Package 'multiview'

Fitted "multiview" or "cv.multiview" object. coefficients are required.

This is the mechanism for passing arguments like ⁠x=⁠ when exact=TRUE; see exact argument.

Fitted "cv.multiview" object.

Value(s) of the penalty parameter lambda at which predictions are required. Default is the value s="lambda.1se" stored on the CV object. Alternatively s="lambda.min" can be used. If s is numeric, it is taken as the value(s) of lambda to be used. (For historical reasons we use the symbol 's' rather than 'lambda' to reference this parameter.)

This is the mechanism for passing arguments like ⁠x=⁠ when exact=TRUE; see exact argument.

Fitted "multiview" object.

Value(s) of the penalty parameter lambda at which coefficients are required.

This is the mechanism for passing arguments like ⁠x=⁠ when exact=TRUE; see exact argument.

Fitted "cv.multiview" object.

Value(s) of the penalty parameter lambda at which predictions are required. Default is the value s="lambda.1se" stored on the CV object. Alternatively s="lambda.min" can be used. If s is numeric, it is taken as the value(s) of lambda to be used. (For historical reasons we use the symbol 's' rather than 'lambda' to reference this parameter.)

This is the mechanism for passing arguments like ⁠x=⁠ when exact=TRUE; see exact argument.

Fitted "multiview" object.

Value(s) of the penalty parameter lambda at which predictions are required. Default is the entire sequence used to create the model.

This is the mechanism for passing arguments like ⁠x=⁠ when exact=TRUE; see exact argument.

a list of named lists all with same names (not checked for efficiency)

Survival response variable, must be a Surv or stratifySurv object.

Model's predictions for y.

Observation weights.

A single value for the lambda hyperparameter.

The elasticnet mixing parameter, with $0 \le \alpha \le 1$.

The model's coefficients.

Penalty factors for each of the coefficients.

a list of lists containing indices of coefficients and associated covariate (view) pairs

the fusion parameter

a list of x matrices with same number of rows nobs

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

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.)

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.

Observation weights; defaults to 1 per observation

Offset vector (matrix) as in multiview

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). Note that this is done for the full model (master sequence), and separately for each fold. The fits are then aligned using the glmnet lambda sequence associated with the master sequence (see the alignment argument for additional details). Adapting lambda for each fold leads to better convergence. When lambda is supplied, the same sequence is used everywhere, but in some GLMs can lead to convergence issues.

loss to use for cross-validation. Currently five options, not all available for all models. The default is type.measure="deviance", which uses squared-error for gaussian models (a.k.a type.measure="mse" there), deviance for logistic and poisson regression, and partial-likelihood for the Cox model. type.measure="class" applies to binomial and multinomial logistic regression only, and gives misclassification error. type.measure="auc" is for two-class logistic regression only, and gives area under the ROC curve. type.measure="mse" or type.measure="mae" (mean absolute error) can be used by all models except the "cox"; they measure the deviation from the fitted mean to the response. type.measure="C" is Harrel's concordance measure, only available for cox models.

number of folds - default is 10. Although nfolds can be as large as the sample size (leave-one-out CV), it is not recommended for large datasets. Smallest value allowable is nfolds=3

an optional vector of values between 1 and nfold identifying what fold each observation is in. If supplied, nfold can be missing.

This is an experimental argument, designed to fix the problems users were having with CV, with possible values "lambda" (the default) else "fraction". With "lambda" the lambda values from the master fit (on all the data) are used to line up the predictions from each of the folds. In some cases this can give strange values, since the effective lambda values in each fold could be quite different. With "fraction" we line up the predictions in each fold according to the fraction of progress along the regularization. If in the call a lambda argument is also provided, alignment="fraction" is ignored (with a warning).

This is an experimental argument, with default TRUE, and can be ignored by most users. For all models except the "cox", this refers to computing nfolds separate statistics, and then using their mean and estimated standard error to describe the CV curve. If grouped=FALSE, an error matrix is built up at the observation level from the predictions from the nfold fits, and then summarized (does not apply to type.measure="auc"). For the "cox" family, grouped=TRUE obtains the CV partial likelihood for the Kth fold by subtraction; by subtracting the log partial likelihood evaluated on the full dataset from that evaluated on the on the (K-1)/K dataset. This makes more efficient use of risk sets. With grouped=FALSE the log partial likelihood is computed only on the Kth fold

If keep=TRUE, a prevalidated array is returned containing fitted values for each observation and each value of lambda. This means these fits are computed with this observation and the rest of its fold omitted. The foldid vector is also returned. Default is keep=FALSE.

