Title:	Quadratic Vector Autoregression
Version:	0.1.2
Description:	Estimate quadratic vector autoregression models with the strong hierarchy using the Regularization Algorithm under Marginality Principle (RAMP) by Hao et al. (2018) <doi:10.1080/01621459.2016.1264956>, compare the performance with linear models, and construct networks with partial derivatives.
License:	GPL (≥ 3)
URL:	https://github.com/Sciurus365/quadVAR, https://sciurus365.github.io/quadVAR/
BugReports:	https://github.com/Sciurus365/quadVAR/issues
Imports:	cli, dplyr, ggplot2, magrittr, ncvreg, qgraph, RAMP, rlang, shiny, shinythemes, stats, stringr, tibble, tidyr
Suggests:	nonlinearTseries, remotes, SIS, testthat (≥ 3.0.0)
Config/testthat/edition:	3
Encoding:	UTF-8
RoxygenNote:	7.3.2
NeedsCompilation:	no
Packaged:	2025-02-11 14:08:33 UTC; jingm
Author:	Jingmeng Cui [aut, cre]
Maintainer:	Jingmeng Cui <jingmeng.cui@outlook.com>
Repository:	CRAN
Date/Publication:	2025-02-11 17:30:05 UTC

Pipe operator

Description

See ⁠magrittr::[\%>\%][magrittr::pipe]⁠ for details.

Usage

lhs %>% rhs

Arguments

Value

The result of calling rhs(lhs).

Use Block Cross-Validation to Evaluate Models

Description

This function uses block cross-validation to evaluate a model. The data is split into blocks, and the model is fit on all but one block and evaluated on the remaining block. This process is repeated for each block, and the mean squared error is calculated for each model.

Usage

block_cv(
  data,
  dayvar = NULL,
  model,
  block = 10,
  lowerbound = -Inf,
  upperbound = Inf,
  detail = FALSE,
  metric = "MSE"
)

Arguments

Value

Depending on detail. If FALSE, it returns a list of mean squared errors for each model. If TRUE, it returns a list with the mean squared errors for each model, the true data, and the predictions for each model.

Compare estimated model with true model for 4-emotion model

Description

This function compares the estimated model with the true model for the 4-emotion model. It prints out the estimated coefficients and the true coefficients for the main effects and interaction effects.

Usage

compare_4_emo(model, silent = FALSE)

Arguments

Value

Silently return data frame with the estimated coefficients and the true coefficients for the main effects and interaction effects, while printing out the results rounded to two digits if silent = FALSE.

Find index of data that satisfies certain conditions

Description

Find index of data that satisfies certain conditions

Usage

find_index(data, dayvar, beepvar)

Arguments

Value

A list of two vectors of indices.

Extract the adjacency matrix from a quadVAR object.

Description

Extract the adjacency matrix from a quadVAR object.

Usage

get_adj_mat(model, value)

Arguments

Value

An adjacency matrix.

Linearize a quadVAR object to produce a network.

Description

A quadVAR object is nonlinear, which means that the relationship between variables are not the same across different values of the variables. This function linearizes a quadVAR object by specifying the values of the variables that the linearized model will be based on, to facilitate interpretation. The linearized model is then expressed in an adjacency matrix, which can be used to produce a network.

Usage

linear_quadVAR_network(model, value = NULL, value_standardized = TRUE)

## S3 method for class 'linear_quadVAR_network'
plot(x, interactive = FALSE, ...)

Arguments

Value

A linear_quadVAR_network with the following elements:

• adj_mat: the adjacency matrix of the linearized network.

• standardized_value: the standardized value that the linearized model is based on.

• actual_value: the value in the raw scale of the input data.

• model: the input quadVAR object.

• value_standardized: the same as the input.

Methods (by generic)

• plot(linear_quadVAR_network): Produce a plot for the linearized quadVAR model. If interactive = FALSE, the output will be a qgraph object, which can be further used to calculate centrality measures using, e.g., qgraph::centrality() and qgraph::centralityPlot().

References

The idea of this linearization function is inspired by Kroc, E., & Olvera Astivia, O. L. (2023). The case for the curve: Parametric regression with second- and third-order polynomial functions of predictors should be routine. Psychological Methods. https://doi.org/10.1037/met0000629

Make a partial plot of a variable in a model This function takes a quadVAR model as input, and returns a plot of the partial effect of a variable on the dependent variable (controlling all other variables and the intercept), for higher and lower levels of the moderator variable split by the median.

