRUE, sigma, ...)

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

Arguments

object: An ncvreg or ncvsurv object.
lambda: The regularization parameter value at which inference should be reported.
which: Alternatively, lambda may be specified by index; which=10 means: report inference for the 10th value of lambda along the regularization path. If both lambda and which are specified, lambda takes precedence.
number: By default, summary will provide an inferential summary for each variable that has been selected (i.e., each variable with a nonzero coefficient). Specifying number=5, for example, means that the summary table will include the 5 features with the lowest mfdr values, regardless of whether they were selected. To see all features, number=Inf.
cutoff: Alternatively, specifying for example cutoff=0.3 will report inference for all features with mfdr under 30%. If both number and cutoff are specified, the intersection between both sets of features is reported.
sort: Should the results be sorted by mfdr? (default: TRUE)
sigma: For linear regression models, users can supply an estimate of the residual standard deviation. The default is to use RSS / DF, where degrees of freedom are approximated using the number of nonzero coefficients.
...: Further arguments; in particular, if you have set returnX=FALSE, you will need to supply X and y in order to calculate local mFDRs.
x: A summary.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.ncvreg. The class has its own print method and contains the following list elements:

penalty: The penalty used by ncvreg or ncvsurv
model: Either "linear", "logistic", or "Cox".
n: Number of instances.
p: Number of regression coefficients (not including the intercept).
lambda: The lambda value at which inference is being reported.
nvars: The number of nonzero coefficients (again, not including the intercept) at that value of lambda.
table: A table containing estimates, normalized test statistics (z), and an estimate of the local mfdr for each coefficient. The mfdr may be loosely interpreted, in an empirical Bayes sense, as the probability that the given feature is null.
unpen.table: If there are any unpenalized coefficients, a separate inferential summary is given for them. Currently, this is based on lm/glm/coxph using the penalized coefficients to provide an offset. This is useful and more or less accurate, but not ideal; we hope to improve the inferential methods for unpenalized variables in the future.

Author

Patrick Breheny patrick-breheny@uiowa.edu

Examples

# Linear regression --------------------------------------------------
data(Prostate)
fit <- ncvreg(Prostate$X, Prostate$y)
summary(fit, lambda=0.08)
#> MCP-penalized linear regression with n=97, p=8
#> At lambda=0.0800:
#> -------------------------------------------------
#>   Nonzero coefficients         :   5
#>   Expected nonzero coefficients:   1.90
#>   Average mfdr (5 features)    :   0.381
#> 
#>           Estimate      z     mfdr Selected
#> lcavol   5.263e-01  8.618  < 1e-04        *
#> svi      6.724e-01  3.867 0.016288        *
#> lweight  6.410e-01  3.815 0.019837        *
#> lbph     1.322e-02  1.295 0.926736        *
#> age     -6.203e-05 -1.095 0.941368        *

# Logistic regression ------------------------------------------------
data(Heart)
fit <- ncvreg(Heart$X, Heart$y, family="binomial")
summary(fit, lambda=0.05)
#> MCP-penalized logistic regression with n=462, p=9
#> At lambda=0.0500:
#> -------------------------------------------------
#>   Nonzero coefficients         :   5
#>   Expected nonzero coefficients:   0.18
#>   Average mfdr (5 features)    :   0.036
#> 
#>         Estimate     z      mfdr Selected
#> age     0.047479 6.645   < 1e-04        *
#> famhist 0.611522 4.332 0.0010983        *
#> tobacco 0.037272 3.465 0.0308975        *
#> ldl     0.075045 3.385 0.0403379        *
#> typea   0.009799 3.057 0.1077203        *

# Cox regression -----------------------------------------------------
data(Lung)
fit <- ncvsurv(Lung$X, Lung$y)
summary(fit, lambda=0.1)
#> MCP-penalized Cox regression with n=137, p=8
#> At lambda=0.1000:
#> -------------------------------------------------
#>   Nonzero coefficients         :   5
#>   Expected nonzero coefficients:   2.93
#>   Average mfdr (5 features)    :   0.586
#> 
#>          Estimate      z    mfdr Selected
#> karno    -0.03196 -6.352 < 1e-04        *
#> squamous -0.64314 -3.120 0.24761        *
#> adeno     0.28017  2.051 0.83922        *
#> large    -0.20731 -1.799 0.89449        *
#> trt       0.03738  1.332 0.94627        *