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

Other arguments that can be passed to multiview

the values of lambda used in the fits.

The mean cross-validated error - a vector of length length(lambda).

estimate of standard error of cvm.

upper curve = cvm+cvsd.

lower curve = cvm-cvsd.

number of non-zero coefficients at each lambda.

a text string indicating type of measure (for plotting purposes).

a fitted multiview object for the full data.

value of lambda that gives minimum cvm.

largest value of lambda such that error is within 1 standard error of the minimum.

if keep=TRUE, this is the array of prevalidated fits. Some entries can be NA, if that and subsequent values of lambda are not reached for that fold

if keep=TRUE, the fold assignments used

a one column matrix with the indices of lambda.min and lambda.1se in the sequence of coefficients, fits etc.

Quantitative response variable.

Model's predictions for y.

Observation weights.

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.

Input matrix, of dimension nobs x nvars; each row is an observation vector. If it is a sparse matrix, it is assumed to be unstandardized. It should have attributes xm and xs, where xm(j) and xs(j) are the centering and scaling factors for variable j respsectively. If it is not a sparse matrix, it is assumed that any standardization needed has already been done.

Quantitative response variable.

Observation weights. elnet.fit does NOT standardize these weights.

A single value for the lambda hyperparameter.

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.

Should intercept be fitted (default=TRUE) or set to zero (FALSE)?

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. Default value is 1e-7.

Maximum number of passes over the data; default is 10^5. (If a warm start object is provided, the number of passes the warm start object performed is included.)

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.

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

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.

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

Either a glmnetfit object or a list (with names beta and a0 containing coefficients and intercept respectively) which can be used as a warm start. Default is NULL, indicating no warm start. For internal use only.

Was elnet.fit() called from glmnet.fit()? Default is FALSE.This has implications for computation of the penalty factors.

Return the warm start object? Default is FALSE.

Intercept value.

A nvars x 1 matrix of coefficients, stored in sparse matrix format.

The number of nonzero coefficients.

Dimension of coefficient matrix.

Lambda value used.

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.

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

Total passes over the data.

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

Always FALSE, since offsets do not appear in the WLS problem. Included for compability with glmnet output.

The call that produced this object.

Number of observations.

If save.fit=TRUE, output of C++ routine, used for warm starts. For internal use only.

Input matrix, of dimension nobs x nvars; each row is an observation vector. If it is a sparse matrix, it is assumed to be unstandardized. It should have attributes xm and xs, where xm(j) and xs(j) are the centering and scaling factors for variable j respsectively. If it is not a sparse matrix, it is assumed to be standardized.

Survival response variable, must be a Surv or stratifySurv object.

The elasticnet mixing parameter, with $0 \le \alpha \le 1$.

Observation weights.

Offset for the model. Default is a zero vector of length nrow(y).

Indices of variables to be excluded from the model.

Separate penalty factors can be applied to each coefficient.

Input matrix, of dimension nobs x nvars; each row is an observation vector. If it is a sparse matrix, it is assumed to be unstandardized. It should have attributes xm and xs, where xm(j) and xs(j) are the centering and scaling factors for variable j respsectively. If it is not a sparse matrix, it is assumed to be standardized.

Feature coefficients.

Intercept.

Input matrix, of dimension nobs x nvars; each row is an observation vector. If it is a sparse matrix, it is assumed to be unstandardized. It should have attributes xm and xs, where xm(j) and xs(j) are the centering and scaling factors for variable j respsectively. If it is not a sparse matrix, it is assumed to be standardized.

Quantitative response variable.

Observation weights.

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. (See family for details on family functions.)

Does the model we are fitting have an intercept term or not?

Is the model being fit with an offset or not?

Offset for the model. If is.offset=FALSE, this should be a zero vector of the same length as y.

