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How to set the coefficient of one variable to 1 for logistic regression model in R?
To set the coefficient of one variable to 1 for logistic regression model, we can use offset function.
For example, if we have a data frame called df that contains a binary column say y and three independent variables say x1, x2, and x3 and we want to create a logistic regression model with x1 coefficient equal to 1 then we can use the below given command −
glm(y~x2+x3,offset=x1,data=df,family=binomial)
Example 1
Following snippet creates a sample data frame −
y1<-sample(0:1,20,replace=TRUE) iv1<-rpois(20,2) iv2<-rpois(20,2) iv3<-rpois(20,5) df1<-data.frame(y1,iv1,iv2,iv3) df1
Output
The following dataframe is created −
y1 iv1 iv2 iv3 1 1 1 5 8 2 1 2 3 6 3 1 2 3 11 4 1 2 1 5 5 1 2 2 2 6 1 2 1 2 7 1 3 2 1 8 1 1 2 5 9 1 0 1 10 10 0 0 0 5 11 1 0 3 5 12 1 2 4 1 13 1 4 5 11 14 0 3 2 2 15 0 1 1 3 16 1 1 3 1 17 0 1 2 7 18 1 1 3 8 19 1 3 6 9 20 1 6 3 9
In order to create logistic regression model with coefficient of x1 set to 1, add the following code to the above snippet −
y1<-sample(0:1,20,replace=TRUE) iv1<-rpois(20,2) iv2<-rpois(20,2) iv3<-rpois(20,5) df1<-data.frame(y1,iv1,iv2,iv3) Model_1<-glm(y1~iv1+iv2,offset=iv3,data=df1,family=binomial) summary(Model_1)
Output
If you execute all the above given snippets as a single program, it generates the following output −
Call: glm(formula = y1 ~ iv1 + iv2, family = binomial, data = df1, offset = iv3) Deviance Residuals: Min 1Q Median 3Q Max -2.95608 0.00035 0.04659 0.45252 1.67587 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) -7.6349 2.4801 -3.078 0.00208 ** iv1 1.3445 0.9276 1.449 0.14723 iv2 1.8234 0.9462 1.927 0.05396 . --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: 31.099 on 19 degrees of freedom Residual deviance: 19.741 on 17 degrees of freedom AIC: 25.741 Number of Fisher Scoring iterations: 7
Example 2
Following snippet creates a sample data frame −
Response<-sample(0:1,20,replace=TRUE) Rate<-sample(1:10,20,replace=TRUE) Score<-sample(0:9,20,replace=TRUE) df2<-data.frame(Response,Rate,Score) df2
The following dataframe is created −
Response Rate Score 1 0 8 9 2 1 7 6 3 1 2 9 4 0 8 9 5 0 9 8 6 0 1 2 7 1 3 9 8 1 7 2 9 0 7 2 10 0 10 5 11 0 3 9 12 0 7 8 13 1 3 6 14 1 7 5 15 0 2 8 16 1 8 9 17 1 7 9 18 1 6 8 19 0 4 4 20 0 8 7
In order to create logistic regression model with coefficient of Rate set to 1, add the following code to the above snippet −
Response<-sample(0:1,20,replace=TRUE) Rate<-sample(1:10,20,replace=TRUE) Score<-sample(0:9,20,replace=TRUE) df2<-data.frame(Response,Rate,Score) Model_2<-glm(Response~Score,offset=Rate,data=df2,family=binomial) summary(Model_2)
Output
If you execute all the above given snippets as a single program, it generates the following output −
Call: glm(formula = Response ~ Score, family = binomial, data = df2, offset = Rate) Deviance Residuals: Min 1Q Median 3Q Max -2.5313 -1.4891 -0.1062 1.1435 2.9733 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) -7.3748 1.6822 -4.384 1.16e-05 *** Score 0.1074 0.2432 0.442 0.659 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: 55.769 on 19 degrees of freedom Residual deviance: 55.571 on 18 degrees of freedom AIC: 59.571 Number of Fisher Scoring iterations: 4
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