# Options ------------------------------------------------------------
fit <- ncvreg(Heart$X, Heart$y, family="binomial")
summary(fit, lambda=0.08, number=3)
#> MCP-penalized logistic regression with n=462, p=9
#> At lambda=0.0800:
#> -------------------------------------------------
#>   Features satisfying criteria       : 3
#>   Average mfdr among chosen features : 0.0026
#> 
#>         Estimate     z       mfdr Selected
#> age     0.041921 7.771    < 1e-04        *
#> famhist 0.277822 4.627 0.00029409        *
#> ldl     0.009273 3.847 0.00751773        *
summary(fit, lambda=0.08, number=Inf)
#> MCP-penalized logistic regression with n=462, p=9
#> At lambda=0.0800:
#> -------------------------------------------------
#>   Features satisfying criteria       : 9
#>   Average mfdr among chosen features : 0.377
#> 
#>           Estimate      z       mfdr Selected
#> age       0.041921 7.7712    < 1e-04        *
#> famhist   0.277822 4.6274 0.00029409        *
#> ldl       0.009273 3.8473 0.00751773        *
#> tobacco   0.005783 3.7881 0.00938405        *
#> typea     0.000000 2.9383 0.13986436         
#> adiposity 0.000000 1.8121 0.70188341         
#> sbp       0.000000 1.7780 0.71453183         
#> alcohol   0.000000 0.7807 0.89965322         
#> obesity   0.000000 0.4339 0.91712823         
summary(fit, lambda=0.08, cutoff=0.5)
#> MCP-penalized logistic regression with n=462, p=9
#> At lambda=0.0800:
#> -------------------------------------------------
#>   Features satisfying criteria       : 5
#>   Average mfdr among chosen features : 0.0314
#> 
#>         Estimate     z       mfdr Selected
#> age     0.041921 7.771    < 1e-04        *
#> famhist 0.277822 4.627 0.00029409        *
#> ldl     0.009273 3.847 0.00751773        *
#> tobacco 0.005783 3.788 0.00938405        *
#> typea   0.000000 2.938 0.13986436         
summary(fit, lambda=0.08, number=3, cutoff=0.5)
#> MCP-penalized logistic regression with n=462, p=9
#> At lambda=0.0800:
#> -------------------------------------------------
#>   Features satisfying criteria       : 3
#>   Average mfdr among chosen features : 0.0026
#> 
#>         Estimate     z       mfdr Selected
#> age     0.041921 7.771    < 1e-04        *
#> famhist 0.277822 4.627 0.00029409        *
#> ldl     0.009273 3.847 0.00751773        *
summary(fit, lambda=0.08, number=5, cutoff=0.1)
#> MCP-penalized logistic regression with n=462, p=9
#> At lambda=0.0800:
#> -------------------------------------------------
#>   Features satisfying criteria       : 4
#>   Average mfdr among chosen features : 0.0043
#> 
#>         Estimate     z       mfdr Selected
#> age     0.041921 7.771    < 1e-04        *
#> famhist 0.277822 4.627 0.00029409        *
#> ldl     0.009273 3.847 0.00751773        *
#> tobacco 0.005783 3.788 0.00938405        *
summary(fit, lambda=0.08, number=Inf, sort=FALSE)
#> MCP-penalized logistic regression with n=462, p=9
#> At lambda=0.0800:
#> -------------------------------------------------
#>   Features satisfying criteria       : 9
#>   Average mfdr among chosen features : 0.377
#> 
#>           Estimate      z       mfdr Selected
#> sbp       0.000000 1.7780 0.71453183         
#> tobacco   0.005783 3.7881 0.00938405        *
#> ldl       0.009273 3.8473 0.00751773        *
#> adiposity 0.000000 1.8121 0.70188341         
#> famhist   0.277822 4.6274 0.00029409        *
#> typea     0.000000 2.9383 0.13986436         
#> obesity   0.000000 0.4339 0.91712823         
#> alcohol   0.000000 0.7807 0.89965322         
#> age       0.041921 7.7712    < 1e-04        *
summary(fit, lambda=0.08, number=3, cutoff=0.5, sort=FALSE)
#> MCP-penalized logistic regression with n=462, p=9
#> At lambda=0.0800:
#> -------------------------------------------------
#>   Features satisfying criteria       : 3
#>   Average mfdr among chosen features : 0.0026
#> 
#>         Estimate     z       mfdr Selected
#> ldl     0.009273 3.847 0.00751773        *
#> famhist 0.277822 4.627 0.00029409        *
#> age     0.041921 7.771    < 1e-04        *

# If X and y are not returned with the fit, they must be supplied
fit <- ncvreg(Heart$X, Heart$y, family="binomial", returnX=FALSE)
summary(fit, X=Heart$X, y=Heart$y, lambda=0.08)
#> MCP-penalized logistic regression with n=462, p=9
#> At lambda=0.0800:
#> -------------------------------------------------
#>   Nonzero coefficients         :   4
#>   Expected nonzero coefficients:   0.02
#>   Average mfdr (4 features)    :   0.004
#> 
#>         Estimate     z       mfdr Selected
#> age     0.041921 7.771    < 1e-04        *
#> famhist 0.277822 4.627 0.00029409        *
#> ldl     0.009273 3.847 0.00751773        *
#> tobacco 0.005783 3.788 0.00938405        *

Usage

Arguments

Value

See also

Author

Examples