I want to control a linear regression model with a specific variable. If i assign variable "c" as 0, i want to estimate the model:
lm(y ~ x) # model with intercept
and if i assign variable "c" as 1 i want to estimate:
lm(y ~ x - 1) # model without intercept
I tried the code below
c <- 1
lm(y ~ x - c)
but it didn't work. c is 1 but in lm function i can't use this variable for argument. How can i assign and use a variable to add intercept and remove?
I don't think you can do that with a simple variable. Rather than conditionally setting the value of a, you can conditionally remove the intercept. Something like
myformula <- y~x
if(TRUE) {
myformula <- update(myformula, ~.-1)
}
myformula
# y ~ x - 1
Formula objects don’t evaluate their arguments (otherwise they fundamentally wouldn’t work). So you need to find a way of interpolating an evaluated value into the unevaluated formula expression.
Like all problems of computer science, this can be solved by one more layer of indirection.
Create an unevaluated expression that creates your formula, and evaluate it after interpolating the variable:
formula = eval(bquote(y ~ x - .(c)))
lm(formula)
Related
In coef(l), where l is a object of class "lm", is (Intercept) always listed first?
R's source code for lm() is not so straightforward. lm() appears to call lm.fit(), which gets coefficients by calling a C function with .Call(C_Cdqrls, x, y, tol, FALSE), which ultimately calls a least squares fitting routine in FORTRAN according to this informative blog post. I'm not really familiar enough with R internals or actual code to do least squares regression to answer my question.
No, only when you have an intercept. Intercept is implicit in formula, but you can specify a model without it using - 1 or 0 +:
x <- rnorm(20)
y <- rnorm(20, 10)
> coef(lm(y ~ x + I(x^2)))
(Intercept) x I(x^2)
10.3035412 -0.1506304 -0.3092836
> coef(lm(y ~ I(x^3) + x - 1))
I(x^3) x
-0.5094851 -0.6598634
The coefficients will be listed in the order they appear in the formula. If there is an intercept, it will be the first. But as in many other situations in R, if you need to obtain the value of a specific component (intercept or any other), it is a good practice to call by it's name. It will return NA if the object don't have it:
intercept <- coef(model)["(Intercept)"]
I am trying to use R to fit a linear model and make predictions. My model includes some constant side parameters that are not in the data frame. Here's a simplified version of what I'm doing:
dat <- data.frame(x=1:5,y=3*(1:5))
b <- 1
mdl <- lm(y~I(b*x),data=dat)
Unfortunately the model object now suffers from a dangerous scoping issue: lm() does not save b as part of mdl, so when predict() is called, it has to reach back into the environment where b was defined. Thus, if subsequent code changes the value of b, the predict value will change too:
y1 <- predict(mdl,newdata=data.frame(x=3)) # y1 == 9
b <- 5
y2 <- predict(mdl,newdata=data.frame(x=3)) # y2 == 45
How can I force predict() to use the original b value instead of the changed one? Alternatively, is there some way to control where predict() looks for the variable, so I can ensure it gets the desired value? In practice I cannot include b as part of the newdata data frame, because in my application, b is a vector of parameters that does not have the same size as the data frame of new observations.
Please note that I have greatly simplified this relative to my actual use case, so I need a robust general solution and not just ad-hoc hacking.
eval(substitute the value into the quoted expression
mdl <- eval(substitute(lm(y~I(b*x),data=dat), list(b=b)))
mdl
# Call:
# lm(formula = y ~ I(1 * x), data = dat)
# ...
We could also use bquote
mdl <- eval(bquote(lm(y~I(.(b)*x), data=dat)))
mdl
#Call:
#lm(formula = y ~ I(1 * x), data = dat)
#Coefficients:
#(Intercept) I(1 * x)
# 9.533e-15 3.000e+00
According to ?bquote description
‘bquote’ quotes its
argument except that terms wrapped in ‘.()’ are evaluated in the
specified ‘where’ environment.
Suppose I was given an data frame df on runtime, how do I fit a polynomial model using polynomial regression, with each predictor is a column from df and has a degree of a constant k >= 2
The difficulty is, 'df' is read during runtime so the number and names of its columns are unknown when the script is written.(but I do know the response variable is the 1st column) So when I call lm I do not know how to write the formula.
In case of k = 1, then I can simply write a generic linear formula
names(df)[1] <- "y"
lm(y ~ ., data = df)
is there something similar I can do for polynomial formula?
One rather convoluted way is to create a formula for the lm regression call by pasting the terms together.
# some data
dat <- data.frame(replicate(10, rnorm(20)))
# Create formula - apply f function to all columns names excluding the first
form <- formula(paste(names(dat)[1], " ~ ",
paste0("poly(", names(dat)[-1], ", 2)", collapse="+")))
# run regression
lm(form , data=dat)
Is there is an equivalent to update for the data part of an lm call object?