Indices of variables to be excluded from the model.

Separate penalty factors can be applied to each coefficient.

The elasticnet mixing parameter, with $0 \le \alpha \le 1$.

list of x matrices

a list of ncol of elements in x_list

an integer vector of two indices

the rho value

a list of x matrices with same number of rows nobs

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

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.

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.)

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

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.

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.

The number of lambda values - default is 100.

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 the number of variables nvars. If nobs > nvars, the default is 0.0001, close to zero. If nobs < nvars, the default is 0.01. A very small value of lambda.min.ratio will lead to a saturated fit in the nobs < nvars case. This is undefined for "binomial" and "multinomial" models, and glmnet will exit gracefully when the percentage deviance explained is almost 1.

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.

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".

Should intercept(s) be fitted (default TRUE)

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.

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

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.

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.

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

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

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

the call that produced this object

Intercept sequence of length length(lambda)

For "elnet", "lognet", "fishnet" and "coxnet" models, a ⁠nvars x length(lambda)⁠ matrix of coefficients, stored in sparse column format ("CsparseMatrix"). For "multnet" and "mgaussian", a list of nc such matrices, one for each class.

The actual sequence of glmnet::glmnet() 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.

The sequence of lambda values

The corresponding sequence of multiview lambda values

The fraction of (null) deviance explained (for "elnet", this is the R-square). 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.

Null deviance (per observation). This is defined to be 2*(loglike_sat -loglike(Null)); The NULL model refers to the intercept model, except for the Cox, where it is the 0 model.

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.

For "multnet" and "mrelnet" only. A matrix consisting of the number of nonzero coefficients per class

dimension of coefficient matrix (ices)

number of observations

total passes over the data summed over all lambda values

a logical variable indicating whether an offset was included in the model

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

minimum fractional change in deviance for stopping path; factory default = 1.0e-5

maximum fraction of explained deviance for stopping path; factory default = 0.999

minimum value of lambda.min.ratio (see multiview); factory default= 1.0e-6

large floating point number; factory default = 9.9e35. Inf in definition of upper.limit is set to big

minimum number of path points (lambda values) allowed; factory default = 5

minimum probability for any class. factory default = 1.0e-9. Note that this implies a pmax of 1-pmin.

maximum allowed exponent. factory default = 250.0

convergence threshold for multi response bounds adjustment solution. factory default = 1.0e-10

maximum iterations for multiresponse bounds adjustment solution. factory default = 100

If 1 then progress bar is displayed when running multiview and cv.multiview. factory default = 0

convergence threshold for multiview.fit. factory default = 1.0e-6

maximum iterations for the IRLS loop in multiview.fit. factory default = 25

If TRUE, reset all the parameters to the factory default; default is FALSE

a list of x matrices with same number of rows nobs

the cbinded matrices in x_list

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

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.

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

A single value for the lambda hyperparameter.

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.

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.

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.

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

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.

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.

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

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

Either a glmnetfit object or a list (with names beta and a0 containing coefficients and intercept respectively) which can be used as a warm start. Default is NULL, indicating no warm start. For internal use only.

Was multiview.cox.fit() called from multiview.path()? Default is FALSE.This has implications for computation of the penalty factors.

Return the warm start object? Default is FALSE.

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

Intercept value, NULL for "cox" family.

A nvars x 1 matrix of coefficients, stored in sparse matrix format.

The number of nonzero coefficients.

Dimension of coefficient matrix.

Lambda value used.

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.

Null deviance (per observation). This is defined to be 2*(loglike_sat -loglike(Null)). The null model refers to the 0 model.

Total passes over the data.

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

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

The call that produced this object.

Number of observations.

If save.fit=TRUE, output of C++ routine, used for warm starts. For internal use only.

Family used for the model, always "cox".

A logical variable: was the algorithm judged to have converged?

A logical variable: is the fitted value on the boundary of the attainable values?

Objective function value at the solution.

a list of x matrices with same number of rows nobs

the cbinded matrices in x_list

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

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.

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

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.

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.

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.

The number of lambda values - default is 100.

