# My.stepwise.lm: Stepwise Variable Selection Procedure for Linear Regression... In My.stepwise: Stepwise Variable Selection Procedures for Regression Analysis

## Description

This stepwise variable selection procedure (with iterations between the 'forward' and 'backward' steps) can be applied to obtain the best candidate final linear regression model.

## Usage

 ```1 2``` ```My.stepwise.lm(Y, variable.list, in.variable = "NULL", data, sle = 0.15, sls = 0.15) ```

## Arguments

 `Y` The response variable. `variable.list` A list of covariates to be selected. `in.variable` A list of covariate(s) to be always included in the regression model. `data` The data to be analyzed. `sle` The chosen significance level for entry (SLE). `sls` The chosen significance level for stay (SLS).

## Details

The goal of regression analysis is to find one or a few parsimonious regression models that fit the observed data well for effect estimation and/or outcome prediction. To ensure a good quality of analysis, the model-fitting techniques for (1) variable selection, (2) goodness-of-fit assessment, and (3) regression diagnostics and remedies should be used in regression analysis. The stepwise variable selection procedure (with iterations between the 'forward' and 'backward' steps) is one of the best ways to obtaining the best candidate final regression model. All the bivariate significant and non-significant relevant covariates and some of their interaction terms (or moderators) are put on the 'variable list' to be selected. The significance levels for entry (SLE) and for stay (SLS) are suggested to be set at 0.15 or larger for being conservative. Then, with the aid of substantive knowledge, the best candidate final regression model is identified manually by dropping the covariates with p value > 0.05 one at a time until all regression coefficients are significantly different from 0 at the chosen alpha level of 0.05. Since the statistical testing at each step of the stepwise variable selection procedure is conditioning on the other covariates in the regression model, the multiple testing problem is not of concern. Any discrepancy between the results of bivariate analysis and regression analysis is likely due to the confounding effects of uncontrolled covariates in bivariate analysis or the masking effects of intermediate variables (or mediators) in regression analysis.

## Value

A model object representing the identified "Stepwise Final Model" with the values of variance inflating factor (VIF) for all included covarites is displayed.

## Warning

The value of variance inflating factor (VIF) is bigger than 10 in continuous covariates or VIF is bigger than 2.5 in categorical covariates indicate the occurrence of multicollinearity problem among some of the covariates in the fitted regression model.

My.stepwise.glm

My.stepwise.coxph

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```data("LifeCycleSavings") names(LifeCycleSavings) dim(LifeCycleSavings) my.variable.list <- c("pop15", "pop75", "dpi") My.stepwise.lm(Y = "sr", variable.list = my.variable.list, in.variable = c("ddpi"), data = LifeCycleSavings) my.variable.list <- c("pop15", "pop75", "dpi", "ddpi") My.stepwise.lm(Y = "sr", variable.list = my.variable.list, data = LifeCycleSavings, sle = 0.25, sls = 0.25) ```

### Example output

```[1] "sr"    "pop15" "pop75" "dpi"   "ddpi"
[1] 50  5
# --------------------------------------------------------------------------------------------------
### iter num = 0, Initial Model

Call:
lm(formula = as.formula(paste(Y, paste(in.variable, collapse = "+"),
sep = "~")), data = data)

Residuals:
Min      1Q  Median      3Q     Max
-8.5535 -3.7349  0.9835  2.7720  9.3104

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)   7.8830     1.0110   7.797 4.46e-10 ***
ddpi          0.4758     0.2146   2.217   0.0314 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 4.311 on 48 degrees of freedom
Multiple R-squared:  0.0929,	Adjusted R-squared:  0.074
F-statistic: 4.916 on 1 and 48 DF,  p-value: 0.03139

# --------------------------------------------------------------------------------------------------
### iter num = 1, Forward Selection by LR Test: + pop15

Call:
lm(formula = sr ~ ddpi + pop15, data = data)

Residuals:
Min      1Q  Median      3Q     Max
-7.5831 -2.8632  0.0453  2.2273 10.4753

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 15.59958    2.33439   6.682 2.48e-08 ***
ddpi         0.44283    0.19240   2.302 0.025837 *
pop15       -0.21638    0.06033  -3.586 0.000796 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 3.861 on 47 degrees of freedom
Multiple R-squared:  0.2878,	Adjusted R-squared:  0.2575
F-statistic: 9.496 on 2 and 47 DF,  p-value: 0.0003438

--------------- Variance Inflating Factor (VIF) ---------------
Multicollinearity Problem: Variance Inflating Factor (VIF) is bigger than 10 (Continuous Variable) or is bigger than 2.5 (Categorical Variable)
ddpi    pop15
1.002293 1.002293
# --------------------------------------------------------------------------------------------------
### iter num = 2, Forward Selection by LR Test: + pop75

Call:
lm(formula = sr ~ ddpi + pop15 + pop75, data = data)

Residuals:
Min      1Q  Median      3Q     Max
-8.2539 -2.6159 -0.3913  2.3344  9.7070

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)  28.1247     7.1838   3.915 0.000297 ***
ddpi          0.4278     0.1879   2.277 0.027478 *
pop15        -0.4518     0.1409  -3.206 0.002452 **
pop75        -1.8354     0.9984  -1.838 0.072473 .
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 3.767 on 46 degrees of freedom
Multiple R-squared:  0.3365,	Adjusted R-squared:  0.2933
F-statistic: 7.778 on 3 and 46 DF,  p-value: 0.0002646

--------------- Variance Inflating Factor (VIF) ---------------
Multicollinearity Problem: Variance Inflating Factor (VIF) is bigger than 10 (Continuous Variable) or is bigger than 2.5 (Categorical Variable)
ddpi    pop15    pop75
1.004186 5.745478 5.736014
# ==================================================================================================
*** Stepwise Final Model (in.lr.test: sle = 0.15; out.lr.test: sls = 0.15):