For example, say i have the following model:
dd = data.frame(y=rnorm(100),x1=rnorm(100))
Model_all <- lm(formula = y ~ x1, data = dd)
Is there a way of operating on the lm object to have the equivalent effect of:
Model_1t50 <- lm(formula = y ~ x1, data = dd[1:50,])
I am trying to construct some psudo out of sample forecast tests, and it would be very convenient to have a single lm object and to simply roll the data.
I'm fairly certain that update actually does what you want!
example(lm)
dat1 <- data.frame(group,weight)
lm1 <- lm(weight ~ group, data=dat1)
dat2 <- data.frame(group,weight=2*weight)
lm2 <- update(lm1,data=dat2)
coef(lm1)
##(Intercept) groupTrt
## 5.032 -0.371
coef(lm2)
## (Intercept) groupTrt
## 10.064 -0.742
If you're hoping for an effiency gain from this, you'll be disappointed -- R just substitutes the new arguments and re-evaluates the call (see the code of update.default). But it does make the code a lot cleaner ...
biglm objects can be updated to include more data, but not less. So you could do this in the opposite order, starting with less data and adding more. See http://cran.r-project.org/web/packages/biglm/biglm.pdf
However, I suspect you're interested in parameters estimated for subpopulations (ie if rows 1:50 correspond to level "a" of factor variable factrvar. In this case, you should use interaction in your formula (~factrvar*x1) rather than subsetting to data[1:50,]. Interaction of this type will give different effect estimates for each level of factrvar. This is more efficient than estimating each parameter separately and will constrain any additional parameters (ie, x2 in ~factrvar*x1 + x2) to be the same across values of factrvar--if you estimated the same model multiple times to different subsets, x2 would receive a separate parameter estimate each time.
I was reading the documentation on R Formula, and trying to figure out how to work with depmix (from the depmixS4 package).
Now, in the documentation of depmixS4, sample formula tends to be something like y ~ 1.
For simple case like y ~ x, it is defining a relationship between input x and output y, so I get that it is similar to y = a * x + b, where a is the slope, and b is the intercept.
If we go back to y ~ 1, the formula is throwing me off. Is it equivalent to y = 1 (a horizontal line at y = 1)?
To add a bit context, if you look at the depmixs4 documentation, there is one example below
depmix(list(rt~1,corr~1),data=speed,nstates=2,family=list(gaussian(),multinomial()))
I think in general, formula that end with ~ 1 is confusing to me. Can any explain what ~ 1 or y ~ 1 mean?
Many of the operators used in model formulae (asterix, plus, caret) in R, have a model-specific meaning and this is one of them: the 'one' symbol indicates an intercept.
In other words, it is the value the dependent variable is expected to have when the independent variables are zero or have no influence. (To use the more common mathematical meaning of model terms, you wrap them in I()). Intercepts are usually assumed so it is most common to see it in the context of explicitly stating a model without an intercept.
Here are two ways of specifying the same model for a linear regression model of y on x. The first has an implicit intercept term, and the second an explicit one:
y ~ x
y ~ 1 + x
Here are ways to give a linear regression of y on x through the origin (that is, without an intercept term):
y ~ 0 + x
y ~ -1 + x
y ~ x - 1
In the specific case you mention ( y ~ 1 ), y is being predicted by no other variable so the natural prediction is the mean of y, as Paul Hiemstra stated:
> data(city)
> r <- lm(x~1, data=city)
> r
Call:
lm(formula = x ~ 1, data = city)
Coefficients:
(Intercept)
97.3
> mean(city$x)
[1] 97.3
And removing the intercept with a -1 leaves you with nothing:
> r <- lm(x ~ -1, data=city)
> r
Call:
lm(formula = x ~ -1, data = city)
No coefficients
formula() is a function for extracting formula out of objects and its help file isn't the best place to read about specifying model formulae in R. I suggest you look at this explanation or Chapter 11 of An Introduction to R.
if your model were of the form y ~ x1 + x2 This (roughly speaking) represents:
y = β0 + β1(x1) + β2(x2)
Which is of course the same as
y = β0(1) + β1(x1) + β2(x2)
There is an implicit +1 in the above formula. So really, the formula above is y ~ 1 + x1 + x2
We could have a very simple formula, whereby y is not dependent on any other variable. This is the formula that you are referencing,
y ~ 1 which roughly would equate to
y = β0(1) = β0
As #Paul points out, when you solve the simple model, you get β0 = mean (y)
Here is an example
# Let's make a small sample data frame
dat <- data.frame(y= (-2):3, x=3:8)
# Create the linear model as above
simpleModel <- lm(y ~ 1, data=dat)
## COMPARE THE COEFFICIENTS OF THE MODEL TO THE MEAN(y)
simpleModel$coef
# (Intercept)
# 0.5
mean(dat$y)
# [1] 0.5
In general such a formula describes the relation between dependent and independent variables in the form of a linear model. The lefthand side are the dependent variables, the right hand side the independent. The independent variables are used to calculate the trend component of the linear model, the residuals are then assumed to have some kind of distribution. When the independent are equal to one ~ 1, the trend component is a single value, e.g. the mean value of the data, i.e. the linear model only has an intercept.