I am doing a regression with several categorial variables and continuous variables mixed together. For simplify my question, I want to create a regression model that predicts the driving time given a certain driver in different zones with driving miles. That's say I have 5 different drivers and 2 zones in my training data.
I know I probably need to build 5*2=10 regression models for prediction. What I am using in R is
m <- lm(driving_time ~ factor(driver)+factor(zone)+miles)
But it seems like R doesn't expend the combination. My problem is if there are any smart way to do the expansion automatically in R. Or I have to write the 10 regression models one by one. Thank you.
Please read ?formula. + in a formula means include that variable as a main effect. You seem to be looking for an interaction term between driver and zone. You create an interaction term using the : operator. There is also a short cut to get both main and interaction effect via the * operator.
There is some confusion as to whether you want miles to also interact, but I'll assume not here as you only mention 2 x 5 terms.
foo <- transform(foo, driver = factor(driver), zone = factor(zone))
m <- lm(driving_time ~ driver * zone + miles, data = foo)
Here I assume your data are in data frame foo. The first line separates the data processing from the model specification/fitting by converting the variables of interest to factors before fitting.
The formula then specifies main and interactive effects for driver and zone plus main effect for miles.
If you want interactions between all three then:
m <- lm(driving_time ~ driver * zone * miles, data = foo)
or
m <- lm(driving_time ~ (driver + zone + miles)^3, data = foo)
would do that for you.
Related
I'm new to applying splines to longitudinal data, so here comes my question:
I've some longitudinal data on growing mice in 3 timepoints: at x, y and z months. It's known from the existent literature that the trajectories of growth in this type of data are usually better modeled in non-linear terms.
However, since I have only 3 timepoints, I wonder if this allows me to apply natural quadratic spline to age variable in my lmer model?
edit:I mean is
lmer<-mincLmer(File ~ ns(Age,2) * Genotype + Sex + (1|Subj_ID),data, mask=mask)
a legit way to go around?
I'm sorry if this is a stupid question - I'm just a lonely PhD student without supervision, and I would be super-grateful for any advice!!!
Marina
With the nls() function you can fit your data to whatever non-linear function you want. Then, from the biological point of view, probably your data is described by a Gompertz-like function (sigmoidal), but as you have only three time points, probably you can simplify these kind of functions into an exponential one. Try the following:
fit_formula <- independent_variable ~ a * exp(b * dependent_variable)
result <- nls(formula = fit_formula, data = your_Dataset)
It will probably give you an error the first times, something like singular matrix gradient at initial estimates ; if this happens, try adding the additional parameter start, where you provide different starting values for a and b more close to the true values. Remember that in your dataset, the column names must be equal to the names of the variables in the formula.
I have a simple model, for which the residuals exhibit auto-correlation beyond one order.
I have a simple model for which I want to include a moving average component up to a third order.
My model is this:
m1<-gamm(y~s(x,k=5), data = Training)
the time series properties of y, shows that this follows an ARMA(0,0,3)
because the residuals of m1 are auto-correlated I want to include a moving average component in m1
The answers for similar questions talk only about an AR(1) process, which is not my case.
You can use the corARMA(p, q) function in package nlme for this. corAR1(p) is just a special case function as there are certain efficiencies for that particular model.
You have to pass q and/or p for the order of the ARMA(p, q) process with p specifying the order of the AR terms and q the order of the MA terms. You also need to pass in a variable that orders the observations. Assuming you have a single time series and you want the MA process to operate at the entire time series level (rather than say within a years but not between) then you should crate a time variable that indexes the order of the observations; here I assume this variable is called time.
Then the call is:
m1 <- gamm(y ~ s(x, k = 5), data = Training,
correlation = corARMA(q = 3, form = ~ time))
When looking at the residuals, be sure to extract the normalised residuals as those will include the effect of the estimated MA process:
resid(m1, type = "normalised")
This question already has an answer here:
Set one or more of coefficients to a specific integer
(1 answer)
Closed 6 years ago.
In R, how can I set weights for particular variables and not observations in lm() function?
Context is as follows. I'm trying to build personal ranking system for particular products, say, for phones. I can build linear model based on price as dependent variable and other features such as screen size, memory, OS and so on as independent variables. I can then use it to predict phone real cost (as opposed to declared price), thus finding best price/goodness coefficient. This is what I have already done.
Now I want to "highlight" some features that are important for me only. For example, I may need a phone with large memory, thus I want to give it higher weight so that linear model is optimized for memory variable.
lm() function in R has weights parameter, but these are weights for observations and not variables (correct me if this is wrong). I also tried to play around with formula, but got only interpreter errors. Is there a way to incorporate weights for variables in lm()?