Call:
lm(formula = sr ~ ddpi + pop15 + pop75, data = data)

Residuals:
Min      1Q  Median      3Q     Max
-8.2539 -2.6159 -0.3913  2.3344  9.7070

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)  28.1247     7.1838   3.915 0.000297 ***
ddpi          0.4278     0.1879   2.277 0.027478 *
pop15        -0.4518     0.1409  -3.206 0.002452 **
pop75        -1.8354     0.9984  -1.838 0.072473 .
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 3.767 on 46 degrees of freedom
Multiple R-squared:  0.3365,	Adjusted R-squared:  0.2933
F-statistic: 7.778 on 3 and 46 DF,  p-value: 0.0002646

--------------- Variance Inflating Factor (VIF) ---------------
Multicollinearity Problem: Variance Inflating Factor (VIF) is bigger than 10 (Continuous Variable) or is bigger than 2.5 (Categorical Variable)
ddpi    pop15    pop75
1.004186 5.745478 5.736014
# --------------------------------------------------------------------------------------------------
### iter num = 0, Initial Model

Call:
lm(formula = as.formula(paste(Y, paste(in.variable, collapse = "+"),
sep = "~")), data = data)

Residuals:
Min     1Q Median     3Q    Max
-9.071 -2.701  0.839  2.946 11.429

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)   9.6710     0.6336   15.26   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 4.48 on 49 degrees of freedom

# --------------------------------------------------------------------------------------------------
### iter num = 1, Forward Selection by LR Test: + pop15

Call:
lm(formula = sr ~ pop15, data = data)

Residuals:
Min     1Q Median     3Q    Max
-8.637 -2.374  0.349  2.022 11.155

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 17.49660    2.27972   7.675 6.85e-10 ***
pop15       -0.22302    0.06291  -3.545 0.000887 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 4.03 on 48 degrees of freedom
Multiple R-squared:  0.2075,	Adjusted R-squared:  0.191
F-statistic: 12.57 on 1 and 48 DF,  p-value: 0.0008866

--------------- Variance Inflating Factor (VIF) ---------------
Multicollinearity Problem: Variance Inflating Factor (VIF) is bigger than 10 (Continuous Variable) or is bigger than 2.5 (Categorical Variable)
# --------------------------------------------------------------------------------------------------
### iter num = 2, Forward Selection by LR Test: + ddpi

Call:
lm(formula = sr ~ pop15 + ddpi, data = data)

Residuals:
Min      1Q  Median      3Q     Max
-7.5831 -2.8632  0.0453  2.2273 10.4753

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 15.59958    2.33439   6.682 2.48e-08 ***
pop15       -0.21638    0.06033  -3.586 0.000796 ***
ddpi         0.44283    0.19240   2.302 0.025837 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 3.861 on 47 degrees of freedom
Multiple R-squared:  0.2878,	Adjusted R-squared:  0.2575
F-statistic: 9.496 on 2 and 47 DF,  p-value: 0.0003438

--------------- Variance Inflating Factor (VIF) ---------------
Multicollinearity Problem: Variance Inflating Factor (VIF) is bigger than 10 (Continuous Variable) or is bigger than 2.5 (Categorical Variable)
pop15     ddpi
1.002293 1.002293
# --------------------------------------------------------------------------------------------------
### iter num = 3, Forward Selection by LR Test: + pop75

Call:
lm(formula = sr ~ pop15 + ddpi + pop75, data = data)

Residuals:
Min      1Q  Median      3Q     Max
-8.2539 -2.6159 -0.3913  2.3344  9.7070

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)  28.1247     7.1838   3.915 0.000297 ***
pop15        -0.4518     0.1409  -3.206 0.002452 **
ddpi          0.4278     0.1879   2.277 0.027478 *
pop75        -1.8354     0.9984  -1.838 0.072473 .
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 3.767 on 46 degrees of freedom
Multiple R-squared:  0.3365,	Adjusted R-squared:  0.2933
F-statistic: 7.778 on 3 and 46 DF,  p-value: 0.0002646

--------------- Variance Inflating Factor (VIF) ---------------
Multicollinearity Problem: Variance Inflating Factor (VIF) is bigger than 10 (Continuous Variable) or is bigger than 2.5 (Categorical Variable)
pop15     ddpi    pop75
5.745478 1.004186 5.736014
# ==================================================================================================
*** Stepwise Final Model (in.lr.test: sle = 0.25; out.lr.test: sls = 0.25):

Call:
lm(formula = sr ~ pop15 + ddpi + pop75, data = data)

Residuals:
Min      1Q  Median      3Q     Max
-8.2539 -2.6159 -0.3913  2.3344  9.7070

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)  28.1247     7.1838   3.915 0.000297 ***
pop15        -0.4518     0.1409  -3.206 0.002452 **
ddpi          0.4278     0.1879   2.277 0.027478 *
pop75        -1.8354     0.9984  -1.838 0.072473 .
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 3.767 on 46 degrees of freedom
Multiple R-squared:  0.3365,	Adjusted R-squared:  0.2933
F-statistic: 7.778 on 3 and 46 DF,  p-value: 0.0002646

--------------- Variance Inflating Factor (VIF) ---------------
Multicollinearity Problem: Variance Inflating Factor (VIF) is bigger than 10 (Continuous Variable) or is bigger than 2.5 (Categorical Variable)
pop15     ddpi    pop75
5.745478 1.004186 5.736014
```

My.stepwise documentation built on May 2, 2019, 4:03 p.m.