R lm interaction terms with categorical and squared continuous variables - r

Question

I am trying to get an lm fit for my data. The problem I am having is that I want to fit a linear model(1st order polynomial) when the factor is "true" and a second order polynomial when the factor is "false". How can I get that done using only one lm.
a=c(1,2,3,4,5,6,7,8,9,10)
b=factor(c("true","false","true","false","true","false","true","false","true","false"))
c=c(10,8,20,15,30,21,40,25,50,31)
DumbData<-data.frame(cbind(a,c))
DumbData<-cbind(DumbData,b=b)
I have tried
Lm2<-lm(c~a + b + b*I(a^2), data=DumbData)
summary(Lm2)
that results in:
summary(Lm2)
Call:
lm(formula = c ~ a + b + b * I(a^2), data = DumbData)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.74483 1.12047 -0.665 0.535640
a 4.44433 0.39619 11.218 9.83e-05 ***
btrue 6.78670 0.78299 8.668 0.000338 ***
I(a^2) -0.13457 0.03324 -4.049 0.009840 **
btrue:I(a^2) 0.18719 0.01620 11.558 8.51e-05 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.7537 on 5 degrees of freedom
Multiple R-squared: 0.9982, Adjusted R-squared: 0.9967
F-statistic: 688 on 4 and 5 DF, p-value: 4.896e-07
here I have I(a^2) for both fits and i want 1 1st order and another with second order polynomials.
If one tries with:
Lm2<-lm(c~a + b + I(b*I(a^2)), data=DumbData)
Error in `contrasts<-`(`*tmp*`, value = contr.funs[1 + isOF[nn]]) :
contrasts can be applied only to factors with 2 or more levels
In addition: Warning message:
In Ops.factor(b, I(a^2)) : * not meaningful for factors
How can I get the proper interaction terms here???
Thanks Andrie, there are still some things I am missing here. In this example the variable b is a logic one, if is a factor of two levels does not work, I guess I have to convert the factor variable in a logic one. The other thing I am missing is the not in the condition, I(!b*a^2) without the ! I get:
Call: lm(formula = c ~ a + I(b * a^2), data = dat)
Coefficients: Estimate Std. Error t value Pr(>|t|)
(Intercept) 7.2692 1.8425 3.945 0.005565 **
a 2.3222 0.3258 7.128 0.000189 ***
I(b * a^2) 0.3005 0.0355 8.465 6.34e-05 ***
I can not relate the formulas with and without the ! condition, which is a bit strange to me.

Answer 1

Try something along the following lines:
dat <- data.frame(
a=c(1,2,3,4,5,6,7,8,9,10),
b=c(TRUE,FALSE,TRUE,FALSE,TRUE,FALSE,TRUE,FALSE,TRUE,FALSE),
c=c(10,8,20,15,30,21,40,25,50,31)
)
fit <- lm(c ~ a + I(!b * a^2), dat)
summary(fit)
This results in:
Call:
lm(formula = c ~ a + I(!b * a^2), data = dat)
Residuals:
Min 1Q Median 3Q Max
-4.60 -2.65 0.50 2.65 4.40
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 10.5000 2.6950 3.896 0.005928 **
a 3.9000 0.4209 9.266 3.53e-05 ***
I(!b * a^2)TRUE -13.9000 2.4178 -5.749 0.000699 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 3.764 on 7 degrees of freedom
Multiple R-squared: 0.9367, Adjusted R-squared: 0.9186
F-statistic: 51.75 on 2 and 7 DF, p-value: 6.398e-05
Note:
I made use of the logical values TRUE and FALSE.
These will coerce to 1 and 0, respectively.
I used the negation !b inside the formula.

Answer 2

Ummm ...
Lm2<-lm(c~a + b + b*I(a^2), data=DumbData)
You say that "The problem I am having is that I want to fit a linear model(1st order polynomial) when the factor is "true" and a second order polynomial when the factor is "false". How can I get that done using only one lm. "
From that I infer that you don't want b to be directly in the model? In addition, a^2 should be included only if b is false.
So that would be...
lm(c~ a + I((!b) * a^2))
If b is true (that is, !b equals FALSE) then a^2 is multiplied by zero (FALSE) and omitted from the equation.
The only problem is that you have defined b as factor instead of logical. That can be cured.
# b=factor(c("true","false","true","false","true","false","true","false","true","false"))
# could use TRUE and FALSE instead of "ture" and "false"
# alternatively, after defining b as above, do
# b <- b=="true" -- that would convert b to logical (i.e boolean TRUE and FALSe values)
Ok to be exact, you defined b as "character" but it was converted to "factor" when adding it to the data frame ("DumbData")
Another minor point about the way you defined the data frame.
a=c(1,2,3,4,5,6,7,8,9,10)
b=factor(c("true","false","true","false","true","false","true","false","true","false"))
c=c(10,8,20,15,30,21,40,25,50,31)
DumbData<-data.frame(cbind(a,c))
DumbData<-cbind(DumbData,b=b)
Here, cbind is unnecessary. You coud have it all on one line:
Dumbdata<- data.frame(a,b,c)
# shorter and cleaner!!
In addition, to convert b to logical use:
Dumbdata<- data.frame(a,b=b=="true",c)
Note. You need to say b=b=="true", it seems redundant but the LHS (b) gives the name of the variable in data frame whereas the RHS (b=="true") is an expression that evaluates to a "logical" (boolean) value.