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")
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'm working with Support Vector Machines from the e1071 package in R. This is my first project using SVM.
I have a dataset containing order histories of ~1k customers over 1 year and I want to predict costumer purchases. For every customer I have the information if a certain item (out of ~50) was bought or not in a certain week (for 52 weeks aka 1 yr).
My goal is to predict next month's purchases for every single customer.
I believe that a purchase let's say 1 month ago is more meaningful for my prediction than a purchase 10 months ago.
My question is now how I can give more recent data a higher impact? There is a 'weight' option in the svm-function but I'm not sure how to use it.
Anyone who can give me a hint? Would be much appreciated!
That's my code
# Fit model using Support Vecctor Machines
# install.packages("e1071")
library(e1071)
response <- train[,5]; # purchases
formula <- response ~ .;
tuned.svm <- tune.svm(train, response, probability=TRUE,
gamma=10^(-6:-3), cost=10^(1:2));
gamma.k <- tuned.svm$best.parameter[[1]];
cost.k <- tuned.svm$best.parameter[[2]];
svm.model <- svm(formula, data = train,
type='eps-regression', probability=TRUE,
gamma=gamma.k, cost=cost.k);
svm.pred <- predict(svm.model, test, probability=TRUE);
Side notes: I'm fitting a model for every single customer. Also, since I'm interested in the probability, that customer i buys item j in week k, I put
probability=TRUE
click here to see a sccreenshot of my data
Weights option in the R SVM Model is more towards assigning weights to solve the problem of imbalance classes. its class.Weights parameter and is used to assign weightage to different classes 1/0 in a biased dataset.
To answer your question: to give more weightage in a SVM Model for recent data, a simple trick in absence of an ibuild weight functionality at observation level is to repeat the recent columns (i.e. create duplicate rows for recent data) hence indirectly assigning them higher weight
Try this package: https://CRAN.R-project.org/package=WeightSVM
It uses a modified version of 'libsvm' and is able to deal with instance weighting. You can assign higher weights to recent data.
For example. You have simulated data (x,y)
x <- seq(0.1, 5, by = 0.05)
y <- log(x) + rnorm(x, sd = 0.2)
This is an unweighted SVM:
model1 <- wsvm(x, y, weight = rep(1,99))
Blue dots is the unweighted SVM and do not fit the first instance well. We want to put more weights on the first several instances.
So we can use a weighted SVM:
model2 <- wsvm(x, y, weight = seq(99,1,length.out = 99))
Green dots is the weighted SVM and fit the first instance better.
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.
I have created a loop to fit a non-linear model to six data points by participants (each participant has 6 data points). The first model is a one parameter model. Here is the code for that model that works great. The time variable is defined. The participant variable is the id variable. The data is in long form (one row for each datapoint of each participant).
Here is the loop code with 1 parameter that works:
1_p_model <- dlply(discounting_long, .(Participant), function(discounting_long) {wrapnls(indiff ~ 1/(1+k*time), data = discounting_long, start = c(k=0))})
However, when I try to fit a two parameter model, I get this error "Error: singular gradient matrix at initial parameter estimates" while still using the wrapnls function. I realize that the model is likely over parameterized, that is why I am trying to use wrapnls instead of just nls (or nlsList). Some in my field insist on seeing both model fits. I thought that the wrapnls model avoids the problem of 0 or near-0 residuals. Here is my code that does not work. The start values and limits are standard in the field for this model.
2_p_model <- dlply(discounting_long, .(Participant), function(discounting_long) {nlxb(indiff ~ 1/(1+k*time^s), data = discounting_long, lower = c (s = 0), start = c(k=0, s=.99), upper = c(s=1))})
I realize that I could use nlxb (which does give me the correct parameter values for each participant) but that function does not give predictive values or residuals of each data point (at least I don't think it does) which I would like to compute AIC values.
I am also open to other solutions for running a loop through the data by participants.
You mention at the end that 'nlxb doesn't give you residuals', but it does. If your result from your call to nlxbis called fit then the residuals are in fit$resid. So you can get the fitted values using just by adding them to the original data. Honestly I don't know why nlxb hasn't been made to work with the predict() function, but at least there's a way to get the predicted values.
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.