Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
How to create a linear model with interaction term only in R?
To create a linear model with interaction term only, we can use the interaction variable while creating the model. For example, if we have a data frame called df that has two independent variables say V1 and V2 and one dependent variable Y then the linear model with interaction term only can be created as lm(Y~V1:V2,data=df).
Consider the below data frame −
Example
x1<-rnorm(20,5,1.2) x2<-rnorm(20,2,1.2) y1<-rnorm(20,3,1.25) df1<-data.frame(x1,x2,y1) df1
Output
x1 x2 y1 1 4.442636 2.63714281 0.9120181 2 5.912804 1.72409663 2.2746513 3 7.881736 3.48780844 3.2675991 4 6.145395 1.51225991 3.2177194 5 6.303181 4.34733534 3.3361897 6 5.689431 0.08564247 2.0863346 7 6.008397 1.30221198 2.7183725 8 6.580716 1.45239970 4.0301650 9 4.000381 3.71539569 3.9404225 10 5.535338 3.48976926 4.9557343 11 5.968661 2.18208048 3.9992293 12 4.783326 -0.90756376 4.2661775 13 3.843528 -0.50299042 0.6496255 14 6.034803 1.06019093 5.2339701 15 4.177977 1.70476660 2.5932408 16 5.746300 0.85021792 3.0145627 17 4.658000 1.49894326 5.2826538 18 3.797983 0.46900834 3.6511403 19 5.415130 -0.31811078 2.6574529 20 4.709443 2.72001915 1.8893078
Creating linear model for y1 with interaction between x1 and x2 −
Model1<-lm(y1~x1:x2,data=df1) summary(Model1)
Call −
lm(formula = y1 ~ x1:x2, data = df1)
Residuals −
Min 1Q Median 3Q Max -2.3517 -0.6387 -0.1708 0.7321 2.1390
Coefficients −
Estimate Std. Error t value Pr(>|t|) (Intercept) 2.96669 0.42803 6.931 1.77e-06 *** x1:x2 0.02535 0.03434 0.738 0.47 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.299 on 18 degrees of freedom Multiple R-squared: 0.02939, Adjusted R-squared: -0.02454 F-statistic: 0.545 on 1 and 18 DF, p-value: 0.4699
Example
v1<-rpois(20,2) v2<-rpois(20,2) v3<-rpois(20,2) Response<-rpois(20,5) df2<-data.frame(v1,v2,v3,Response) df2
Output
v1 v2 v3 Response 1 2 2 4 10 2 1 1 2 2 3 3 4 3 4 4 2 1 2 5 5 0 0 2 4 6 0 2 1 5 7 1 3 0 5 8 0 0 1 6 9 1 3 1 6 10 3 0 2 6 11 2 1 0 3 12 1 3 1 2 13 2 1 3 5 14 0 1 0 8 15 0 3 1 4 16 1 0 3 2 17 3 1 3 2 18 0 4 1 9 19 1 2 3 9 20 3 2 0 9
Creating linear model for Response with interaction between v1, v2, and v3 −
Model2<-lm(Response~v1:v2+v2:v3+v1:v3+v1:v2:v3,data=df2) summary(Model2)
Call −
lm(formula = Response ~ v1:v2 + v2:v3 + v1:v3 + v1:v2:v3, data = df2)
Residuals −
Min 1Q Median 3Q Max -4.3677 -1.7339 -0.0289 1.7127 4.0160
Coefficients −
Estimate Std. Error t value Pr(>|t|) (Intercept) 3.98404 1.21641 3.275 0.00511 ** v1:v2 0.31934 0.44221 0.722 0.48131 v2:v3 0.83716 0.46012 1.819 0.08886 . v1:v3 0.02783 0.30125 0.092 0.92762 v1:v2:v3 -0.37123 0.28280 -1.313 0.20901 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 2.609 on 15 degrees of freedom Multiple R-squared: 0.1907, Adjusted R-squared: -0.02517 F-statistic: 0.8834 on 4 and 15 DF, p-value: 0.4973
Updated on: 06-Feb-2021
819 Views
Advertisements