Description

Make a partial plot of a variable in a model This function takes a quadVAR model as input, and returns a plot of the partial effect of a variable on the dependent variable (controlling all other variables and the intercept), for higher and lower levels of the moderator variable split by the median.

Usage

partial_plot(model, y, x, moderator)

Arguments

Value

A ggplot object

Predict the values of the dependent variables using the quadVAR model

Description

Predict the values of the dependent variables using the quadVAR model

Usage

## S3 method for class 'quadVAR'
predict(
  object,
  newdata = NULL,
  donotpredict = NULL,
  lowerbound = -Inf,
  upperbound = Inf,
  with_const = FALSE,
  ...
)

Arguments

Value

A data frame or tibble containing the predicted values of the dependent variables. If a value cannot be predicted (e.g., because the corresponding previous time point is not in the data), it will be NA.

Estimate lag-1 quadratic vector autoregression models

Description

This function estimate regularized nonlinear quadratic vector autoregression models with strong hierarchy using the RAMP::RAMP() algorithm, and also compare it with the linear AR, regularized VAR, and unregularized (full) VAR and quadratic VAR models.

Usage

quadVAR(
  data,
  vars,
  dayvar = NULL,
  beepvar = NULL,
  penalty = "LASSO",
  tune = "EBIC",
  donotestimate = NULL,
  SIS_options = list(),
  RAMP_options = list()
)

## S3 method for class 'quadVAR'
print(x, ...)

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

## S3 method for class 'quadVAR'
coef(object, ...)

## S3 method for class 'coef_quadVAR'
print(
  x,
  use_actual_names = TRUE,
  abbr = FALSE,
  minlength = 3,
  omit_zero = TRUE,
  digits = 2,
  row.names = FALSE,
  ...
)

## S3 method for class 'quadVAR'
plot(x, value = NULL, value_standardized = TRUE, interactive = FALSE, ...)

Arguments

Value

An quadVAR object that contains the following elements:

• NULL_model: A list of NULL models for each variable.

• AR_model: A list of linear AR models for each variable.

• VAR_model: A list of regularized VAR models for each variable.

• VAR_full_model: A list of unregularized (full) VAR models for each variable.

• quadVAR_model: A list of regularized nonlinear quadratic VAR models for each variable.

• quadVAR_full_model: A list of unregularized (full) nonlinear quadratic VAR models for each variable.

• data,vars,penalty,tune,SIS_options,RAMP_options: The input arguments.

• data_x,data_y: The data directly used for modeling.

Methods (by generic)

• print(quadVAR): Print the coefficients for a quadVAR object. See coef.quadVAR() and print.coef_quadVAR() for details.

• summary(quadVAR): Summary of a quadVAR object. Different IC definitions used by different packages (which differ by a constant) are unified to make them comparable to each other.

• coef(quadVAR): Extract the coefficients from a quadVAR object.

• plot(quadVAR): Produce a plot for the linearized quadVAR model. Equivalent to first produce a linear quadVAR network using linear_quadVAR_network(), then use plot.linear_quadVAR_network().

Functions

• print(coef_quadVAR): Print the coefficients from a quadVAR object.

See Also

linear_quadVAR_network()

Examples

set.seed(1614)
data <- sim_4_emo(time = 200, sd = 1)
plot(data[, "x1"])
qV1 <- quadVAR(data, vars = c("x1", "x2", "x3", "x4"))
summary(qV1)
coef(qV1)
plot(qV1)
# Compare the estimation with the true model
plot(true_model_4_emo())
plot(qV1, value = 0, value_standardized = FALSE, layout = plot(true_model_4_emo())$layout)

Transform a quadVAR object to a list of dynamic equations.

Description

Transform a quadVAR object to a list of dynamic equations.

Usage

quadVAR_to_dyn_eqns(model, minus_self = TRUE)

Arguments

Value

A list of dynamic equations in characters. You can also use rlang::parse_expr() to parse them into expressions.

Simulate a 4-emotion model

Description

This function simulates a 4-emotion model which is nonlinear, bistable, discrete, and (almost) centered to zero. Adapted from the model described by van de Leemput et al. (2014).

Usage

sim_4_emo(time = 200, init = c(1.36, 1.36, 4.89, 4.89), sd = 1)

Arguments

Value

A matrix with the simulated data.

References

van de Leemput, I. A., Wichers, M., Cramer, A. O., Borsboom, D., Tuerlinckx, F., Kuppens, P., ... & Scheffer, M. (2014). Critical slowing down as early warning for the onset and termination of depression. Proceedings of the National Academy of Sciences, 111(1), 87-92.