Of course, lm() function is not the only option. If you know how to do it with other similar solutions (e.g. glm()), this is pretty fine too.
UPD. After few comments I understood that the way I was thinking about the problem is wrong. Linear model, obtained by call to lm(), gives optimal coefficients for training examples, and there's no way (and no need) to change weights of variables, sorry for confusion I made. What I'm actually looking for is the way to change coefficients in existing linear model to manually make some parameters more important than others. Continuing previous example, let's say we've got following formula for price:
price = 300 + 30 * memory + 56 * screen_size + 12 * os_android + 9 * os_win8
This formula describes best possible linear model for dependence between price and phone parameters. However, now I want to manually change number 30 in front of memory variable to, say, 60, so it becomes:
price = 300 + 60 * memory + 56 * screen_size + 12 * os_android + 9 * os_win8
Of course, this formula doesn't reflect optimal relationship between price and phone parameters any more. Also dependent variable doesn't show actual price, just some value of goodness, taking into account that memory is twice more important for me than for average person (based on coefficients from first formula). But this value of goodness (or, more precisely, value of fraction goodness/price) is just what I need - having this I can find best (in my opinion) phone with best price.
Hope all of this makes sense. Now I have one (probably very simple) question. How can I manually set coefficients in existing linear model, obtained with lm()? That is, I'm looking for something like:
coef(model)[2] <- 60
This code doesn't work of course, but you should get the idea. Note: it is obviously possible to just double values in memory column in data frame, but I'm looking for more elegant solution, affecting model, not data.
The following code is a bit complicated because lm() minimizes residual sum of squares and with a fixed, non optimal coefficient it is no longed minimal, so that would be against what lm() is trying to do and the only way is to fix all the rest coefficients too.
To do that, we have to know coefficients of the unrestricted model first. All the adjustments have to be done by changing formula of your model, e.g. we have
price ~ memory + screen_size, and of course there is a hidden intercept. Now neither changing the data directly nor using I(c*memory) is good idea. I(c*memory) is like temporary change of data too, but to change only one coefficient by transforming the variables would be much more difficult.
So first we change price ~ memory + screen_size to price ~ offset(c1*memory) + offset(c2*screen_size). But we haven't modified the intercept, which now would try to minimize residual sum of squares and possibly become different than in original model. The final step is to remove the intercept and to add a new, fake variable, i.e. which has the same number of observations as other variables:
price ~ offset(c1*memory) + offset(c2*screen_size) + rep(c0, length(memory)) - 1
# Function to fix coefficients
setCoeffs <- function(frml, weights, len){
el <- paste0("offset(", weights[-1], "*",
unlist(strsplit(as.character(frml)[-(1:2)], " +\\+ +")), ")")
el <- c(paste0("offset(rep(", weights[1], ",", len, "))"), el)
as.formula(paste(as.character(frml)[2], "~",
paste(el, collapse = " + "), " + -1"))
}
# Example data
df <- data.frame(x1 = rnorm(10), x2 = rnorm(10, sd = 5),
y = rnorm(10, mean = 3, sd = 10))
# Writing formula explicitly
frml <- y ~ x1 + x2
# Basic model
mod <- lm(frml, data = df)
# Prime coefficients and any modifications. Note that "weights" contains
# intercept value too
weights <- mod$coef
# Setting coefficient of x1. All the rest remain the same
weights[2] <- 3
# Final model
mod2 <- update(mod, setCoeffs(frml, weights, nrow(df)))
# It is fine that mod2 returns "No coefficients"
Also, probably you are going to use mod2 only for forecasting (actually I don't know where else it could be used now) so that could be made in a simpler way, without setCoeffs:
# Data for forecasting with e.g. price unknown
df2 <- data.frame(x1 = rpois(10, 10), x2 = rpois(5, 5), y = NA)
mat <- model.matrix(frml, model.frame(frml, df2, na.action = NULL))
# Forecasts
rowSums(t(t(mat) * weights))
It looks like you are doing optimization, not model fitting (though there can be optimization within model fitting). You probably want something like the optim function or look into linear or quadratic programming (linprog and quadprog packages).
If you insist on using modeling tools like lm then use the offset argument in the formula to specify your own multiplyer rather than computing one.
Let's say I have the following data and I'm interested in examining some counterfactuals. In particular, I want to examine whether there would be changes in predicted income given a change in income. The best way I can think to do this is to write a loop that runs this regression 1:n. However, how do I also make adjustments to the data frame while running through the loop. I'm really hoping that there is a base R function or something in a package that someone can point me to.
df = data.frame(year=c(2000,2001,2002,2003,2004,2005,2006,2007,2009,2010),
income=c(100,50,70,80,50,40,60,100,90,80),
age=c(26,30,35,30,28,29,31,34,20,35),
gpa=c(2.8,3.5,3.9,4.0,2.1,2.65,2.9,3.2,3.3,3.1))
df
mod = lm(income ~ age + gpa, data=df)
summary(mod)
Here are some counter factuals that may be worth considering when looking at the relationship between age, gpa, and income.
