multiview.path {multiview}

Fit a GLM with elastic net regularization for a path of lambda values

Description

Fit a generalized linear model via penalized maximum likelihood for a path of lambda values. Can deal with any GLM family.

Usage

multiview.path(
  x_list,
  y,
  rho = 0,
  weights = NULL,
  lambda,
  nlambda,
  user_lambda = FALSE,
  alpha = 1,
  offset = NULL,
  family = gaussian(),
  standardize = TRUE,
  intercept = TRUE,
  thresh = 1e-07,
  maxit = 1e+05,
  penalty.factor = rep(1, nvars),
  exclude = integer(0),
  lower.limits = -Inf,
  upper.limits = Inf,
  trace.it = 0,
  x,
  nvars,
  nobs,
  xm,
  xs,
  control,
  vp,
  vnames,
  start_val,
  is.offset
)

Arguments

x_list

a list of x matrices with same number of rows nobs

y

the quantitative response with length equal to nobs, the (same) number of rows in each x matrix

rho

the weight on the agreement penalty, default 0. rho=0 is a form of early fusion, and rho=1 is a form of late fusion. We recommend trying a few values of rho including 0, 0.1, 0.25, 0.5, and 1 first; sometimes rho larger than 1 can also be helpful.

weights

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

lambda

A user supplied lambda sequence, default NULL. Typical usage is to have the program compute its own lambda sequence. This sequence, in general, is different from that used in the glmnet::glmnet() call (named lambda) Supplying a value of lambda overrides this. WARNING: use with care. Avoid supplying a single value for lambda (for predictions after CV use stats::predict() instead. Supply instead a decreasing sequence of lambda values as multiview relies on its warms starts for speed, and its often faster to fit a whole path than compute a single fit.

nlambda

The number of lambda values - default is 100.

user_lambda

a flag indicating if user supplied the lambda sequence

alpha

The elasticnet mixing parameter, with 0\le\alpha\le 1. The penalty is defined as

(1-\alpha)/2||\beta||_2^2+\alpha||\beta||_1.

alpha=1 is the lasso penalty, and alpha=0 the ridge penalty.

offset

A vector of length nobs that is included in the linear predictor (a nobs x nc matrix for the "multinomial" family). Useful for the "poisson" family (e.g. log of exposure time), or for refining a model by starting at a current fit. Default is NULL. If supplied, then values must also be supplied to the predict function.

family

A description of the error distribution and link function to be used in the model. This is the result of a call to a family function. Default is stats::gaussian. (See stats::family for details on family functions.)

standardize

Logical flag for x variable standardization, prior to fitting the model sequence. The coefficients are always returned on the original scale. Default is standardize=TRUE. If variables are in the same units already, you might not wish to standardize. See details below for y standardization with family="gaussian".

intercept

Should intercept(s) be fitted (default TRUE)

thresh

Convergence threshold for coordinate descent. Each inner coordinate-descent loop continues until the maximum change in the objective after any coefficient update is less than thresh times the null deviance. Defaults value is 1E-7.

maxit

Maximum number of passes over the data for all lambda values; default is 10^5.

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 the model. Default is 1 for all variables (and implicitly infinity for variables listed in exclude). Note: the penalty factors are internally rescaled to sum to nvars, and the lambda sequence will reflect this change.

exclude

Indices of variables to be excluded from the model. Default is none. Equivalent to an infinite penalty factor for the variables excluded (next item). Users can supply instead an exclude function that generates the list of indices. This function is most generally defined as ⁠function(x_list, y, ...)⁠, and is called inside multiview to generate the indices for excluded variables. The ... argument is required, the others are optional. This is useful for filtering wide data, and works correctly with cv.multiview. See the vignette 'Introduction' for examples.

lower.limits

Vector of lower limits for each coefficient; default -Inf. Each of these must be non-positive. Can be presented as a single value (which will then be replicated), else a vector of length nvars

upper.limits

Vector of upper limits for each coefficient; default Inf. See lower.limits

trace.it

If trace.it=1, then a progress bar is displayed; useful for big models that take a long time to fit.

x

the cbinded matrices in x_list

nvars

the number of variables (total)

nobs

the number of observations

xm

the column means vector (could be zeros if standardize = FALSE)

xs

the column std dev vector (could be 1s if standardize = FALSE)

control

the multiview control object

vp

the variable penalities (processed)

vnames

the variable names

start_val

the result of first call to get_start

is.offset

a flag indicating if offset is supplied or not

Details

multiview.path solves the elastic net problem for a path of lambda values. It generalizes multiview::multiview in that it works for any GLM family.

Sometimes the sequence is truncated before nlam values of lambda have been used. This happens when multiview.path detects that the decrease in deviance is marginal (i.e. we are near a saturated fit).

Value

An object with class "multiview" "glmnetfit" and "glmnet"

a0

Intercept sequence of length length(lambda).

beta

A ⁠nvars x length(lambda)⁠ matrix of coefficients, stored in sparse matrix format.

df

The number of nonzero coefficients for each value of lambda.

dim

Dimension of coefficient matrix.

lambda

The actual sequence of lambda values used. When alpha=0, the largest lambda reported does not quite give the zero coefficients reported (lambda=inf would in principle). Instead, the largest lambda for alpha=0.001 is used, and the sequence of lambda values is derived from this.

lambda

The sequence of lambda values

mvlambda

The corresponding sequence of multiview lambda values

dev.ratio

The fraction of (null) deviance explained. The deviance calculations incorporate weights if present in the model. The deviance is defined to be 2*(loglike_sat - loglike), where loglike_sat is the log-likelihood for the saturated model (a model with a free parameter per observation). Hence dev.ratio=1-dev/nulldev.

nulldev

Null deviance (per observation). This is defined to be 2*(loglike_sat -loglike(Null)). The null model refers to the intercept model.

npasses

Total passes over the data summed over all lambda values.

jerr

Error flag, for warnings and errors (largely for internal debugging).

offset

A logical variable indicating whether an offset was included in the model.

call

The call that produced this object.

family

Family used for the model.

nobs

Number of observations.