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 the number of variables nvars. If nobs > nvars, the default is 0.0001, close to zero. If nobs < nvars, the default is 0.01. A very small value of lambda.min.ratio will lead to a saturated fit in the nobs < nvars case. This is undefined for "binomial" and "multinomial" models, and glmnet will exit gracefully when the percentage deviance explained is almost 1.

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".

Should intercept(s) be fitted (default TRUE)

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.

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.

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.

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

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

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

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

the number of variables (total)

the number of observations

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

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

the multiview control object

the variable penalities (processed)

the variable names

a flag indicating if offset is supplied or not

Intercept value, NULL for "cox" family.

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

The number of nonzero coefficients for each value of lambda.

Dimension of coefficient matrix.

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.

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.

Null deviance (per observation). This is defined to be 2*(loglike_sat -loglike(Null)). The null model refers to the 0 model.

Total passes over the data summed over all lambda values.

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

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

The call that produced this object.

Number of observations.

a list of x matrices with same number of rows nobs

the column-binded entries of x_list

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

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.

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

A single value for the lambda hyperparameter.

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.

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.

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.)

Should intercept(s) be fitted (default TRUE)

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.

Maximum number of passes over the data; default is 10^5. (If a warm start object is provided, the number of passes the warm start object performed is included.)

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.

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.

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

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

Either a multiview object or a list (with names beta and a0 containing coefficients and intercept respectively) which can be used as a warm start. Default is NULL, indicating no warm start. For internal use only.

Was multiview.fit() called from multiview.path()? Default is FALSE.This has implications for computation of the penalty factors.

Return the warm start object? Default is FALSE.

Controls how much information is printed to screen. If trace.it = 2, some information about the fitting procedure is printed to the console as the model is being fitted. Default is trace.it = 0 (no information printed). (trace.it = 1 not used for compatibility with multiview.path.)

a flag indicating if user supplied the lambda sequence

Intercept value.

A nvars by 1 matrix of coefficients, stored in sparse matrix format.

The number of nonzero coefficients.

Dimension of coefficient matrix.

Lambda value used.

The multiview lambda scale factor

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.

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

Total passes over the data.

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

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

The call that produced this object.

Number of observations.

If save.fit = TRUE, output of C++ routine, used for warm starts. For internal use only.

Family used for the model.

A logical variable: was the algorithm judged to have converged?

A logical variable: is the fitted value on the boundary of the attainable values?

Objective function value at the solution.

a list of x matrices with same number of rows nobs

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

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.

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

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.

The number of lambda values - default is 100.

a flag indicating if user supplied the lambda sequence

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.

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.

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.)

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".

Should intercept(s) be fitted (default TRUE)

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.

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

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.

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.

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

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

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

the cbinded matrices in x_list

the number of variables (total)

the number of observations

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

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

the multiview control object

the variable penalities (processed)

the variable names

the result of first call to get_start

a flag indicating if offset is supplied or not

Intercept sequence of length length(lambda).

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

The number of nonzero coefficients for each value of lambda.

Dimension of coefficient matrix.

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.

The sequence of lambda values

The corresponding sequence of multiview lambda values

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.

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

Total passes over the data summed over all lambda values.

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

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

The call that produced this object.

Family used for the model.

Number of observations.

Quantitative response variable.

Model's predictions for y.

Observation weights.

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.

A single value for the lambda hyperparameter.

The elasticnet mixing parameter, with $0 \le \alpha \le 1$.

The model's coefficients (excluding intercept).

Penalty factors for each of the coefficients.

a list of lists containing indices of coefficients and associated covariate (view) pairs

the fusion parameter

The model's coefficients (excluding intercept).

The elasticnet mixing parameter, with $0 \le \alpha \le 1$.

Penalty factors for each of the coefficients.

A fitted "multiview" model.

A set of colors to use for indicating different views. If NULL, the function will use the color palette "Set1" from the RColorBrewer package.

If TRUE, label the curves with variable sequence. numbers.

Other graphical parameters to plot.

Fitted "cv.multiview" or object.

List of new view matrices at which predictions are to be made.

Value(s) of the penalty parameter lambda at which predictions are required. Default is the value s="lambda.1se" stored on the CV object. Alternatively s="lambda.min" can be used. If s is numeric, it is taken as the value(s) of lambda to be used. (For historical reasons we use the symbol 's' rather than 'lambda' to reference this parameter)

Not used. Other arguments to predict.

