My.stepwise.glm: Stepwise Variable Selection Procedure for Generalized Linear...
In My.stepwise: Stepwise Variable Selection Procedures for Regression Analysis
Description
Usage
Arguments
Details
Value
Warning
See Also
Examples
Description
This stepwise variable selection procedure (with iterations between the 'forward' and 'backward' steps) can be applied to obtain the best candidate final generalized linear model.
Usage
1
2
My.stepwise.glm(Y, variable.list, in.variable = "NULL", data, sle = 0.15,
sls = 0.15, myfamily, myoffset = "NULL")
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).
myfamily
The 'family' for the sepcified generalized linear model as in glm().
myoffset
The 'offset' for the sepcified generalized linear model as in glm().
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.
See Also
My.stepwise.lm
My.stepwise.coxph
Examples
1
2
3
4
5
6
7
8
9
10
11
12
13
14
data("iris")
names(iris)
my.data <- iris[51:150, ]
my.data$Width <- (my.data$Sepal.Width + my.data$Petal.Width)/2
names(my.data)
dim(my.data)
my.data$Species1 <- ifelse(my.data$Species == "virginica", 1, 0)
my.variable.list <- c("Sepal.Length", "Petal.Length")
My.stepwise.glm(Y = "Species1", variable.list = my.variable.list,
in.variable = c("Width"), data = my.data, myfamily = "binomial")
my.variable.list <- c("Sepal.Length", "Sepal.Width", "Width")
My.stepwise.glm(Y = "Species1", variable.list = my.variable.list,
data = my.data, sle = 0.25, sls = 0.25, myfamily = "binomial")
Example output
[1] "Sepal.Length" "Sepal.Width" "Petal.Length" "Petal.Width" "Species"
[1] "Sepal.Length" "Sepal.Width" "Petal.Length" "Petal.Width" "Species"
[6] "Width"
[1] 100 6
# --------------------------------------------------------------------------------------------------
# Initial Model:
Call:
glm(formula = as.formula(paste(Y, paste(in.variable, collapse = "+"),
sep = "~")), family = binomial(logit), data = data)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.00174 -0.67631 -0.00153 0.56553 2.60904
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -18.250 3.699 -4.934 8.04e-07 ***
Width 8.044 1.627 4.943 7.70e-07 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 138.629 on 99 degrees of freedom
Residual deviance: 77.335 on 98 degrees of freedom
AIC: 81.335
Number of Fisher Scoring iterations: 6
# --------------------------------------------------------------------------------------------------
### iter num = 1, Forward Selection by LR Test: + Petal.Length
Call:
glm(formula = Species1 ~ Width + Petal.Length, family = binomial(logit),
data = data)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.96297 -0.10813 -0.00005 0.07046 2.64996
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -46.543 12.380 -3.759 0.000170 ***
Width 2.137 2.487 0.859 0.390172
Petal.Length 8.572 2.387 3.592 0.000329 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 138.629 on 99 degrees of freedom
Residual deviance: 32.677 on 97 degrees of freedom
AIC: 38.677
Number of Fisher Scoring iterations: 8
--------------- Variance Inflating Factor (VIF) ---------------
Multicollinearity Problem: Variance Inflating Factor (VIF) is bigger than 10 (Continuous Variable) or is bigger than 2.5 (Categorical Variable)
Width Petal.Length
1.010299 1.010299
# --------------------------------------------------------------------------------------------------
### iter num = 2, Forward Selection by LR Test: + Sepal.Length
Call:
glm(formula = Species1 ~ Width + Petal.Length + Sepal.Length,
family = binomial(logit), data = data)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.61739 -0.03752 0.00001 0.01995 1.53322
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -43.103 14.434 -2.986 0.00282 **
Width 3.697 2.956 1.251 0.21096
Petal.Length 12.847 4.014 3.201 0.00137 **
Sepal.Length -4.495 1.791 -2.511 0.01206 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 138.629 on 99 degrees of freedom
Residual deviance: 22.205 on 96 degrees of freedom
AIC: 30.205
Number of Fisher Scoring iterations: 9
--------------- Variance Inflating Factor (VIF) ---------------
Multicollinearity Problem: Variance Inflating Factor (VIF) is bigger than 10 (Continuous Variable) or is bigger than 2.5 (Categorical Variable)
Width Petal.Length Sepal.Length
1.188266 2.294930 2.564059
# ==================================================================================================
*** Stepwise Final Model (in.lr.test: sle = 0.15; out.lr.test: sls = 0.15):
Call:
glm(formula = Species1 ~ Width + Petal.Length + Sepal.Length,
family = binomial(logit), data = data)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.61739 -0.03752 0.00001 0.01995 1.53322
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -43.103 14.434 -2.986 0.00282 **
Width 3.697 2.956 1.251 0.21096