# What is everyone in the class had a lower/higher gpa?
df$gpa2 = df$gpa + 0.55
# what if one person had a lower/higher gpa?
df$gpa2[3] = 1.6
# what if the most recent employee/person had a lower/higher gpa?
df[10,4] = 4.0
With or without looping, what would be the best way to "simulate" a large (1000+) number of regression models in order examine various counter factuals, and then save those results in some data structure? Is there a "counter factual" analysis package which could save me a bit of work?
Calling all experts on local regression and/or R!
I have run into a limitation of the standard loess function in R and hope you have some advice. The current implementation supports only 1-4 predictors. Let me set out our application scenario to show why this can easily become a problem as soon as we want to employ globally fit parametric covariables.
Essentially, we have a spatial distortion s(x,y) overlaid over a number of measurements z:
z_i = s(x_i,y_i) + v_{g_i}
These measurements z can be grouped by the same underlying undistorted measurement value v for each group g. The group membership g_i is known for each measurement, but the underlying undistorted measurement values v_g for the groups are not known and should be determined by (global, not local) regression.
We need to estimate the two-dimensional spatial trend s(x,y), which we then want to remove. In our application, say there are 20 groups of at least 35 measurements each, in the most simple scenario. The measurements are randomly placed. Taking the first group as reference, there are thus 19 unknown offsets.
The below code for toy data (with a spatial trend in one dimension x) works for two or three offset groups.
Unfortunately, the loess call fails for four or more offset groups with the error message
Error in simpleLoess(y, x, w, span, degree, parametric, drop.square,
normalize, :
only 1-4 predictors are allowed"
I tried overriding the restriction and got
k>d2MAX in ehg136. Need to recompile with increased dimensions.
How easy would that be to do? I cannot find a definition of d2MAX anywhere, and it seems this might be hardcoded -- the error is apparently triggered by line #1359 in loessf.f
if(k .gt. 15) call ehg182(105)
Alternatively, does anyone know of an implementation of local regression with global (parametric) offset groups that could be applied here?
Or is there a better way of dealing with this? I tried lme with correlation structures but that seems to be much, much slower.
Any comments would be greatly appreciated!
Many thanks,
David
###
#
# loess with parametric offsets - toy data demo
#
x<-seq(0,9,.1);
x.N<-length(x);
o<-c(0.4,-0.8,1.2#,-0.2 # works for three but not four
); # these are the (unknown) offsets
o.N<-length(o);
f<-sapply(seq(o.N),
function(n){
ifelse((seq(x.N)<= n *x.N/(o.N+1) &
seq(x.N)> (n-1)*x.N/(o.N+1)),
1,0);
});
f<-f[sample(NROW(f)),];
y<-sin(x)+rnorm(length(x),0,.1)+f%*%o;
s.fs<-sapply(seq(NCOL(f)),function(i){paste('f',i,sep='')});
s<-paste(c('y~x',s.fs),collapse='+');
d<-data.frame(x,y,f)
names(d)<-c('x','y',s.fs);
l<-loess(formula(s),parametric=s.fs,drop.square=s.fs,normalize=F,data=d,
span=0.4);
yp<-predict(l,newdata=d);
plot(x,y,pch='+',ylim=c(-3,3),col='red'); # input data
points(x,yp,pch='o',col='blue'); # fit of that
d0<-d; d0$f1<-d0$f2<-d0$f3<-0;
yp0<-predict(l,newdata=d0);
points(x,y-f%*%o); # spatial distortion
lines(x,yp0,pch='+'); # estimate of that
op<-sapply(seq(NCOL(f)),function(i){(yp-yp0)[!!f[,i]][1]});
cat("Demo offsets:",o,"\n");
cat("Estimated offsets:",format(op,digits=1),"\n");
Why don't you use an additive model for this? Package mgcv will handle this sort of model, if I understand your Question, just fine. I might have this wrong, but the code you show is relating x ~ y, but your Question mentions z ~ s(x, y) + g. What I show below for gam() is for response z modelled by a spatial smooth in x and y with g being estimated parametrically, with g stored as a factor in the data frame:
require(mgcv)
m <- gam(z ~ s(x,y) + g, data = foo)
Or have I misunderstood what you wanted? If you want to post a small snippet of data I can give a proper example using mgcv...?