Fitted "multiview" object.

list of new matrices for x at which predictions are to be made. Must be a list of matrices. This argument is not used for type = c("coefficients","nonzero").

Value(s) of the penalty parameter lambda at which predictions are required. Default is the entire sequence used to create the model.

Type of prediction required. Type "link" gives the linear predictors (eta scale); Type "response" gives the fitted values (mu scale). Type "coefficients" computes the coefficients at the requested values for s. Type "nonzero" returns a list of the indices of the nonzero coefficients for each value of s. Type "class" returns class labels for binomial family only.

This argument is relevant only when predictions are made at values of s (lambda) different from those used in the fitting of the original model. If exact=FALSE (default), then the predict function uses linear interpolation to make predictions for values of s (lambda) that do not coincide with those used in the fitting algorithm. While this is often a good approximation, it can sometimes be a bit coarse. With exact=TRUE, these different values of s are merged (and sorted) with object$lambda, and the model is refit before predictions are made. In this case, it is required to supply the original data x= and y= as additional named arguments to predict() or coef(). The workhorse predict.multiview() needs to update the model, and so needs the data used to create it. The same is true of weights, offset, penalty.factor, lower.limits, upper.limits if these were used in the original call. Failure to do so will result in an error.

If an offset is used in the fit, then one must be supplied for making predictions (except for type="coefficients" or type="nonzero").

This is the mechanism for passing arguments like ⁠x=⁠ when exact=TRUE; see exact argument.

the column-binded entries of x_list

a list of x matrices with same number of rows nobs

Response variable. Either a class "Surv" object or a two-column matrix with columns named 'time' and 'status'.

a list of x matrices with same number of rows nobs

a vector of indices in 1:nvars

a list of x matrices with same number of rows nobs

a list of column indices for each matrix, including possibly column indices of length 0

a list of x matrices with same number of rows nobs

vector of indices between 1 and nvars = sum of ncol(x) for x in x_list

a list of x matrices with same number of rows nobs

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

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.)

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.

Value(s) of the penalty parameter lambda at which predictions are required. Default is the value s="lambda.1se" stored on the CV object. Alternatively s="lambda.min" can be used. If s is numeric, it is taken as the value(s) of lambda to be used. (For historical reasons we use the symbol 's' rather than 'lambda' to reference this parameter)

If train, we evaluate the contribution of data views based on training data using cross validation error; if test, we evaluate the contribution of data views based on test data. Default is train. If set to test, users need to provide the test data, i.e. x_list_test and y_test.

Observation weights; defaults to 1 per observation

loss to use for cross-validation. Currently five options, not all available for all models. The default is type.measure="deviance", which uses squared-error for gaussian models (a.k.a type.measure="mse" there), deviance for logistic and poisson regression, and partial-likelihood for the Cox model. type.measure="class" applies to binomial and multinomial logistic regression only, and gives misclassification error. type.measure="auc" is for two-class logistic regression only, and gives area under the ROC curve. type.measure="mse" or type.measure="mae" (mean absolute error) can be used by all models except the "cox"; they measure the deviation from the fitted mean to the response. type.measure="C" is Harrel's concordance measure, only available for cox models.

A list of x matrices in the test data for evaluation.

The quantitative response in the test data with length equal to the number of rows in each x matrix of the test data.

number of folds - default is 10. Although nfolds can be as large as the sample size (leave-one-out CV), it is not recommended for large datasets. Smallest value allowable is nfolds=3

an optional vector of values between 1 and nfold identifying what fold each observation is in. If supplied, nfold can be missing.

If NULL, the data view contribution is benchmarked by the null model. If users want to benchmark by the model fit on a specified list of data views, force needs to be set to this list of benchmarking data views, i.e. a list of x matrices. The function then evaluates the marginal contribution of each additional data, i.e. the data views in x_list but not in force, on top of the benchmarking views.

Other arguments that can be passed to multiview

Observation matrix.

Optional weight vector.

vector of weighted means of columns of x

vector of weighted standard deviations of columns of x