# [R] Questions on factors in regression analysis

David Winsemius dwinsemius at comcast.net
Thu Aug 20 20:13:22 CEST 2009

```On Aug 20, 2009, at 1:46 PM, guox at ucalgary.ca wrote:

> I got two questions on factors in regression:
>
> Q1.
> In a table, there a few categorical/factor variables, a few numerical
> variables and the response variable is numeric. Some factors are
> important
> but others not.
> How to determine which categorical variables are significant to the
> response variable?

Seems that you should engage the services of a consulting statistician
for that sort of question. Or post in a venue where statistical
consulting is supposed to occur, such as one of the sci.stat.*
newsgroups.

>
> Q2.
> As we knew, lm can deal with categorical variables.
> I thought, when there is a categorical predictor, we may use lm
> directly
> without quantifying these factors and assigning different values to
> factors
> would not change the fittings as shown:

The "numbers" that you are attempting to assign are really just labels
for the factor levels. The regression functions in R will not use them
for any calculations. They should not be thought of as having
"values". Even if the factor is an ordered factor, the labels may not
be interpretable as having the same numerical order as the string
values might suggest.

>
> x <- 1:20 ## numeric predictor
> yes.no <- c("yes","no")
> factors <- gl(2,10,20,yes.no) ##factor predictor
> factors.quant <-  rep(c(18.8,29.9),c(10,10)) ##quantificatio of
> factors

Not sure what that is supposed to mean. It is not a factor object even
though you may be misleading yourself in to believing it should be.
It's a numeric vector.
> str(factors.quant)
num [1:20] 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 ...

> factors.quant.1 <-  rep(c(16.9,38.9),c(10,10))
>   ##second quantificatio of factors
> response <- 0.8*x + 18 + factors.quant + rnorm(20) ##response
> lm.quant <- lm(response ~ x + factors.quant) ##lm with quantifications
> lm.fact <- lm(response ~ x + factors) ##lm with factors

> lm.quant

Call:
lm(formula = response ~ x + factors.quant)

Coefficients:
(Intercept)              x  factors.quant
14.9098         0.5385         1.2350

> lm.fact

Call:
lm(formula = response ~ x + factors)

Coefficients:
(Intercept)            x    factorsno
38.1286       0.5385      13.7090
>
> lm.quant.1 <- lm(response ~ x + factors.quant.1) ##lm with
> quantifications

> lm.quant.1

Call:
lm(formula = response ~ x + factors.quant.1)

Coefficients:
(Intercept)                x  factors.quant.1
27.5976           0.5385           0.6231

> lm.fact.1 <- lm(response ~ x + factors) ##lm with factors
>
> par(mfrow=c(2,2)) ## comparisons of two fittings
> plot(x, response)
> lines(x,fitted(lm.quant),col="blue")
> grid()
> plot(x,response)
> lines(x,fitted(lm.fact),col = "red")
> grid()
> plot(x, response)
> lines(x,fitted(lm.quant.1),lty =2,col="blue")
> grid()
> plot(x,response)
> lines(x,fitted(lm.fact.1),lty =2,col = "red")
> grid()
> par(mfrow = c(1,1))
>
> So, is it right that we can assign any numeric values to factors,
> for example, c(yes, no) = c(18.8,29.9) or (16.9,38.9) in the above,
> before doing lm, glm, aov, even nls?

You can give factor levels any name you like, including any sequence
of digit characters. Unlike "ordinary R where unquoted numbers cannot
start variable names, factor functions will coerce numeric vectors to
character vectors when assigning level names. But you seem to be
conflating factors with numeric vectors that have many ties. Those two
entities would have different handling by R's regression functions.

--

David Winsemius, MD
Heritage Laboratories
West Hartford, CT

```