See Also

true_model_4_emo(), compare_4_emo(), quadVAR()

True model for 4-emotion model

Description

This function generate the true model for the 4-emotion model. It can used to compare the estimated model with the true model, or to plot the true model.

Usage

true_model_4_emo(...)

## S3 method for class 'true_model_4_emo'
coef(object, ...)

## S3 method for class 'true_model_4_emo'
print(x, which = NULL, ...)

Arguments

Value

A true_model_4_emo object.

NULL, but prints out the true model.

Methods (by generic)

• coef(true_model_4_emo): This function returns the coefficients for the 4-emotion model. It is also used in other functions to generate the linearized version of the true model and to make plots. It returns a list of coefficients for the 4-emotion model, in the same format as coef.quadVAR()

• print(true_model_4_emo): This function prints out the true model for the 4-emotion model in the same format as RAMP::RAMP(), to help users to compare the true model and the estimated model.

See Also

true_model_4_emo(), compare_4_emo(), quadVAR()

Examples

coef(true_model_4_emo())
plot(true_model_4_emo())

if (interactive()) {
  # This code will only run in an interactive session
  plot(true_model_4_emo(), interactive = TRUE)
}

Using the glmnet and ncvreg packages, fits a Generalized Linear Model or Cox Proportional Hazards Model using various methods for choosing the regularization parameter \lambda

Description

This function is modified from SIS::tune.fit(). It is used to tune the regularization parameter for the regularized VAR models. This wrapper is used because of the following reasons.

1. The original SIS::tune.fit() function does not return the value of the information criteria that we would like to use.

2. We use the ncvreg package exclusively (so we removed the code using the glmnet package). This is to make the result more consistent, and also because the ncvreg package has better support for the calculation of information criteria.

3. We also removed the generalized linear model (GLM) option, and the cross-validation option because we do not use them.

4. We use stats::AIC() and stats::BIC() instead of the ones using SIS:::loglik() to make the calculation methods more consistent.

5. We added ... to allow the user to pass additional arguments to the ncvreg::ncvreg() function.

Usage

tune.fit(
  x,
  y,
  family = "gaussian",
  penalty = c("SCAD", "MCP", "lasso"),
  concavity.parameter = switch(penalty, SCAD = 3.7, 3),
  tune = c("aic", "bic", "ebic"),
  type.measure = c("deviance", "class", "auc", "mse", "mae"),
  gamma.ebic = 1,
  ...
)

Arguments

Details

Original description from SIS::tune.fit():

This function fits a generalized linear model or a Cox proportional hazards model via penalized maximum likelihood, with available penalties as indicated in the glmnet and ncvreg packages. Instead of providing the whole regularization solution path, the function returns the solution at a unique value of \lambda, the one optimizing the criterion specified in tune.

Value

Returns an object with

Author(s)

Jianqing Fan, Yang Feng, Diego Franco Saldana, Richard Samworth, and Yichao Wu

References

Jerome Friedman and Trevor Hastie and Rob Tibshirani (2010) Regularization Paths for Generalized Linear Models Via Coordinate Descent. Journal of Statistical Software, 33(1), 1-22.

Noah Simon and Jerome Friedman and Trevor Hastie and Rob Tibshirani (2011) Regularization Paths for Cox's Proportional Hazards Model Via Coordinate Descent. Journal of Statistical Software, 39(5), 1-13.

Patrick Breheny and Jian Huang (2011) Coordiante Descent Algorithms for Nonconvex Penalized Regression, with Applications to Biological Feature Selection. The Annals of Applied Statistics, 5, 232-253.

Hirotogu Akaike (1973) Information Theory and an Extension of the Maximum Likelihood Principle. In Proceedings of the 2nd International Symposium on Information Theory, BN Petrov and F Csaki (eds.), 267-281.

Gideon Schwarz (1978) Estimating the Dimension of a Model. The Annals of Statistics, 6, 461-464.

Jiahua Chen and Zehua Chen (2008) Extended Bayesian Information Criteria for Model Selection with Large Model Spaces. Biometrika, 95, 759-771.

Examples

set.seed(0)
data("leukemia.train", package = "SIS")
y.train <- leukemia.train[, dim(leukemia.train)[2]]
x.train <- as.matrix(leukemia.train[, -dim(leukemia.train)[2]])
x.train <- SIS::standardize(x.train)
model <- tune.fit(x.train[, 1:3500], y.train, family = "binomial", tune = "bic")
model$ix
model$a0
model$beta