Petal.Length 12.847 4.014 3.201 0.00137 **
Sepal.Length -4.495 1.791 -2.511 0.01206 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 138.629 on 99 degrees of freedom
Residual deviance: 22.205 on 96 degrees of freedom
AIC: 30.205
Number of Fisher Scoring iterations: 9
--------------- Variance Inflating Factor (VIF) ---------------
Multicollinearity Problem: Variance Inflating Factor (VIF) is bigger than 10 (Continuous Variable) or is bigger than 2.5 (Categorical Variable)
Width Petal.Length Sepal.Length
1.188266 2.294930 2.564059
# --------------------------------------------------------------------------------------------------
# Initial Model:
Call:
glm(formula = as.formula(paste(Y, paste(in.variable, collapse = "+"),
sep = "~")), family = binomial(logit), data = data)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.177 -1.177 0.000 1.177 1.177
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.0 0.2 0 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 138.63 on 99 degrees of freedom
Residual deviance: 138.63 on 99 degrees of freedom
AIC: 140.63
Number of Fisher Scoring iterations: 2
# --------------------------------------------------------------------------------------------------
### iter num = 1, Forward Selection by LR Test: + Width
Call:
glm(formula = Species1 ~ Width, family = binomial(logit), data = data)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.00174 -0.67631 -0.00153 0.56553 2.60904
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -18.250 3.699 -4.934 8.04e-07 ***
Width 8.044 1.627 4.943 7.70e-07 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 138.629 on 99 degrees of freedom
Residual deviance: 77.335 on 98 degrees of freedom
AIC: 81.335
Number of Fisher Scoring iterations: 6
--------------- 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: + Sepal.Width
Call:
glm(formula = Species1 ~ Width + Sepal.Width, family = binomial(logit),
data = data)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.79060 -0.12811 -0.00554 0.08197 2.29438
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -14.379 5.097 -2.821 0.00478 **
Width 31.401 7.323 4.288 1.80e-05 ***
Sepal.Width -19.607 4.882 -4.016 5.92e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 138.629 on 99 degrees of freedom
Residual deviance: 27.399 on 97 degrees of freedom
AIC: 33.399
Number of Fisher Scoring iterations: 7
--------------- Variance Inflating Factor (VIF) ---------------
Multicollinearity Problem: Variance Inflating Factor (VIF) is bigger than 10 (Continuous Variable) or is bigger than 2.5 (Categorical Variable)
Width Sepal.Width
11.72704 11.72704
# --------------------------------------------------------------------------------------------------
### iter num = 3, Forward Selection by LR Test: + Sepal.Length
Call:
glm(formula = Species1 ~ Width + Sepal.Width + Sepal.Length,
family = binomial(logit), data = data)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.62754 -0.12171 -0.00435 0.06825 2.32596
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -20.287 8.055 -2.519 0.011785 *
Width 31.845 7.961 4.000 6.33e-05 ***
Sepal.Width -20.746 5.469 -3.794 0.000149 ***
Sepal.Length 1.295 1.089 1.189 0.234357
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 138.629 on 99 degrees of freedom
Residual deviance: 25.902 on 96 degrees of freedom
AIC: 33.902
Number of Fisher Scoring iterations: 8
--------------- Variance Inflating Factor (VIF) ---------------
Multicollinearity Problem: Variance Inflating Factor (VIF) is bigger than 10 (Continuous Variable) or is bigger than 2.5 (Categorical Variable)
Width Sepal.Width Sepal.Length
11.260830 12.139373 1.274881
# ==================================================================================================
*** Stepwise Final Model (in.lr.test: sle = 0.25; out.lr.test: sls = 0.25):
Call:
glm(formula = Species1 ~ Width + Sepal.Width + Sepal.Length,
family = binomial(logit), data = data)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.62754 -0.12171 -0.00435 0.06825 2.32596
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -20.287 8.055 -2.519 0.011785 *
Width 31.845 7.961 4.000 6.33e-05 ***
Sepal.Width -20.746 5.469 -3.794 0.000149 ***
Sepal.Length 1.295 1.089 1.189 0.234357
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 138.629 on 99 degrees of freedom
Residual deviance: 25.902 on 96 degrees of freedom
AIC: 33.902
Number of Fisher Scoring iterations: 8
--------------- Variance Inflating Factor (VIF) ---------------
Multicollinearity Problem: Variance Inflating Factor (VIF) is bigger than 10 (Continuous Variable) or is bigger than 2.5 (Categorical Variable)
Width Sepal.Width Sepal.Length
11.260830 12.139373 1.274881
My.stepwise documentation built on May 2, 2019, 4:03 p.m.
