stepwise: Stepwise Linear Model Regression

In StepReg: Stepwise Regression Analysis

Stepwise Linear Model Regression

Description

Stepwise linear regression analysis selects model based on information criteria and F or approximate F test with 'forward', 'backward', 'bidirection' and 'score' model selection method.

Usage

stepwise(
  formula,
  data,
  include = NULL,
  selection = c("forward", "backward", "bidirection", "score"),
  select = c("AIC", "AICc", "BIC", "CP", "HQ", "HQc", "Rsq", "adjRsq", "SL", "SBC"),
  sle = 0.15,
  sls = 0.15,
  multivarStat = c("Pillai", "Wilks", "Hotelling-Lawley", "Roy"),
  weights = NULL,
  best = NULL
)

Arguments

formula	Model formulae. The models fitted by the lm functions are specified in a compact symbolic form. The basic structure of a formula is the tilde symbol (~) and at least one independent (righthand) variable. In most (but not all) situations, a single dependent (lefthand) variable is also needed. Thus we can construct a formula quite simple formula (y ~ x). Multiple independent variables by simply separating them with the plus (+) symbol (y ~ x1 + x2). Variables in the formula are removed with a minus(-) symbol (y ~ x1 - x2). One particularly useful feature is the . operator when modelling with lots of variables (y ~ .). The %in% operator indicates that the terms on its left are nested within those on the right. For example y ~ x1 + x2 %in% x1 expands to the formula y ~ x1 + x1:x2. A model with no intercept can be specified as y ~ x - 1 or y ~ x + 0 or y ~ 0 + x. Multivariate multiple regression can be specified as cbind(y1,y2) ~ x1 + x2.
data	Data set including dependent and independent variables to be analyzed
include	Force vector of effects name to be included in all models.
selection	Model selection method including "forward", "backward", "bidirection" and 'score',forward selection starts with no effects in the model and adds effects, backward selection starts with all effects in the model and removes effects, while bidirection regression is similar to the forward method except that effects already in the model do not necessarily stay there, and score method requests specifies the best-subset selection method, which uses the branch-and-bound technique to efficiently search for subsets of model effects that best predict the response variable.
select	Specify the criterion that uses to determine the order in which effects enter and leave at each step of the specified selection method including "AIC","AICc","BIC","CP","HQ","HQc","Rsq","adjRsq","SBC" and "SL".
sle	Specify the significance level for entry, default is 0.15
sls	Specify the significance level for staying in the model, default is 0.15
multivarStat	Statistic for multivariate regression analysis, including Wilks' lamda ("Wilks"), Pillai Trace ("Pillai"), Hotelling-Lawley's Trace ("Hotelling"), Roy's Largest Root ("Roy")
weights	Numeric vector to provide a weight for each observation in the input data set. Note that weights should be ranged from 0 to 1, while negative numbers are forcibly converted to 0, and numbers greater than 1 are forcibly converted to 1. If you do not specify a weight vector, each observation has a default weight of 1.
best	Control the number of models displayed in the output, default is NULL, which means all possible model will be displayed.

Author(s)

Junhui Li

References

Alsubaihi, A. A., Leeuw, J. D., and Zeileis, A. (2002). Variable selection in multivariable regression using sas/iml. , 07(i12).

Darlington, R. B. (1968). Multiple regression in psychological research and practice. Psychological Bulletin, 69(3), 161.

Dharmawansa, P. , Nadler, B. , & Shwartz, O. . (2014). Roy's largest root under rank-one alternatives:the complex valued case and applications. Statistics.

Hannan, E. J., & Quinn, B. G. (1979). The determination of the order of an autoregression. Journal of the Royal Statistical Society, 41(2), 190-195.

Harold Hotelling. (1992). The Generalization of Student's Ratio. Breakthroughs in Statistics. Springer New York.

Hocking, R. R. (1976). A biometrics invited paper. the analysis and selection of variables in linear regression. Biometrics, 32(1), 1-49.

Hurvich, C. M., & Tsai, C. (1989). Regression and time series model selection in small samples. Biometrika, 76(2), 297-307.

Judge, & GeorgeG. (1985). The Theory and practice of econometrics /-2nd ed. The Theory and practice of econometrics /. Wiley.

Mallows, C. L. (1973). Some comments on cp. Technometrics, 15(4), 661-676.

Mardia, K. V., Kent, J. T., & Bibby, J. M. (1979). Multivariate analysis. Mathematical Gazette, 37(1), 123-131.

Mckeon, J. J. (1974). F approximations to the distribution of hotelling's t20. Biometrika, 61(2), 381-383.

Mcquarrie, A. D. R., & Tsai, C. L. (1998). Regression and Time Series Model Selection. Regression and time series model selection /. World Scientific.

Pillai, K. . (1955). Some new test criteria in multivariate analysis. The Annals of Mathematical Statistics, 26(1), 117-121.

R.S. Sparks, W. Zucchini, & D. Coutsourides. (1985). On variable selection in multivariate regression. Communication in Statistics- Theory and Methods, 14(7), 1569-1587.

Sawa, T. (1978). Information criteria for discriminating among alternative regression models. Econometrica, 46(6), 1273-1291.

Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6(2), pags. 15-18.

Examples

data(mtcars)
mtcars$yes <- mtcars$wt
formula <- cbind(mpg,drat) ~ . + 0
stepwise(formula=formula,
         data=mtcars,
         selection="bidirection",
         select="AIC")

StepReg documentation built on Dec. 28, 2022, 1:07 a.m.