## Description

Select optimal model using various stepwise regression strategies, e.g., Forward Selection, Backward Elimination, Bidirectional Elimination; meanwhile, it also supports Best Subset method. Four types of models are currently implemented: linear regression, logistic regression, Cox regression, Poisson, and Gamma regression. For selection criteria, a.k.a, stop rule, users can choose from AIC, AICc, BIC, HQ, Significant Level, and more.

## Usage

`stepwise( formula, data, type = c("linear", "logit", "cox", "poisson", "gamma", "negbin"), include = NULL, strategy = c("forward", "backward", "bidirection", "subset"), metric = c("AIC", "AICc", "BIC", "CP", "HQ", "Rsq", "adjRsq", "SL", "SBC", "IC(3/2)", "IC(1)"), sle = 0.15, sls = 0.15, test_method_linear = c("Pillai", "Wilks", "Hotelling-Lawley", "Roy"), test_method_glm = c("Rao", "LRT"), test_method_cox = c("efron", "breslow", "exact"), tolerance = 1e-07, weight = NULL, best_n = 3, num_digits = 6)`

## Value

A list containing multiple tables will be returned.

Summary of arguments for model selection: Arguments used in the stepwise function, either default or user-supplied values.

Summary of variables in dataset: Variable names, types, and classes in dataset.

Summary of selection process under xxx(strategy) with xxx(metric): Overview of the variable selection process under specified strategy and metric.

Summary of coefficients for the selected model with xxx(dependent variable) under xxx(strategy) and xxx(metric): Coefficients for the selected models under specified strategy with metric. Please note that this table will not be generated for the strategy 'subset' when using the metric 'SL'.

## Arguments

- formula
(formula) The formula used for model fitting by defining the scope of dependent and independent variables. The formula takes the form of a '~' (tilde) symbol, with the response variable(s) on the left-hand side, and the predictor variable(s) on the right-hand side. The 'lm()' function uses this formula to fit a regression model. A formula can be as simple as 'y ~ x'. For multiple predictors, they must be separated by the '+' (plus) symbol, e.g. 'y ~ x1 + x2'. To include an interaction term between variables, use the ':' (colon) symbol: 'y ~ x1 + x1:x2'. Use the '.' (dot) symbol to indicate that all other variables in the dataset should be included as predictors, e.g. 'y ~ .'. In the case of multiple response variables (multivariate), the formula can be specified as 'cbind(y1, y2) ~ x1 + x2'. By default, an intercept term is always included in the models, to exclude it, include '0' or '- 1' in your formula: 'y ~ 0 + x1', 'y ~ x1 + 0', and 'y ~ x1 - 1'.

- data
(data.frame) A dataset consisting of predictor variable(s) and response variable(s).

- type
(character) The stepwise regression type. Choose from 'linear', 'logit', 'poisson', 'cox', 'gamma' and 'negbin'. Default is 'linear'. More information, see StepReg_vignettes

- include
(NULL|character) A character vector specifying predictor variables that will always stay in the model. A subset of the predictors in the dataset.

- strategy
(character) The model selection strategy. Choose from 'forward', 'backward', 'bidirectional' and 'subset'. Default is 'forward'. More information, see StepReg_vignettes

- metric
(character) The model selection criterion (model fit score). Used for the evaluation of the predictive performance of an intermediate model. Choose from 'AIC', 'AICc', 'BIC', 'CP', 'HQ', 'Rsq', 'adjRsq', 'SL', 'SBC', 'IC(3/2)', 'IC(1)'. Default is 'AIC'. More information, see StepReg_vignettes

- sle
(numeric) Significance Level to Enter. It is the statistical significance level that a predictor variable must meet to be included in the model. E.g. if 'sle = 0.05', a predictor with a P-value less than 0.05 will 'enter' the model. Default is 0.15.

- sls
(numeric) Significance Level to Stay. Similar to 'sle', 'sls' is the statistical significance level that a predictor variable must meet to 'stay' in the model. E.g. if 'sls = 0.1', a predictor that was previously included in the model but whose P-value is now greater than 0.1 will be removed.

- test_method_linear
(character) Test method for multivariate linear regression analysis, choose from 'Pillai', 'Wilks', 'Hotelling-Lawley', 'Roy'. Default is 'Pillai'. For univariate regression, 'F-test' will be used.

- test_method_glm
(character) Test method for logit, Poisson, Gamma, and negative binomial regression analysis, choose from 'Rao', 'LRT'. Default is 'Rao'. Only "Rao" is available for strategy = 'subset'.

- test_method_cox
(character) Test method for cox regression analysis, choose from 'efron', 'breslow', 'exact'. Default is 'efron'.

- tolerance
(numeric) A statistical measure used to assess multicollinearity in a multiple regression model. It is calculated as the proportion of the variance in a predictor variable that is not accounted for by the other predictor variables in the model. Default is 1e-07.

- weight
(numeric) A numeric vector specifying the coefficients assigned to the predictor variables. The magnitude of the weight reflects the degree to which each predictor variable contributes to the prediction of the response variable. The range of weight should be from 0 to 1. Values greater than 1 will be coerced to 1, and values less than 0 will be coerced to 0. Default is NULL, which means that all weight are set equal.

- best_n
(numeric(integer)) The number of models to be retained in the process output. Default is 3, indicating that only the top 3 best models with the same number of variables are displayed. If all models are displayed, set it to Inf.

- num_digits
(numeric(integer)) The number of digits to keep when rounding the results. Default is 6.

## Author

Junhui Li, Kai Hu, Xiaohuan Lu

## References

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## Examples

`## perform multivariate linear stepwise regression with 'bidirection' ## strategy and 'AIC' stop rule, excluding intercept.data(mtcars)mtcars$yes <- mtcars$wtformula <- cbind(mpg,drat) ~ . + 0stepwise(formula = formula, data = mtcars, type = "linear", strategy = "bidirection", metric = "AIC")## perform linear stepwise regression with 'bidirection' strategy and ## "AIC","SBC","SL","AICc","BIC", and "HQ" stop rule.formula <- mpg ~ . + 1stepwise(formula = formula, data = mtcars, type = "linear", strategy = c("forward","bidirection"), metric = c("AIC","SBC","SL","AICc","BIC","HQ"))## perform logit stepwise regression with 'forward' strategy and significance## level as stop rule.data(remission)formula <- remiss ~ .stepwise(formula = formula, data = remission, type = "logit", strategy = "forward", metric = "SL", sle=0.05, sls=0.05)`

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