glmnet (version 1.1-1)

glmnet: fit an elasticnet model path

Description

Fit a regularization path for the elasticnet at a grid of values for the regularization parameter lambda. Can deal with all shapes of data, including very large sparse data matrices. Fits linear, logistic and multinomial regression models.

Usage

glmnet(x, y, family=c("gaussian","binomial","multinomial"), weights, alpha = 1,
  nlambda = 100, lambda.min = ifelse(nobs

Arguments

x

input matrix, of dimension nobs x nvars; each row is an observation vector. Can be in sparse column format (class "dgCMatrix" as in package Matrix)

y

response variable. Quantitative for family="gaussian". For family="binomial" should be either a factor with two levels, or a two-column matrix of counts or proportions. For family="multinomial", can be a nc>=2<

family

Response type (see above)

weights

observation weights. Can be total counts if responses are proportion matrices. Default is 1 for each observation

alpha

The elasticnet mixing parameter, with $0<\alpha\le 1$.="" the="" penalty="" is="" defined="" as="" $$(1-\alpha)="" 2||\beta||_2^2+\alpha||\beta||_1.$$="" alpha=1 is the lasso penalty; Currently alpha<0.01< code=""> not reliable, unless you supply

nlambda

The number of lambda values - default is 100.

lambda.min

Smallest value for lambda, as a fraction of lambda.max, the (data derived) entry value (i.e. the smallest value for which all coefficients are zero). The default depends on the sample size nobs relative to th

lambda

A user supplied lambda sequence. Typical usage is to have the program compute its own lambda sequence based on nlambda and lambda.min. Supplying a value of lambda overides t

standardize

Logical flag for variable standardization, prior to fitting the model sequence. The coefficients are always returned on the original scale. Default is is standardize=TRUE

thresh

Convergence threshold for coordinate descent. Each inner coordinate-descent loop continues until the relative change in any coefficient is less than thresh. Defaults value is 1E-4.

dfmax

Limit the maximum number of variables in the model. Useful for very large nvars, if a partial path is desired.

pmax

Limit the maximum number of variables ever to be nonzero

exclude

Indices of variables to be excluded from the model. Default is none. Equivalent to an infinite penalty factor (next item).

penalty.factor

Separate penalty factors can be applied to each coefficient. This is a number that multiplies lambda to allow differential shrinkage. Can be 0 for some variables, which implies no shrinkage, and that variable is always included in

maxit

Maximum number of outer-loop iterations for "binomial" or "multinomial" families. Default is 100.

HessianExact

Only applies to "binomial" or "multinomial" families. If FALSE (the default), an upper-bound approximation is made to the hessian, which is not recalculated at each outer loop.

type

Two algorithm types are supported for (only) family="gaussian". The default type="covariance" saves all inner-products ever computed, and can be much faster than type="naive". The latter can be more effic

Value

• An object with S3 class "glmnet","*", where "*" is "elnet", "lognet" or "multnet" for the three types of models.
• call
  the call that produced this object
• a0
  Intercept sequence of length length(lambda)
• beta
  For "elnet" and "lognet" models, a nvars x length(lambda) matrix of coefficients, stored in sparse column format ("dgCMatrix"). For "multnet", a list of nc such matrices, one for each class.
• lambda
  The actual sequence of lambda values used
• dev
  The percentage deviance explained (for "elnet", this is the R-square).
• nulldev
  Null deviance
• df
  The number of nonzero coefficients for each value of lambda. For "multnet", this is the number of variables with a nonzero coefficient for any class.
• dfmat
  For "multnet" only. A matrix consisting of the number of nonzero coefficients per class
• dim
  dimension of coefficient matrix (ices)
• npasses
  total passes over the data summed over all lambda values
• jerr
  error flag, for warnings and errors (largely for internal debugging).

Details

The sequence of models implied by lambda is fit by coordinate descent. For family="gaussian" this is the lasso sequence if alpha=1, else it is the elasticnet sequence. For family="binomial" or family="multinomial", this is a lasso or elasticnet regularization path for fitting the linear logistic or multinomial logistic regression paths. Sometimes the sequence is truncated before nlambda values of lambda have been used, because of instabilities in the logistic or multinomial models near a saturated fit. glmnet(...,family="binomial") fits a traditional logistic regression model for the log-odds. glmnet(...,family="multinomial") fits a symmetric multinomial model, where each class is represented by a linear model (on the log-scale). The penalties take care of redundancies. A two-class "multinomial" model will produce the same fit as the corresponding "binomial" model, except the pair of coefficient matrices will be equal in maxnitude and opposite in sign, and half the "binomial" values. Note that the objective function for "gaussian" is $$1/(2*nobs)RSS + \lambda*penalty$$, and for the logistic models it is $$1/nobs loglik + \lambda*penalty$$

References

Friedman, J., Hastie, T. and Tibshirani, R. (2008) Regularization Paths for Generalized Linear Models via Coordinate Descenthttp://www-stat.stanford.edu/~hastie/Papers/glmnet.pdf

See Also

print, predict and coef methods.

Examples

x=matrix(rnorm(100*20),100,20)
y=rnorm(100)
g2=sample(1:2,100,replace=TRUE)
g4=sample(1:4,100,replace=TRUE)
fit1=glmnet(x,y)
print(fit1)
coef(fit1,s=0.01) # extract coefficients at a single value of lambda
predict(fit1,newx=x[1:10,],s=c(0.01,0.005)) # make predictions
fit2=glmnet(x,g2,family="binomial")
fit3=glmnet(x,g4,family="multinomial")