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Description Usage Arguments Details Value Warning See Also Examples
Description
This stepwise variable selection procedure (with iterations between the 'forward' and 'backward' steps) can be applied to obtain the best candidate final generalized linear model.
Usage
1 2 | My.stepwise.glm(Y, variable.list, in.variable = "NULL", data, sle = 0.15,
sls = 0.15, myfamily, myoffset = "NULL")
|
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). |
myfamily |
The 'family' for the sepcified generalized linear model as in glm(). |
myoffset |
The 'offset' for the sepcified generalized linear model as in glm(). |
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.
See Also
My.stepwise.lm
My.stepwise.coxph
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 | data("iris")
names(iris)
my.data <- iris[51:150, ]
my.data$Width <- (my.data$Sepal.Width + my.data$Petal.Width)/2
names(my.data)
dim(my.data)
my.data$Species1 <- ifelse(my.data$Species == "virginica", 1, 0)
my.variable.list <- c("Sepal.Length", "Petal.Length")
My.stepwise.glm(Y = "Species1", variable.list = my.variable.list,
in.variable = c("Width"), data = my.data, myfamily = "binomial")
my.variable.list <- c("Sepal.Length", "Sepal.Width", "Width")
My.stepwise.glm(Y = "Species1", variable.list = my.variable.list,
data = my.data, sle = 0.25, sls = 0.25, myfamily = "binomial")
|
Example output
[1] "Sepal.Length" "Sepal.Width" "Petal.Length" "Petal.Width" "Species"
[1] "Sepal.Length" "Sepal.Width" "Petal.Length" "Petal.Width" "Species"
[6] "Width"
[1] 100 6
# --------------------------------------------------------------------------------------------------
# Initial Model:
Call:
glm(formula = as.formula(paste(Y, paste(in.variable, collapse = "+"),
sep = "~")), family = binomial(logit), data = data)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.00174 -0.67631 -0.00153 0.56553 2.60904
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -18.250 3.699 -4.934 8.04e-07 ***
Width 8.044 1.627 4.943 7.70e-07 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 138.629 on 99 degrees of freedom
Residual deviance: 77.335 on 98 degrees of freedom
AIC: 81.335
Number of Fisher Scoring iterations: 6
# --------------------------------------------------------------------------------------------------
### iter num = 1, Forward Selection by LR Test: + Petal.Length
Call:
glm(formula = Species1 ~ Width + Petal.Length, family = binomial(logit),
data = data)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.96297 -0.10813 -0.00005 0.07046 2.64996
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -46.543 12.380 -3.759 0.000170 ***
Width 2.137 2.487 0.859 0.390172
Petal.Length 8.572 2.387 3.592 0.000329 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 138.629 on 99 degrees of freedom
Residual deviance: 32.677 on 97 degrees of freedom
AIC: 38.677
Number of Fisher Scoring iterations: 8
--------------- Variance Inflating Factor (VIF) ---------------
Multicollinearity Problem: Variance Inflating Factor (VIF) is bigger than 10 (Continuous Variable) or is bigger than 2.5 (Categorical Variable)
Width Petal.Length
1.010299 1.010299
# --------------------------------------------------------------------------------------------------
### iter num = 2, Forward Selection by LR Test: + Sepal.Length
Call:
glm(formula = Species1 ~ Width + Petal.Length + Sepal.Length,
family = binomial(logit), data = data)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.61739 -0.03752 0.00001 0.01995 1.53322
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -43.103 14.434 -2.986 0.00282 **
Width 3.697 2.956 1.251 0.21096
Petal.Length 12.847 4.014 3.201 0.00137 **
Sepal.Length -4.495 1.791 -2.511 0.01206 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 138.629 on 99 degrees of freedom
Residual deviance: 22.205 on 96 degrees of freedom
AIC: 30.205
Number of Fisher Scoring iterations: 9
--------------- Variance Inflating Factor (VIF) ---------------
Multicollinearity Problem: Variance Inflating Factor (VIF) is bigger than 10 (Continuous Variable) or is bigger than 2.5 (Categorical Variable)
Width Petal.Length Sepal.Length
1.188266 2.294930 2.564059
# ==================================================================================================
*** Stepwise Final Model (in.lr.test: sle = 0.15; out.lr.test: sls = 0.15):
Call:
glm(formula = Species1 ~ Width + Petal.Length + Sepal.Length,
family = binomial(logit), data = data)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.61739 -0.03752 0.00001 0.01995 1.53322
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -43.103 14.434 -2.986 0.00282 **
Width 3.697 2.956 1.251 0.21096
Petal.Length 12.847 4.014 3.201 0.00137 **
Sepal.Length -4.495 1.791 -2.511 0.01206 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 138.629 on 99 degrees of freedom
Residual deviance: 22.205 on 96 degrees of freedom
AIC: 30.205
Number of Fisher Scoring iterations: 9
--------------- Variance Inflating Factor (VIF) ---------------
Multicollinearity Problem: Variance Inflating Factor (VIF) is bigger than 10 (Continuous Variable) or is bigger than 2.5 (Categorical Variable)
Width Petal.Length Sepal.Length
1.188266 2.294930 2.564059
# --------------------------------------------------------------------------------------------------
# Initial Model:
Call:
glm(formula = as.formula(paste(Y, paste(in.variable, collapse = "+"),
sep = "~")), family = binomial(logit), data = data)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.177 -1.177 0.000 1.177 1.177
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.0 0.2 0 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 138.63 on 99 degrees of freedom
Residual deviance: 138.63 on 99 degrees of freedom
AIC: 140.63
Number of Fisher Scoring iterations: 2
# --------------------------------------------------------------------------------------------------
### iter num = 1, Forward Selection by LR Test: + Width
Call:
glm(formula = Species1 ~ Width, family = binomial(logit), data = data)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.00174 -0.67631 -0.00153 0.56553 2.60904
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -18.250 3.699 -4.934 8.04e-07 ***
Width 8.044 1.627 4.943 7.70e-07 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 138.629 on 99 degrees of freedom
Residual deviance: 77.335 on 98 degrees of freedom
AIC: 81.335
Number of Fisher Scoring iterations: 6
--------------- 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: + Sepal.Width
Call:
glm(formula = Species1 ~ Width + Sepal.Width, family = binomial(logit),
data = data)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.79060 -0.12811 -0.00554 0.08197 2.29438
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -14.379 5.097 -2.821 0.00478 **
Width 31.401 7.323 4.288 1.80e-05 ***
Sepal.Width -19.607 4.882 -4.016 5.92e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 138.629 on 99 degrees of freedom
Residual deviance: 27.399 on 97 degrees of freedom
AIC: 33.399
Number of Fisher Scoring iterations: 7
--------------- Variance Inflating Factor (VIF) ---------------
Multicollinearity Problem: Variance Inflating Factor (VIF) is bigger than 10 (Continuous Variable) or is bigger than 2.5 (Categorical Variable)
Width Sepal.Width
11.72704 11.72704
# --------------------------------------------------------------------------------------------------
### iter num = 3, Forward Selection by LR Test: + Sepal.Length
Call:
glm(formula = Species1 ~ Width + Sepal.Width + Sepal.Length,
family = binomial(logit), data = data)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.62754 -0.12171 -0.00435 0.06825 2.32596
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -20.287 8.055 -2.519 0.011785 *
Width 31.845 7.961 4.000 6.33e-05 ***
Sepal.Width -20.746 5.469 -3.794 0.000149 ***
Sepal.Length 1.295 1.089 1.189 0.234357
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 138.629 on 99 degrees of freedom
Residual deviance: 25.902 on 96 degrees of freedom
AIC: 33.902
Number of Fisher Scoring iterations: 8
--------------- Variance Inflating Factor (VIF) ---------------
Multicollinearity Problem: Variance Inflating Factor (VIF) is bigger than 10 (Continuous Variable) or is bigger than 2.5 (Categorical Variable)
Width Sepal.Width Sepal.Length
11.260830 12.139373 1.274881
# ==================================================================================================
*** Stepwise Final Model (in.lr.test: sle = 0.25; out.lr.test: sls = 0.25):
Call:
glm(formula = Species1 ~ Width + Sepal.Width + Sepal.Length,
family = binomial(logit), data = data)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.62754 -0.12171 -0.00435 0.06825 2.32596
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -20.287 8.055 -2.519 0.011785 *
Width 31.845 7.961 4.000 6.33e-05 ***
Sepal.Width -20.746 5.469 -3.794 0.000149 ***
Sepal.Length 1.295 1.089 1.189 0.234357
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 138.629 on 99 degrees of freedom
Residual deviance: 25.902 on 96 degrees of freedom
AIC: 33.902
Number of Fisher Scoring iterations: 8
--------------- Variance Inflating Factor (VIF) ---------------
Multicollinearity Problem: Variance Inflating Factor (VIF) is bigger than 10 (Continuous Variable) or is bigger than 2.5 (Categorical Variable)
Width Sepal.Width Sepal.Length
11.260830 12.139373 1.274881
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